Tarski defined a way of assigning to each Boolean algebra, B, an invariant inv(B) ∈ In, where In is a set of triples from ℕ, such that two Boolean algebras have the same invariant if and only if they are elementarily equivalent. Moreover, given the invariant of a Boolean algebra, there is a computable procedure that decides its elementary theory. If we restrict our attention to dense Boolean algebras, these invariants determine the algebra up to isomorphism. (...) In this paper we analyze the complexity of the question "Does B have invariant x?" For each x ∈ In we define a complexity class Γx that could be either Σⁿ, Πⁿ, Σⁿ ∧ Πⁿ, or Πω+1 depending on x, and we prove that the set of indices for computable Boolean algebras with invariant x is complete for the class Γx. Analogs of many of these results for computably enumerable Boolean algebras were proven in earlier works by Selivanov. In a more recent work, he showed that similar methods can be used to obtain the results for computable ones. Our methods are quite different and give new results as well. As the algebras we construct to witness hardness are all dense, we establish new similar results for the complexity of various isomorphism problems for dense Boolean algebras. (shrink)

This dissertation examines aspects of the interplay between computing and scientific practice. The appropriate foundational framework for such an endeavour is rather real computability than the classical computability theory. This is so because physical sciences, engineering, and applied mathematics mostly employ functions defined in continuous domains. But, contrary to the case of computation over natural numbers, there is no universally accepted framework for real computation; rather, there are two incompatible approaches --computable analysis and BSS model--, both claiming to formalise (...) algorithmic computation and to offer foundations for scientific computing. The dissertation consists of three parts. In the first part, we examine what notion of 'algorithmic computation' underlies each approach and how it is respectively formalised. It is argued that the very existence of the two rival frameworks indicates that 'algorithm' is not one unique concept in mathematics, but it is used in more than one way. We test this hypothesis for consistency with mathematical practice as well as with key foundational works that aim to define the term. As a result, new connections between certain subfields of mathematics and computer science are drawn, and a distinction between 'algorithms' and 'effective procedures' is proposed. In the second part, we focus on the second goal of the two rival approaches to real computation; namely, to provide foundations for scientific computing. We examine both frameworks in detail, what idealisations they employ, and how they relate to floating-point arithmetic systems used in real computers. We explore limitations and advantages of both frameworks, and answer questions about which one is preferable for computational modelling and which one for addressing general computability issues. In the third part, analog computing and its relation to analogue (physical) modelling in science are investigated. Based on some paradigmatic cases of the former, a certain view about the nature of computation is defended, and the indispensable role of representation in it is emphasized and accounted for. We also propose a novel account of the distinction between analog and digital computation and, based on it, we compare analog computational modelling to physical modelling. It is concluded that the two practices, despite their apparent similarities, are orthogonal. (shrink)

This dissertation examines aspects of the interplay between computing and scientific practice. The appropriate foundational framework for such an endeavour is rather real computability than the classical computability theory. This is so because physical sciences, engineering, and applied mathematics mostly employ functions defined in continuous domains. But, contrary to the case of computation over natural numbers, there is no universally accepted framework for real computation; rather, there are two incompatible approaches --computable analysis and BSS model--, both claiming to formalise (...) algorithmic computation and to offer foundations for scientific computing. -/- The dissertation consists of three parts. In the first part, we examine what notion of 'algorithmic computation' underlies each approach and how it is respectively formalised. It is argued that the very existence of the two rival frameworks indicates that 'algorithm' is not one unique concept in mathematics, but it is used in more than one way. We test this hypothesis for consistency with mathematical practice as well as with key foundational works that aim to define the term. As a result, new connections between certain subfields of mathematics and computer science are drawn, and a distinction between 'algorithms' and 'effective procedures' is proposed. -/- In the second part, we focus on the second goal of the two rival approaches to real computation; namely, to provide foundations for scientific computing. We examine both frameworks in detail, what idealisations they employ, and how they relate to floating-point arithmetic systems used in real computers. We explore limitations and advantages of both frameworks, and answer questions about which one is preferable for computational modelling and which one for addressing general computability issues. -/- In the third part, analog computing and its relation to analogue (physical) modelling in science are investigated. Based on some paradigmatic cases of the former, a certain view about the nature of computation is defended, and the indispensable role of representation in it is emphasized and accounted for. We also propose a novel account of the distinction between analog and digital computation and, based on it, we compare analog computational modelling to physical modelling. It is concluded that the two practices, despite their apparent similarities, are orthogonal. (shrink)

In the technical literature of computer science, the concept of an effective procedure is closely associated with the notion of an instruction that precisely specifies an action. Turing machine instructions are held up as providing paragons of instructions that "precisely describe" or "well define" the actions they prescribe. Numerical algorithms and computer programs are judged effective just insofar as they are thought to be translatable into Turing machine programs. Nontechnical procedures (e.g., recipes, methods) are summarily dismissed (...) as ineffective on the grounds that their instructions lack the requisite precision. But despite the pivotal role played by the notion of a precisely specified instruction in classifying procedures as effective and ineffective, little attention has been paid to the manner in which instructions "precisely specify" the actions they prescribe. It is the purpose of this paper to remedy this defect. The results are startling. The reputed exemplary precision of Turing machine instructions turns out to be a myth. Indeed, the most precise specifications of action are provided not by the procedures of theoretical computer science and mathematics (algorithms) but rather by the nontechnical procedures of everyday life. I close with a discussion of some of the rumifications of these conclusions for understanding and designing concrete computers and their programming languages. (shrink)

ABSTRACT I argue that this examination and appreciation for the shift to abductive reasoning should be extended to the intersection of neuroscience and novel brain-computer interfaces too. This paper highlights the implications of applying abductive reasoning to personalized implantable neurotechnologies. Then, it explores whether abductive reasoning is sufficient to justify insurance coverage for devices absent widespread clinical trials, which are better applied to one-size-fits-all treatments. INTRODUCTION In contrast to the classic model of randomized-control trials, often with a large number (...) of subjects enrolled, precision medicine attempts to optimize therapeutic outcomes by focusing on the individual.[i] A recent publication highlights the strengths and weakness of both traditional evidence-based medicine and precision medicine.[ii] Plus, it outlines a tension in the shift from evidence-based medicine’s inductive reasoning style (the collection of data to postulate general theories) to precision medicine’s abductive reasoning style (the generation of an idea from the limited data available).[iii] The paper’s main example is the application of precision medicine for the treatment of cancer.[iv] I argue that this examination and appreciation for the shift to abductive reasoning should be extended to the intersection of neuroscience and novel brain-computer interfaces too. As the name suggests, brain-computer interfaces are a significant advancement in neurotechnology that directly connects someone’s brain to external or implanted devices.[v] Among the various kinds of brain-computer interfaces, adaptive deep brain stimulation devices require numerous personalized adjustments to their settings during the implantation and computation stages in order to provide adequate relief to patients with treatment-resistant disorders. What makes these devices unique is how adaptive deep brain stimulation integrates a sensory component to initiate the stimulation. While not commonly at the level of sophistication as self-supervising or generative large language models,[vi] they currently allow for a semi-autonomous form of neuromodulation. This paper highlights the implications of applying abductive reasoning to personalized implantable neurotechnologies. Then, it explores whether abductive reasoning is sufficient to justify insurance coverage for devices absent widespread clinical trials, which are better applied to one-size-fits-all treatments.[vii] ANALYSIS I. The State of Precision Medicine in Oncology and the Epistemological Shift While a thorough overview of precision medicine for the treatment of cancer is beyond the scope of this article, its practice can be roughly summarized as identifying clinically significant characteristics a patient possesses (e.g., genetic traits) to land on a specialized treatment option that, theoretically, should benefit the patient the most.[viii] However, in such a practice of stratification patients fall into smaller and smaller populations and the quality of evidence that can be applied to anyone outside these decreases in turn.[ix] As inductive logic helps to articulate, the greater the number of patients that respond to a particular therapy the higher the probability of its efficacy. By straying from this logical framework, precision medicine opens the treatment of cancer to more uncertainty about the validity of these approaches to the resulting disease subcategories.[x] Thus, while contemporary medical practices explicitly describe some treatments as “personalized”, they ought not be viewed as inherently better founded than other therapies.[xi] A relevant contemporary case of precision medicine out of Norway focuses on the care of a patient with cancer between the ventricles of the heart and esophagus, which had failed to respond to the standard regimen of therapies over four years.[xii] In a last-ditch effort, the patient elected to pay out-of-pocket for an experimental immunotherapy (nivolumab) at a private hospital. He experienced marked improvements and a reduction in the size of the tumor. Understandably, the patient tried to pursue further rounds of nivolumab at a public hospital. However, the hospital initially declined to pay for it given the “lack of evidence from randomised clinical trials for this drug relating to this [patient’s] condition.”[xiii] In rebuttal to this claim, the patient countered that he was actually similar to a subpopulation of patients who responded in “open‐label, single arm, phase 2 studies on another immune therapy drug” (pembrolizumab).[xiv] Given this interpretation of the prior studies and the patient’s response, further rounds of nivolumab were approved. Had the patient not had improvements in the tumor’s size following a round of nivolumab, then pembrolizumab’s prior empirical evidence in isolation would have been insufficient, inductively speaking, to justify his continued use of nivolumab.[xv] The case demonstrates a shift in reasoning from the traditional induction to abduction. The phenomenon of ‘cancer improvement’ is considered causally linked to nivolumab and its underlying physiological mechanisms.[xvi] However, “the weakness of abductions is that there may always be some other better, unknown explanation for an effect. The patient may for example belong to a special subgroup that spontaneously improves, or the change may be a placebo effect. This does not mean, however, that abductive inferences cannot be strong or reasonable, in the sense that they can make a conclusion probable.”[xvii] To demonstrate the limitations of relying on the abductive standard in isolation, commentators have pointed out that side effects in precision medicine are hard to rule out as being related to the initial intervention itself unless trends from a group of patients are taken into consideration.[xviii] As artificial intelligence (AI) assists the development of precision medicine for oncology, this uncertainty ought to be taken into consideration. The implementation of AI has been crucial to the development of precision medicine by providing a way to combine large patient datasets or a single patient with a large number of unique variables with machine learning to recommend matches based on statistics and probability of success upon which practitioners can base medical recommendations.[xix] The AI is usually not establishing a causal relationship[xx] – it is predicting. So, as AI bleeds into medical devices, like brain-computer interfaces, the same cautions about using abductive reasoning alone should be carried over. II. Responsive Neurostimulation, AI, and Personalized Medicine Like precision medicine in cancer treatment, computer-brain interface technology similarly focuses on the individual patient through personalized settings. In order to properly expose the intersection of AI, precision medicine, abductive reasoning, and implantable neurotechnologies, the descriptions of adaptive deep brain stimulation systems need to deepen.[xxi] As a broad summary of adaptive deep brain stimulation, to provide a patient with the therapeutic stimulation, a neural signal, typically referred to as a local field potential,[xxii] must first be detected and then interpreted by the device. The main adaptive deep brain stimulation device with premarket approval, the NeuroPace Responsive Neurostimulation system, is used to treat epilepsy by detecting and storing “programmer-defined phenomena.”[xxiii] Providers can optimize the detection settings of the device to align with the patient’s unique electrographic seizures as well as personalize the reacting stimulation’s parameters.[xxiv] The provider adjusts the technology based on trial and error. One day machine learning algorithms will be able to regularly aid this process in myriad ways, such as by identifying the specific stimulation settings a patient may respond to ahead of time based on their electrophysiological signatures.[xxv] Either way, with AI or programmers, adaptive neurostimulation technologies are individualized and therefore operate in line with precision medicine rather than standard treatments based on large clinical trials. Contemporary neurostimulation devices are not usually sophisticated enough to be prominent in AI discussions where the topics of neural networks, deep learning, generative models, and self-attention dominate the conversation. However, implantable high-density electrocorticography arrays (a much more sensitive version than adaptive deep brain stimulation systems use) have been used in combination with neural networks to help patients with neurologic deficits from a prior stroke “speak” through a virtual avatar.[xxvi] In some experimental situations, algorithms are optimizing stimulation parameters with increasing levels of independence.[xxvii] An example of neurostimulation that is analogous to the use of nivolumab in Norway surrounds a patient in the United States who was experiencing both treatment-resistant OCD and temporal lobe epilepsy.[xxviii]Given the refractory nature of her epilepsy, implantation of an adaptive deep brain stimulation system was indicated. As a form of experimental therapy, her treatment-resistant OCD was also indicated for the off-label use of an adaptive deep brain stimulation set-up. Another deep brain stimulation lead, other than the one implanted for epilepsy, was placed in the patient’s right nucleus accumbens and ventral pallidum region given the correlation these nuclei had with OCD symptoms in prior research. Following this, the patient underwent “1) ambulatory, patient-initiated magnet-swipe storage of data during moments of obsessive thoughts; (2) lab-based, naturalistic provocation of OCD-related distress (naturalistic provocation task); and (3) lab-based, VR [virtual reality] provocation of OCD-related distress (VR provocation task).”[xxix] Such signals were used to identify when to deliver the therapeutic stimulation in order to counter the OCD symptoms. Thankfully, following the procedure and calibration the patient exhibited marked improvements in their OCD symptoms and recently shared her results publicly.[xxx] In both cases, there is a similar level of abductive justification for the efficacy of the delivered therapy. In the case study in which the patient was treated with adaptive deep brain stimulation, they at least had their neural activity tested in various settings to determine the optimum parameters for treatment to avoid them being based on guesswork. Additionally, the adaptive deep brain stimulation lead was already placed before the calibration trials were conducted, meaning that the patient had already taken on the bulk of the procedural risk before the efficacy could be determined. Such an efficacy test could have been replicated in the first patient’s cancer treatment, had it been biopsied and tested against the remaining immunotherapies in vitro. Yet, in the case of cancer with few options, one previous dose of a drug that appeared to work on the patient may justify further doses. However, as the Norwegian case presents, corroboration with known responses to a similar drug (from a clinical trial) could be helpful to validate the treatment strategy. (It should be noted that both patients were resigned to these last resort options regardless of the efficacy of treatment.) There are some elements of inductive logic seen with adaptive deep brain stimulation research in general. For example, abductively the focus could be that patient X’s stimulation parameters are different from patient Y’s and patient Z’s. In contrast, when grouped as subjects who obtained personalized stimulation, patients X, Y, and Z demonstrate an inductive aspect to this approach’s safety and/or efficacy. The OCD case holds plenty of abductive characteristics in line with precision medicine’s approach to treating cancer and as more individuals try the method, there will be additional data. With the gradual integration of AI into brain-computer interfaces in the name of efficacy, this reliance on abduction will continue, if not grow, over time. Moving forward, if a responsive deep brain stimulation treatment is novel and individualized (like the dose of nivolumab) and there is some other suggestion of efficacy (like clinical similarities to other patients in the literature), then it may justify insurance coverage for the investigative intervention, absent other unrelated reasons to deny it. III. Ethical Implications and Next Steps While AI’s use in oncology and neurology is not yet as prominent as its use in other fields (e.g., radiology), it appears to be on the horizon for both.[xxxi] AI can be found in both the functioning of the neurotechnologies as well as the implementation of precision medicine. The increasing use of AI may serve to further individualize both oncologic and neurological therapies. Given these implications and the handful of publications cited in this article, it is important to have a nuanced evaluation of how these treatments, which heavily rely on abductive justification, ought to be managed. The just use an abductive approach may be difficult as AI infused precision medicine is further pursued. At baseline, such technology relies on a level of advanced technology literacy among the general public and could exclude populations who lack access to basic technological infrastructure or know-how from participation.[xxxii] Even among nations with adequate infrastructure, as more patients seek out implantable neurotechnologies, which require robust healthcare resources, the market will favor patient populations that can afford this complex care.[xxxiii] If patients already have the means to pay for an initial dose/use of a precision medicine product out of pocket, should insurance providers be required to cover subsequent treatments?[xxxiv] That is, if a first dose of a cancer drug or a deep brain stimulator over its initial battery life is successful, patients may feel justified in having the costs of further treatments covered. The Norwegian patient’s experience implies there is a precedent for the idea that some public insurance companies ought to cover successful cancer therapies, however, insurance companies may not all see themselves as obligated to cover neurotechnologies that rely on personalized settings or that are based on precision/abductive research more than on clinical trials. CONCLUSION The fact that the cases outlined above rely on abductive style of reasoning implies that there may not be as strong a justification for coverage by insurance, as they are both experimental and individualized, when compared to the more traditional large clinical trials in which groups have the same or a standardized protocol (settings/doses). If a study is examining the efficacy of a treatment with a large cohort of patients or with different experimental groups/phases, insurance companies may conclude that the resulting symptom improvements are more likely to be coming from the devices themselves. A preference for inductive justification may take priority when ruling in favor of funding someone’s continued use of an implantable neurostimulator. There are further nuances to this discussion surrounding the classifications of these interventions as research versus clinical care that warrant future exploration, since such a distinction is more of a scale[xxxv] than binary and could have significant impacts on the “right-to-try” approach to experimental therapies in the United States.[xxxvi] Namely, given the inherent limitations of conducting large cohort trials for deep brain stimulation interventions on patients with neuropsychiatric disorders, surgically innovative frameworks that blend abductive and inductive methodologies, like with sham stimulation phases, have traditionally been used.[xxxvii] Similarly, for adaptive brain-computer interface systems, if there are no large clinical trials and instead only publications that demonstrate that something similar worked for someone else, then, in addition to the evidence that the first treatment/dose worked for the patient in question, the balance of reasoning would be valid and arguably justify insurance coverage. As precision approaches to neurotechnology become more common, frameworks for evaluating efficacy will be crucial both for insurance coverage and for clinical decision making. ACKNOWLEDGEMENT This article was originally written as an assignment for Dr. Francis Shen’s “Bioethics & AI” course at Harvard’s Center for Bioethics. I would like to thank Dr. Shen for his comments as well as my colleagues in the Lázaro-Muñoz Lab for their feedback. - [i] Jonathan Kimmelman and Ian Tannock, “The Paradox of Precision Medicine,” Nature Reviews. Clinical Oncology 15, no. 6 (June 2018): 341–42, https://doi.org/10.1038/s41571-018-0016-0. [ii] Henrik Vogt and Bjørn Hofmann, “How Precision Medicine Changes Medical Epistemology: A Formative Case from Norway,” Journal of Evaluation in Clinical Practice 28, no. 6 (December 2022): 1205–12, https://doi.org/10.1111/jep.13649. [iii] David Barrett and Ahtisham Younas, “Induction, Deduction and Abduction,” Evidence-Based Nursing 27, no. 1 (January 1, 2024): 6–7, https://doi.org/10.1136/ebnurs-2023-103873. [iv] Vogt and Hofmann, “How Precision Medicine Changes Medical Epistemology,” 1208. [v] Wireko Andrew Awuah et al., “Bridging Minds and Machines: The Recent Advances of Brain-Computer Interfaces in Neurological and Neurosurgical Applications,” World Neurosurgery, May 22, 2024, S1878-8750(24)00867-2, https://doi.org/10.1016/j.wneu.2024.05.104. [vi] Mark Riedl, “A Very Gentle Introduction to Large Language Models without the Hype,” Medium (blog), May 25, 2023, https://mark-riedl.medium.com/a-very-gentle-introduction-to-large-language-models-without-the-hype-5 f67941fa59e. [vii] David E. Burdette and Barbara E. Swartz, “Chapter 4 - Responsive Neurostimulation,” in Neurostimulation for Epilepsy, ed. Vikram R. Rao (Academic Press, 2023), 97–132, https://doi.org/10.1016/B978-0-323-91702-5.00002-5. [viii] Kimmelman and Tannock, 2018. [ix] Kimmelman and Tannock, 2018. [x] Simon Lohse, “Mapping Uncertainty in Precision Medicine: A Systematic Scoping Review,” Journal of Evaluation in Clinical Practice 29, no. 3 (April 2023): 554–64, https://doi.org/10.1111/jep.13789. [xi] Kimmelman and Tannock, “The Paradox of Precision Medicine.” [xii] Vogt and Hofmann, 1206. [xiii] Vogt and Hofmann, 1206. [xiv] Vogt and Hofmann, 1206. [xv] Vogt and Hofmann, 1207. [xvi] Vogt and Hofmann, 1207. [xvii] Vogt and Hofmann, 1207. [xviii] Vogt and Hofmann, 1210. [xix] Mehar Sahu et al., “Chapter Three - Artificial Intelligence and Machine Learning in Precision Medicine: A Paradigm Shift in Big Data Analysis,” in Progress in Molecular Biology and Translational Science, ed. David B. Teplow, vol. 190, 1 vols., Precision Medicine (Academic Press, 2022), 57–100, https://doi.org/10.1016/bs.pmbts.2022.03.002. [xx] Stefan Feuerriegel et al., “Causal Machine Learning for Predicting Treatment Outcomes,” Nature Medicine 30, no. 4 (April 2024): 958–68, https://doi.org/10.1038/s41591-024-02902-1. [xxi] Sunderland Baker et al., “Ethical Considerations in Closed Loop Deep Brain Stimulation,” Deep Brain Stimulation 3 (October 1, 2023): 8–15, https://doi.org/10.1016/j.jdbs.2023.11.001. [xxii] David Haslacher et al., “AI for Brain-Computer Interfaces,” 2024, 7, https://doi.org/10.1016/bs.dnb.2024.02.003. [xxiii] Burdette and Swartz, “Chapter 4 - Responsive Neurostimulation,” 103–4; “Premarket Approval (PMA),” https://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfpma/pma.cfm?id=P100026. [xxiv] Burdette and Swartz, “Chapter 4 - Responsive Neurostimulation,” 104. [xxv] Burdette and Swartz, 126. [xxvi] Sean L. Metzger et al., “A High-Performance Neuroprosthesis for Speech Decoding and Avatar Control,” Nature 620, no. 7976 (August 2023): 1037–46, https://doi.org/10.1038/s41586-023-06443-4. [xxvii] Hao Fang and Yuxiao Yang, “Predictive Neuromodulation of Cingulo-Frontal Neural Dynamics in Major Depressive Disorder Using a Brain-Computer Interface System: A Simulation Study,” Frontiers in Computational Neuroscience 17 (March 6, 2023), https://doi.org/10.3389/fncom.2023.1119685; Mahsa Malekmohammadi et al., “Kinematic Adaptive Deep Brain Stimulation for Resting Tremor in Parkinson’s Disease,” Movement Disorders 31, no. 3 (2016): 426–28, https://doi.org/10.1002/mds.26482. [xxviii] Young-Hoon Nho et al., “Responsive Deep Brain Stimulation Guided by Ventral Striatal Electrophysiology of Obsession Durably Ameliorates Compulsion,” Neuron 0, no. 0 (October 20, 2023), https://doi.org/10.1016/j.neuron.2023.09.034. [xxix] Nho et al. [xxx] Nho et al.; Erik Robinson, “Brain Implant at OHSU Successfully Controls Both Seizures and OCD,” OHSU News, accessed March 3, 2024, https://news.ohsu.edu/2023/10/25/brain-implant-at-ohsu-successfully-controls-both-seizures-and-ocd. [xxxi] Awuah et al., “Bridging Minds and Machines”; Haslacher et al., “AI for Brain-Computer Interfaces.” [xxxii] Awuah et al., “Bridging Minds and Machines.” [xxxiii] Sara Green, Barbara Prainsack, and Maya Sabatello, “The Roots of (in)Equity in Precision Medicine: Gaps in the Discourse,” Personalized Medicine 21, no. 1 (January 2024): 5–9, https://doi.org/10.2217/pme-2023-0097. [xxxiv] Green, Prainsack, and Sabatello, 7. [xxxv] Robyn Bluhm and Kirstin Borgerson, “An Epistemic Argument for Research-Practice Integration in Medicine,” The Journal of Medicine and Philosophy: A Forum for Bioethics and Philosophy of Medicine 43, no. 4 (July 9, 2018): 469–84, https://doi.org/10.1093/jmp/jhy009. [xxxvi] Vijay Mahant, “‘Right-to-Try’ Experimental Drugs: An Overview,” Journal of Translational Medicine 18 (June 23, 2020): 253, https://doi.org/10.1186/s12967-020-02427-4. [xxxvii] Michael S. Okun et al., “Deep Brain Stimulation in the Internal Capsule and Nucleus Accumbens Region: Responses Observed during Active and Sham Programming,” Journal of Neurology, Neurosurgery & Psychiatry 78, no. 3 (March 1, 2007): 310–14, https://doi.org/10.1136/jnnp.2006.095315. (shrink)

In this article, we discuss expertise by considering the activity of reading. Cognitive scientists have traditionally conceptualised reading as a single, well-defined task, namely the decoding of letter sequences into meaningful sequences of speech sounds. This definition captures a core feature of the reading activity at the computational level, but it is an overly narrow model of how reading behaviour occurs in the real world. We propose a more expansive model of expertise. In our view, expertise in (...) general is best conceptualised as a distributed process that takes place within a cultural-cognitive ecosystem. Our model allows for a more inclusive view of expertise in reading. We argue that reading is better understood as a manifold task domain that admits multiple reasonable criteria for evaluating performance. We draw on ethnographic data to show how our model allows for a wider appreciation of what expertise in reading amounts to in educational contexts. (shrink)

We sketch an axiomatic reformalization of Generalized Phrase StructureGrammar (GPSG) – a definition purely within the language ofmathematical logic of the theory GPSG embodies. While this treatment raisesa number of theoretical issues for GPSG, our focus is not thereformalization itself but rather the method we employ. The model-theoreticapproach it exemplifies can be seen as a natural step in the evolution ofconstraint-based theories from their grammar-based antecedents. One goal ofthis paper is to introduce this approach to a broader audience and todemonstrate (...) its application to an existing theory. As such, it joins agrowing literature of similar studies. Prior studies, however, have had anumber of weaknesses – they generally offer little in the way ofconcrete examples of the advantages the approach has to offer, theytypically ignore significant portions of the theories they address, and, byfully abstracting away from the notion of grammar mechanism, they largelyabandon the possibility of establishing meaningful complexity results. Thesecond goal of the paper is to address these issues. Our thrust is to sketchthe reformalization sufficiently to illustrate the way in which it capturesFeature Specification Defaults (FSDs) and the Exhaustive Constant PartialOrdering (ECPO) property. Our definition of FSDs is considerably simplifiedrelative to the original formalization and is free of the procedural flavorthat has led some to assume that FSDs are inherently dynamic. Our treatmentof ECPO uncovers a gap in its definition in the context of partialcategories that has heretofore gone unnoticed. We offer these as ademonstration of the kind of insight that a model-theoretic reinterpretationcan bring to an existing theory. Further, since these are the types ofproperties that prior studies in this genre have failed to address, FSDs andECPO provide a means for us to explore the limitations of these approachesand to offer ways of overcoming them. Finally, the logical framework weemploy has a well defined generative capacity – definability in thisframework characterizes strong context-freeness in a particular sense. Thus,despite being more abstract than its constraint-based predecessors, themodel-theoretic approach, as exemplified here, can offer stronger complexityresults than are typically available in the constraint-based framework. (shrink)

Three main lines of arguments are presented as a defense of randomization in experimental design. The first concerns the computational advantages of randomizing when a well-defined underlying theoretical model is not available, as is often the case in much experimentation in the medical and social sciences. The high desirability, even for the most dedicated Bayesians, of physical randomization in some special cases is stressed. The second line of argument concerns communication of methodology and results, especially in terms (...) of concerns about bias. The third line of argument concerns the use of randomization to guarantee causal inferences, whether the inference consists of the identification of a prima facie or a genuine cause. In addition, the relation of randomization to measures of complexity and the possibility of accepting only random procedures that produce complex results are discussed. (shrink)

ABSTRACT The individual-community relationship has always been one of the most fundamental topics of social sciences. In sociology, this is known as the micro-macro relationship while in economics it refers to the processes, through which, individual actions lead to macroeconomic phenomena. Based on philosophical discourse and systems theory, many sociologists even use the term "emergence" in their understanding of micro-macro relationship, which refers to collective phenomena that are created by the cooperation of individuals, but cannot be reduced to individual (...) actions. "Emergence" theories attempt to explain the nature of society as a complex system by examining how individuals and their relationships lead to the creation of integrated and macro-social phenomena such as markets, educational systems, cultural beliefs, and shared social practices. As a prelude to activity, every researcher has to answer the question from the methodological point of view, how is it possible to study the behavior of social groups and how can we gain knowledge about the laws related to social groups? Anyone who deals with humanities and social sciences or any reality and phenomenon that affects human beings, inevitably deals with the reality that is emerging. In fact, emergence occurs when one level of reality emerges radically from another level. Examples of emergent levels of reality include how the mind emerges from the body; or the way society emerges from human beings. Therefore, when there is an emerging factor, different scientific disciplines should be used, because it is inevitable to talk about social affairs, psychology and neurobiology, as well as physical and even chemical. -/- INTRODUCTION Since its beginning in the 19th century, sociology has faced the fundamental question of what a social phenomena stands for? At a glance, sociologists deal with the study of social groups, collective behavior, institutions, social structures, social networks, and social dynamics, and ultimately all such phenomena are composed of individuals. Therefore, social phenomena seem to have no independent ontological status, and in this case, sociology is ultimately about reducible individuals. Different approaches about the micro-macro relationship, using the concept of "emergence", argue that although collective phenomena are created by individuals, they cannot be reduced to individual action. The term "emergence" is used to distinguish "emergent results" from " Procedural results". Results are called Procedural that can only be calculated by adding or subtracting the causes that act together. On the contrary, they are emergent outcomes that are qualitatively novel compared to the causes from which they originate. An example of such emergent results is mental characteristics that emerge from neural processes, but are not considered among the characteristics of neural processes of components - which are their origin. Philosophical debates about emergentism and reductionism focus on the mind-brain relationship, but as many philosophers have noted, they can be generalized to apply to any hierarchical set of features. The cognitive revolution reactivated a 19th century controversy between theorists of Identity and dualism. The theorists of Identity believe in reductionist materialism and elimination of metaphysics, according to which the mind is nothing more than the biological, while the dualists believe that the mind and the brain are distinct from each other. Emergence has been considered as a third way between the theories of Identity and dualism. -/- METHODOLOGY Interdisciplinarity Is fundamentally indicated by the dominance of open systems as well as social and emerging systems at different levels. Therefore, as long as we are facing a new emergentism, there will necessarily be different fields and an interdisciplinary method. The commonality of social sciences and cognitive sciences on the issue of emergence provides the possibility of interaction and exchange of concepts between these two for deeper research. Therefore, in this research, apart from the concepts of Subvenience and downward causation, we have used multiple realization and wildly disjunctive, which are used to explain the emerging concept in cognitive sciences, including neurobiology, psychology, and philosophy. For analytical and interdisciplinary approaches, after examining the concepts of subvenience, and wildly disjunctive, Individualistic and collectivist emergentism have been reviewed. And then their adequacy is criticized and evaluated in meeting strong emergence conditions. -/- FINDINGS Philosophers of the mind have been able to define the conditions of irreducibility and downward causation, which are essential for strong emergence, by using the principle of subvenience with the help of multiple realization and wildly disjunctive principles. Therefore, by definition, emergentist individualism suffers from the problem of how to explain downward causality and irreducibility, and emergentist collectivism faces the challenge of reification. The analysis of the challenges facing the two methodological approaches of individualism and collectivism leads us to three unresolved issues about the emerging phenomenon, which are realism, downward causality, and mechanism. Despite the differences in the stances of these two approaches regarding the aforementioned triple problems, individualists and collectivists both agree that some social characteristics are reducible; and some others are irreducible due to their complexity, the determination of which, depends on the case study of the mechanism of emergence of each social characteristic. -/- CONCLUSION An emergence that is consistent with reductionism is called a weak emergence. And strong emergence includes the principle of irreducibility and downward causality. According to strong emergence, the characteristics of social phenomena have downward causal power, which cannot be reduced to the causal forces. The principle of subvenience, together with multiple realization and wildly disjunctive, can provide the conditions of irreducibility and downward causality, which are essential conditions of strong emergence. Based on the philosophical analysis of two methodological approaches, individualist and collectivist, it can be concluded that emergentist individualism suffers from the problem of how to explain downward causality and irreducibility, and reification collectivism faces the challenge of reification. The analysis of the problems faced by these two approaches leads us to three unresolved issues, which are realism, downward causality, and mechanism. individualist emergentists acknowledge the existence of emergent social characteristics, but despite this, they believe that these characteristics are not real but merely analytical constructs that require explanation based on individuals and their mutual actions. But collectivists argue that emergentism yields a categorical ontology and supports social realism. They accept the dependence of social characteristics on individuals, but claim that social entities and structures are ontologically independent. Individualists and collectivists both agree that some social characteristics are reducible; and others are irreducible due to their complexity; and the only way to recognize this is to engage in empirical studies of the mechanisms and temporal processes of "emergence" that create social characteristics. -/- NOVELTY The newness of this compact article is as follows: a) Presenting an interdisciplinary approach using the analysis of philosophy of cognitive sciences, including the philosophy of mind, neurobiology and psychology to formulate the issue of social emergence; b) Criticizing individualist and collectivist methodological approaches to the issue of social emergence and explaining the sufficiency and shortcomings of both in providing weak and strong emerging conditions; c) Explaining and categorizing the challenges facing methodological approaches in explaining the phenomenon of social emergence, in three categories: realism, downward causality, and mechanism. BIBLIOGRAPHY Beckermann, A., Flohr, H., & Kim, J. (eds.) (1992). Emergence or reduction? Essays on the prospects of nonreductive physicalism. Berlin: Walter de Gruyter. Bhaskar, R. (1979). The possibility of Naturalism. New York: Routledge. Bhaskar, R., Danermark, B. & Price, L. (2018). Interdisciplinarity and wellbeing: A critical realist general theory of interdisciplinarity. London and New York: Routledge. Blau, P.M. (1981). Introduction: diverse views of social structure and their common denominator. In Blau, P.M. & Merton, R.K. (eds.), Continuity in Structural Inquiry (pp. 1–23). Beverly Hills: Sage. Blau, P.M. (1987). Microprocess and macrostructure. In K.S. Cook (ed.), Social Exchange Theory (pp. 83–100). Newbury Park, CA: Sage. Brooks, R.A., & Maes, P. (eds). (1994). Artificial life IV; proceedings of the Fourth International Workshop on the Synthesis and Simulation of Living Systems. Cambridge, Mass: MIT Press. Clark, A. (1997). Being there: Putting brain, body, and world together again. Cambridge, Mass.: MIT Press. Coleman, J. S. (1987). Microfoundations and macrosocial behavior. In: J. C. Alexander, B. Giesen, R. Munch, & Neil J. Smelser (Eds.). The Micro-Macro Link (pp. 153–73). Berkeley: University of California. Coleman, J. S. (1990). Foundations of social theory. Cambridge, MA: Harvard University Press. Elster, J. (1985). Making sense of Marx. New York: Cambridge University Press. Fodor, J.A. (1974). Special sciences (Or: The disunity of science as a working hypothesis). Synthese, 28(2), 97–115. Fodor, J.A. (1989). Making mind matter more. Philosophical Topics, 17, 59-79. Giddens, A. (1984). The constitution of society: Outline of the theory of structuration. Berkeley: University of California Press. Hempel, C.G. (1965). Aspects of scientific explanation and other essays in the philosophy of science. New York: The Free Press. Horgan, T. (1993). From supervenience to superdupervenience: meeting the demands of a material world. Mind, 102, 555-586. Humphreys, P. (1997). How properties emerge”. Philosophy of Science, 64, 1-17. Kim, J. (1999). Making sense of emergence. Philosophical Studies, 95, 3–36. Kincaid, H. (1997). Individualism and the unity of science. New York: Rowman & Littlefield. Lewis, D.K. (1986). The plurality of worlds. Oxford: Oxford University Press. Nigel, G., & Conte, R. (eds.) (1995). Artificial societies; The computer simulation of social life. London: UCL Press. O’Connor, T. (1994). Emergent properties. American Philosophical Quarterly, 31, 91-104. Popper, K.R. (1968). Conjectures and refutations: The Growth of Scientific Knowledge. New York: Harper & Row. Sawyer, R. K. (2001). Emergence in sociology: contemporary philosophy of mind and some implications for sociological theory. American Journal of Sociology, 107, 551-585. Sawyer, R. K. (2004). The mechanisms of emergence. Philosophy of the Social Sciences, 34, 260–282. Sawyer, R. K. (2005). Social emergence: societies as complex systems. Cambridge: Cambridge University Press. Sawyer, R.K. (2003). Nonreductive individualism: Part 2, Social causation. Philosophy of the Social Sciences, 33, 203–224. Winch, P. (1993). The idea of a social science and its relation to philosophy‭ (SAMT, Trans.). Tehran, Iran: SAMT. (shrink)

Resolution is an effective deduction procedure for classical logic. There is no similar "resolution" system for non-classical logics (though there are various automated deduction systems). The paper presents resolution systems for intuistionistic predicate logic as well as for modal and temporal logics within the framework of labelled deductive systems. Whereas in classical predicate logic resolution is applied to literals, in our system resolution is applied to L(abelled) R(epresentation) S(tructures). Proofs are discovered by a refutation procedure defined (...) on LRSs, that imposes a hierarchy on clause sets of such structures together with an inheritance discipline. This is a form of Theory Resolution. For intuitionistic logic these structures are called I(ntuitionistic) R(epresentation) S(tructures). Their hierarchical structure allows the restriction of unification of individual variables and/or constants without using Skolem functions. This structures must therefore be preserved when we consider other (non-modal) logics. Variations between different logics are captured by fine tuning of the inheritance properties of the hierarchy. For modal and temporal logics IRS's are extended to structures that represent worlds and/or times. This enables us to consider all kinds of combined logics. (shrink)

In this paper we show that the subvarieties of BL, the variety of BL-algebras, generated by single BL-chains on [0, 1], determined by continous t-norms, are finitely axiomatizable. An algorithm to check the subsethood relation between these subvarieties is provided, as well as another procedure to effectively find the equations of each subvariety. From a logical point of view, the latter corresponds to find the axiomatization of every residuated many-valued calculus defined by a continuous t-norm and (...) its residuum. Actually, the paper proves the results for a more general class than t-norm BL-chains, the so-called regular BL-chains. (shrink)

The Church-Turing Thesis (CTT) is often paraphrased as ``every computable function is computable by means of a Turing machine.'' The author has constructed a family of equational theories that are not Turing-decidable, that is, given one of the theories, no Turing machine can recognize whether an arbitrary equation is in the theory or not. But the theory is called pseudorecursive because it has the additional property that when attention is limited to equations with a bounded number of (...) variables, one obtains, for each number of variables, a fragment of the theory that is indeed Turing-decidable. In a 1982 conversation, Alfred Tarski announced that he believed the theory to be decidable, despite this contradicting CTT. The article gives the background for this proclamation, considers alternate interpretations, and sets the stage for further research. (shrink)

This paper considers the probative burdens of proposing action or policy options in deliberation dialogues. Do proposers bear a burden of proof? Building on pioneering work by Douglas Walton (2010), and following on a growing literature within computer science, the prevailing answer seems to be “No.” Instead, only recommenders—agents who put forward an option as the one to be taken—bear a burden of proof. Against this view, we contend that proposers have burdens of proof with respect to their proposals. (...) Specifically, we argue that, while recommenders that Φ bear a burden of proof to show that □Φ (We should / ought to / must Φ), proposers that Φ have a burden of proof to show that ◇Φ (We may / can Φ). A burden of proposing may be defined as, which reads: Those who propose that we might Φ are obliged, if called upon, to show that Φ is possible in any of four ways which we call worldly, deontic, instrumental, and practical. So understood, burdens of proposing satisfy the standard formal definition of burden of proof. (shrink)

In (Fund Math 60:175–186 1967), Wolk proved that every well partial order (wpo) has a maximal chain; that is a chain of maximal order type. (Note that all chains in a wpo are well-ordered.) We prove that such maximal chain cannot be found computably, not even hyperarithmetically: No hyperarithmetic set can compute maximal chains in all computable wpos. However, we prove that almost every set, in the sense of category, can compute maximal chains (...) in all computable wpos. Wolk’s original result actually shows that every wpo has a strongly maximal chain, which we define below. We show that a set computes strongly maximal chains in all computable wpo if and only if it computes all hyperarithmetic sets. (shrink)

In this short monograph, John Horty explores the difficulties presented for Gottlob Frege's semantic theory, as well as its modern descendents, by the treatment of defined expressions. The book begins by focusing on the psychological constraints governing Frege's notion of sense, or meaning, and argues that, given these constraints, even the treatment of simple stipulative definitions led Frege to important difficulties. Horty is able to suggest ways out of these difficulties that are both philosophically and logically (...) plausible and Fregean in spirit. This discussion is then connected to a number of more familiar topics, such as indexicality and the discussion of concepts in recent theories of mind and language. In the latter part of the book, after introducing a simple semantic model of senses as procedures, Horty considers the problems that definitions present for Frege's idea that the sense of an expression should mirror its grammatical structure. The requirement can be satisfied, he argues, only if defined expressions--and incomplete expressions as well--are assigned senses of their own, rather than treated contextually. He then explores one way in which these senses might be reified within the procedural model, drawing on ideas from work in the semantics of computer programming languages. With its combination of technical semantics and history of philosophy, Horty's book tackles some of the hardest questions in the philosophy of language. It should interest philosophers, logicians, and linguists. (shrink)

The classical Hahn–Banach Theorem states that any linear bounded functional defined on a linear subspace of a normed space admits a norm-preserving linear bounded extension to the whole space. The constructive and computational content of this theorem has been studied by Bishop, Bridges, Metakides, Nerode, Shore, Kalantari Downey, Ishihara and others and it is known that the theorem does not admit a general computable version. We prove a new computable version of this theorem without unrolling the (...) classical proof of the theorem itself. More precisely, we study computability properties of the uniform extension operator which maps each functional and subspace to the set of corresponding extensions. It turns out that this operator is upper semi-computable in a well-defined sense. By applying a computable version of the Banach–Alaoglu Theorem we can show that computing a Hahn–Banach extension cannot be harder than finding a zero in a compact metric space. This allows us to conclude that the Hahn–Banach extension operator is ${\bf {\Sigma^{0}_{2}}}$ -computable while it is easy to see that it is not lower semi-computable in general. Moreover, we can derive computable versions of the Hahn–Banach Theorem for those functionals and subspaces which admit unique extensions. (shrink)

The paper is meant as a survey of issues in computational complexity from the standpoint of its relevance to social research. Moreover, the threads are hinted at that lead to computer science from mathematical logic and from philosophical questions about the limits and the power both of mathematics and the human mind. Especially, the paper addresses Turing's idea of oracle, considering its impact on computational (i.e., relying on simulations) economy, sociology etc. Oracle is meant as a device (...) capable of finding the values of uncomputable functions. Such an idealized entity is exemplified by the human mind's procedure of recognizing the truth of the Gödelian sentence, of identifying uncomputable numbers through Turing's diagonal procedure, etc. Since such procedures are strictly defined and are as reliable as any calculations, they are worth to be called computation as well. From the computation in the strict sense, that defined as purely algorithmic (mechanical) process, one distinguishes them with the term "hipercomputation". Now the following questions arise. - Are there undecidable problems (ie. not decidable with appropriate algorithms) in social research as are (according to what is reported esp. By S. Wolfram) in natural sciences? The answer in the negative would impose limitations on computer simulations (as entirely relying on algorithms). - If there are, then we have the next question: can such problems be addressed with hipercomputational procedures? - How such hipercomputational procedures would be related to analog computation (coextensive, everlappiing, etc.)? Another set of issues is stated in terms of tractability of decidable problems, that is, the efficiency of algorithms needed for solutions. As inefficient are regarded those which require more resources (time, memory, etc.) than is available in a foreseeable future. In this context, one discusses methods of such an efficient organizing computational processes to overcome the scarcity of resources; thus parallel, distributive, interactive, etc. computing are used as remedies. The paper claims, hinting at F.Hayek's ideas, that in some social systems (e.g., stock exchange, and free market in general) such an efficient organization of their computational activities spontaneously evolves. And this is the main source of its advantages over the central economic planning (as defended by O. Lange). This noticing (in terms of complexity theory) of analogy between Hayek's point and the current discussion of efficiency of algorithms is what may count as an original contribution of the present paper. (shrink)

Marr's levels of analysis—computational, algorithmic, and implementation—have served cognitive science well over the last 30 years. But the recent increase in the popularity of the computational level raises a new challenge: How do we begin to relate models at different levels of analysis? We propose that it is possible to define levels of analysis that lie between the computational and the algorithmic, providing a way to build a bridge between computational- and algorithmic-level models. (...) The key idea is to push the notion of rationality, often used in defining computational-level models, deeper toward the algorithmic level. We offer a simple recipe for reverse-engineering the mind's cognitive strategies by deriving optimal algorithms for a series of increasingly more realistic abstract computational architectures, which we call “resource-rational analysis.”. (shrink)

We show that the fundamental legal structure of a well-written financial contract follows a state-transition logic that can be formalized mathematically as a finite-state machine (specifically, a deterministic finite automaton or DFA). The automaton defines the states that a financial relationship can be in, such as “default,” “delinquency,” “performing,” etc., and it defines an “alphabet” of events that can trigger state transitions, such as “payment arrives,” “due date passes,” etc. The core of a contract describes (...) the rules by which different sequences of events trigger particular sequences of state transitions in the relationship between the counterparties. By conceptualizing and representing the legal structure of a contract in this way, we expose it to a range of powerful tools and results from the theory of computation. These allow, for example, automated reasoning to determine whether a contract is internally coherent and whether it is complete relative to a particular event alphabet. We illustrate the process by representing a simple loan agreement as an automaton. (shrink)

Combinatorial operations on sets are almost never well defined on Turing degrees, a fact so obvious that counterexamples are worth exhibiting. The case we focus on is the symmetric-difference operator; there are pairs of degrees for which the symmetric-difference operation is well defined. Some examples can be extracted from the literature, e.g. from the existence of nonzero degrees with strong minimal covers. We focus on the case of incomparable r.e. degrees for which the symmetric-difference operation (...) is well defined. (shrink)

Diagnosis of dementia in primary care is both difficult and important. The recommendations by several authors to improve the diagnosis of dementia by general practitioners are important, but insufficient. It is argued that perhaps the disease concept in itself is a cause of confusion for clinicians. Primary care physicians need an adapted procedure, gradually leading to the final diagnosis of dementia. It has to be a stepwise labelling strategy, using global descriptions and non-disease specific labels in the beginning, (...) ending up with well-defined disease criteria. In this process, there is circularity: previous diagnoses have to be kept in mind because symptoms and signs may gradually change during the progression of the disease, leading to reconsideration of previous deleted options. To frame this properly, the primary care physician needs to adopt a broad frail elderly geriatric concept. Implementation of this concept not only helps the diagnostic process, but also stimulates the care for dementing patients and their caregivers. Relevant arguments for early diagnostic involvement of primary care physicians can be put forward on condition that a new concept, adapted procedures and adapted instruments are used. (shrink)

1. One theory or many? In 2004 a very interesting and readable article by Lenore Blum, entitled “Computing over the reals: Where Turing meets Newton,” appeared in the Notices of the American Mathematical Society. It explained a basic model of computation over the reals due to Blum, Michael Shub and Steve Smale (1989), subsequently exposited at length in their influential book, Complexity and Real Computation (1997), coauthored with Felipe Cucker. The ‘Turing’ in the title of Blum’s article refers of course (...) to Alan Turing, famous for his explication of the notion of mechanical computation on discrete data such as the integers. The ‘Newton’ there has to do to with the well known numerical method due to Isaac Newton for approximating the zeros of continuous functions under suitable conditions that is taken to be a paradigm of scientific computing. Finally, the meaning of “Turing meets Newton” in the title of Blum’s article has another, more particular aspect: in connection with the problem of controlling errors in the numerical solution of linear equations and inversion of matrices,Turing (1948) defined a notion of condition for the relation of changes in the output of a computation due to small changes in the input that is analogous to Newton’s definition of the derivative. The thrust of Blum’s 2004 article was that the BSS model of computation on the reals is the appropriate foundation for scientific computing in general. By way of response, two years later another very interesting and equally readable article appeared in the Notices, this time by Mark Braverman and Stephen Cook (2006) entitled “Computing over the reals: Foundations for scientific computing,” in which the authors argued that the requisite foundation is provided by a quite different “bit computation” model, that is in fact prima facie incompatible with the BSS model. The bit computation model goes back to ideas due to Stefan Banach and Stanislaw Mazur in the latter part of the 1930s, but the first publication was not made until Mazur (1963).. (shrink)

This is the first paper on constructive concurrent dynamic logic . For the first time, either for concurrent or sequential dynamic logic, we give a satisfactory treatment of what statements are forced to be true by partial information about the underlying computer. Dynamic logic was developed by Pratt [V. Pratt, Semantical considerations on Floyd–Hoare logic, in: 17th Annual IEEE Symp. on Found. Comp. Sci., New York, 1976, pp. 109–121, V. Pratt, Applications of modal logic to programming, Studia Logica 39 257–274] (...) for nondeterministic sequential programs, and by Peleg [D. Peleg, Concurrent dynamic logic, Journal of the Association for Computing Machinery 34 , D. Peleg, Communication in concurrent dynamic logic, Journal of Computer and System Sciences 35 ] for concurrent programs, for the purpose of proving properties of programs such as correctness. Here we define what it means for a dynamic logic formula to be forced to be true knowing only partial information about the results of assignments and tests. This informal CCDL semantics is formalized by intuitionistic Kripke frames modeling this partial information, and each such frame is interpreted as an idealized concurrent machine . In CCDL, proofs and deductions are ω-height, ω-branching, well-founded labeled subtrees of ωω. These are a generalization of the signed tableaux of Nerode [A. Nerode, Some lectures in modal logic, Technical Report, M.S.I. Cornell University, 1989, CIME Logic and Computer Science Montecatini Volume, Springer-Verlag Lecture Notes, 1990, A. Nerode, Some lectures in intuitionistic logic, Technical Report, M.S.I. Cornell University, 1988, Marktoberdorf Logic and Computation NATO Summer School Volume, NATO Science Series, 1990 ] stemming from the prefix tableaux of Fitting [M.C. Fitting, Proof Methods for Modal and Intuitionistic Logic, Reidel, 1983]. We demonstrate the correctness of our tableau proofs, define consistency properties, prove that consistency properties yield models, construct systematic tableaux, prove that systematic tableaux yield a consistency property, and conclude that CCDL is complete. This infinitary semantics and proof procedure will be the primary guide for defining, in a sequel, the correct finitary CCDL based on induction principles. FCCDL is suitable for implementation in constructive logic software systems such as Constable’s NUPRL or Huet-Coquand’s CONSTRUCTIONS. Our goal is to develop a constructive logic programming tool for specification and modular verification of programs in any imperative concurrent language, and for the extraction of concurrent programs from constructive proofs. Subsequent papers will introduce analogous logics for declarative and functional concurrent languages. (shrink)

The whistleblower system assumes that an element necessary for proper functioning about an organization is to see irregularities occurring in it. For this reason, whistleblowing and follow-up internal investigations occupy a central place in the organization’s compliance management system and an important role in the organization’s culture. These two areas constantly complement each other. However, compliance systems seem to be a broader concept, where the organization’s culture is part of it. The culture of an organization represents the habits, traditions, (...) and customs of organizations, which are not always written down. It is often referred to as the “company atmosphere.” Compliance is a system of procedures and rules, most often written down, which define procedures for dealing with specific situations, rights and obligations of employees, co-workers, or contractors. The regulations that emerge from the compliance system derive from laws, industry regulations, ethical norms, including the culture of a particular organization. Well-developed and implemented whistleblowing procedures that become part of the organization’s culture for good influence the existence of a highly developed compliance system that guarantees the multifaceted success of the organization. (shrink)

According to Church’s thesis, we can identify the intuitive concept of effective computability with such well-defined mathematical concepts as Turing computability and partial recursiveness. The almost universal acceptance of Church’s thesis among logicians and computer scientists is puzzling from some epistemological perspectives, since no formal proof is possible of a thesis that involves an informal concept such as effectiveness. Elliott Mendelson has recently argued, however, that equivalencies between intuitive notions and precise notions need not always be (...) considered unprovable theses, and that Church’s thesis should be accepted as true.I want to discuss a thesis that is nearly as important in current research in computer science as Church’s thesis. I call the newer thesis the tractability thesis, since it identifies the intuitive class of computationally tractable problems with a precise class of problems whose solutions can be computed in polynomial time. After briefly reviewing the theory of intractability, I compare the grounds for accepting the tractability thesis with the grounds for accepting Church's thesis. Intimately connected with the tractability thesis is the mathematical conjecture, whose meaning I shall shortly explain, that P≠NP. Unlike Church's thesis, this conjecture is precise enough to be capable of mathematical proof, but most computer scientists believe it even though no proof has been found. As we shall see below, understanding the grounds for acceptance of the conjecture that P≠NP has implications for general questions in the philosophy of mathematics and science, especially concerning the epistemological importance of explanatory and conceptual coherence. (shrink)

The Faculty of Medicine and Health Sciences of the University of Sherbrooke has observed year after year, that certain students have not started and or completed their immunizations for common infectious diseases, which in effect makes them inadmissible for their clinical internships in healthcare establishments. The program administrators have posed a series of questions on the best way to proceed with these students as, a certain number remain reluctant to vaccination. They are often confronted with ethical dilemmas, are not (...) necessarily comfortable with their rights and responsibilities and wish to be guided throughout the process. This article aims to put forth a procedure that would be put in place to support the administrators in a way for them to obtain a more favorable vaccination level for all of their students in the most reasonable amount of time possible. The interest of the procedure is to move forward in a few simple and well defined steps that are supported by a rigorous legal framework, while respecting the rights and freedoms of the students. It is also designed so that it could be replicated in other faculties of medicine. (shrink)

Formalizing commonsense knowledge for reasoning about time has long been a central issue in AI. It has been recognized that the existing formalisms do not provide satisfactory solutions to some fundamental problems, viz. the frame problem. Moreover, it has turned out that the inferences drawn do not always coincide with those one had intended when one wrote the axioms. These issues call for a well-defined formalism and useful computational utilities for reasoning about time and change. (...) Yoav Shoham of Stanford University introduced in his 1986 Yale doctoral thesis an appealing temporal nonmonotonic logic and identified a class of theories, causal theories, which have computationally simple model-theoretic properties. This paper is a study towards building upon Shoham's work on causal theories. We concentrate on improving computational aspects of causal theories while preserving their model-theoretic properties. (shrink)

Two very different insights motivate characterizing the brain as a computer. One depends on mathematical theory that defines computability in a highly abstract sense. Here the foundational idea is that of a Turing machine. Not an actual machine, the Turing machine is really a conceptual way of making the point that any well-defined function could be executed, step by step, according to simple 'if-you-are-in-state-P-and-have-input-Q-then-do-R' rules, given enough time (maybe infinite time) [see COMPUTATION]. Insofar as the (...) brain is a device whose input and output can be characterized in terms of some mathematical function -- however complicated -- then in that very abstract sense, it can be mimicked by a Turning machine. Given what is known so far brains do seem to depend on cause-effect operations, and hence brains appear to be, in some formal sense, equivalent to a Turing machine [see CHURCH-TURING THESIS]. On its own, however, this reveals nothing at all of how the mind-brain actually works. The second insight depends on looking at the brain as a biological device that processes information from the environment to build complex representations that enable the brain to make predictions and select advantageous behaviors. Where necessary to avoid ambiguity, we will refer to the first notion of computation as algorithmic computation, and the second as information processing computation. (shrink)

A linear order is -decidable if its universe is and the relations defined by formulas are uniformly computable. This means that there is a computable procedure which, when applied to a formula and a sequence of elements of the linear order, will determine whether or not is true in the structure. A linear order is decidable if the relations defined by all formulas are uniformly computable. These definitions suggest two questions. Are there, for each , -decidable (...) linear orders that are not -decidable? Are there linear orders that are -decidable for all but not decidable? The former was answered in the positive by Moses in 1993. Here we answer the latter, also positively. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 37.1 (2003) 13-31 [Access article in PDF] A Philosophical Inquiry into the Nature of Computer Art Holle Humphries Before the computer is accepted unquestioningly as a legitimate artistic medium, some of the challenging aesthetic and philosophical issues raised by [computer art] must be solved. The most haunting questions concern the impact of the technology on the artist, the creative process, and the nature of (...) art. 1How might we lead students in an exploration of the philosophical issues regarding art created with a computer? The most important step is first to guide them in exploring ontological concepts and questions asked about the nature of art and computer art, before investigating related issues of epistemology, value, and criticism. Students need to understand the nature of their art tool and medium of choice. Therefore, it becomes a matter of concern to discover that when discussing and writing about computer art, students sometimes use such terms interchangeably as "computer art" and "computer-generated art," when they are not synonymous, and talk about "virtual reality" as though engaging in any activity that involves a computer constitutes experiencing one. It is clear that this problem arises because many have not paused to examine the nature of computer art within the context of the process and product of art, and the subtle nuances regarding what might distinguish each from other human enterprise. To help clarify their thinking, we might use the foundation of art theory and the strategy of philosophical inquiry, implemented by adopting questioning strategies, to guide students through an exploration of the ontological nature of computer art. This can begin by launching the question: "What is the nature of art — or computer art?" Philosophy of Art: "What is the Nature of Art?" Many philosophers have attempted to describe or define the nature of art formulated in a theory of art. A theory of art attempts to specify where the essence of art is thought to reside, or what exactly art's essence is. [End Page 13]The imitation theory, initiated in the 5th century B.C. by Plato, held that to be a work of art, an object must mirror reality. 2 As this theory placed the essence of art in the objective properties of the art work itself, we consider the imitation theory to be object-centered or objective in nature. Similarly, with his formalist theory of art, Clive Bell claimed that the essence of art lies in the object — within the structural design properties of a work of art. To qualify as a work of art, an object must exhibit significant form. Significant form consists of certain formal properties such as the art elements of lines and color combined in a particular way according to art principles, all used to create certain forms and relations of forms. 3The expression theories of art shifted attention to the artist and audience and thus are considered subject centered, or subjective, bound up in notions of the experience of creation by the artist and/or the response of the audience. Benedetto Croce asserted that a work of art resides in the mind of the artist. An artist must experience an intuition, and it is this mental process that constitutes art, not the object which the artist might create thereafter. 4 Robin Collingwood claimed that art is an exploration, clarification, and expression of an artist's emotion, made clear to an audience through a medium. 5 Leo Tolstoy believed that art should be a vehicle by which the emotion experienced by the artist at the time of creation is transmitted to an audience, so that the audience can experience that emotion as well. 6Morris Weitz asserted that none of these theories capture an essence of art because they are either too broad, too narrow, or else are circular. He claimed that the concept of art cannot be limited to one essence delimited in a definition. Weitz suggested that we must instead look at what theories of art have to say is important about art so that we know what to... (shrink)

Despite the widespread use of automated decision-making (ADM) systems, they are often developed without involving the public or those directly affected, leading to concerns about systematic biases that may perpetuate structural injustices. Existing formal fairness approaches primarily focus on statistical outcomes across demographic groups or individual fairness, yet these methods reveal ambiguities and limitations in addressing fairness comprehensively. This paper argues for a holistic approach to algorithmic fairness that integrates procedural fairness, considering both decision-making processes and their outcomes. (...) Procedural fairness emphasizes the importance of fair decision-making procedures, which aligns with theories of relational justice that stress the quality of social relations and power dynamics. We highlight the need for substantive procedural fairness to ensure better outcomes and address forward-looking responsibilities. Additionally, we propose leveraging Public Engagement, a core dimension within the well-established Responsible Research and Innovation framework, to enhance procedural fairness in ADM systems. Our contribution underscores the value of Public Engagement in fostering fairer ADM processes, thereby expanding the current focus beyond technical outcome-based approaches to encompass broader procedural considerations. (shrink)

A medical intervention is a medical procedure or application intended to relieve or prevent illness or injury. Examples of medical interventions include vaccination and drug administration. After a medical intervention, adverse events (AEs) may occur which lie outside the intended consequences of the intervention. The representation and analysis of AEs are critical to the improvement of public health. Description: The Ontology of Adverse Events (OAE), previously named Adverse Event Ontology (AEO), is a community-driven ontology developed to standardize and integrate (...) data relating to AEs arising subsequent to medical interventions, as well as to support computer-assisted reasoning. OAE has over 3,000 terms with unique identifiers, including terms imported from existing ontologies and more than 1,800 OAE-specific terms. In OAE, the term ‘adverse event’ denotes a pathological bodily process in a patient that occurs after a medical intervention. Causal adverse events are defined by OAE as those events that are causal consequences of a medical intervention. OAE represents various adverse events based on patient anatomic regions and clinical outcomes, including symptoms, signs, and abnormal processes. OAE has been used in the analysis of several different sorts of vaccine and drug adverse event data. (shrink)

What''s computation? The received answer is that computation is a computer at work, and a computer at work is that which can be modelled as a Turing machine at work. Unfortunately, as John Searle has recently argued, and as others have agreed, the received answer appears to imply that AI and Cog Sci are a royal waste of time. The argument here is alarmingly simple: AI and Cog Sci (of the Strong sort, anyway) are committed to the (...) view that cognition is computation (or brains are computers); butall processes are computations (orall physical things are computers); so AI and Cog Sci are positively silly.I refute this argument herein, in part by defining the locutions x is a computer and c is a computation in a way that blocks Searle''s argument but exploits the hard-to-deny link between What''s Computation? and the theory of computation. However, I also provide, at the end of this essay, an argument which, it seems to me, implies not that AI and Cog Sci are silly, but that they''re based on a form of computation that is well beneath human persons. (shrink)

Structured argumentation systems, and their implementation, represent an important research subject in the area of Knowledge Representation and Reasoning. Structured argumentation advances over abstract argumentation frameworks by providing the internal construction of the arguments that are usually defined by a set of (strict and defeasible) rules. By considering the structure of arguments, it becomes possible to analyze reasons for and against a conclusion, and the warrant status of such a claim in the context of a knowledge base represents (...) the main output of a dialectical process. Computing such statuses is a costly process, and any update to the knowledge base could potentially have a huge impact if done naively. In this work, we investigate the case of updates consisting of both additions and removals of pieces of knowledge in the Defeasible Logic Programming (DeLP) framework, first analyzing the complexity of the problem and then identifying conditions under which we can avoid unnecessary computations—central to this is the development of structures (e.g. graphs) to keep track of which results can potentially be affected by a given update. We introduce a technique for the incremental computation of the warrant statuses of conclusions in DeLP knowledge bases that evolve due to the application of (sets of) updates. We present the results of a thorough experimental evaluation showing that our incremental approach yields significantly faster running times in practice, as well as overall fewer recomputations, even in the case of sets of updates performed simultaneously. (shrink)

This is a non-technical version of "The Decision Problem for Effective Procedures." The “somewhat vague, intuitive” notion from computability theory of an effective procedure (method) or algorithm can be fairly precisely defined, even if it does not have a purely mathematical definition—and even if (as many have asserted) for that reason, the Church–Turing thesis (that the effectively calculable functions on natural numbers are exactly the general recursive functions), cannot be proved. However, it is logically provable from (...) the notion of an effective procedure--without reliance on any (partially) mathematical thesis or conjecture concerning effective procedures, such as the Church–Turing thesis--that the class of effective procedures is undecidable, i.e., that no effective procedure is possible for ascertaining whether a given procedure is effective. The proof does not appeal to a precise definition of ‘effective procedure’. Instead, it relies solely and entirely on a basic grasp of the intuitive notion of such a procedure. Though this undecidability result itself is not surprising, it is also not without significance. It has the consequence, for example, that the solution to a decision problem, if it is to be complete, must be accompanied by a separate argument that the proposed ascertainment procedure is, in fact, a decision procedure, i.e., effective—for example, that it invariably terminates with the correct verdict. (shrink)

The relation between computational and intentional psychology has always been a vexing issue. The worry is that if mental processes are computational, then these processes, which are defined over symbols, are sensitive solely to the non-semantic properties of symbols. If so, perhaps psychology could dispense with adverting in its laws to intentional/semantic properties of symbols. Stich, as is well-known, has made a great deal out of this tension and argued for a purely "syntactic" psychology by (...) driving a wedge between a semantic individuation of symbol tokens and their narrow functional individuation. If the latter can be carried out, he claimed, we do not need semantic typing. I argue that since a narrow functional individuation cannot type-identify symbol tokens across organisms, a semantic account of typing must be the only option given that interpersonal physical individuation of tokens is not to be taken seriously. (shrink)

Chapter 1 First Person Access to Mental States. Mind Science and Subjective Qualities -/- Abstract. The philosophy of mind as we know it today starts with Ryle. What defines and at the same time differentiates it from the previous tradition of study on mind is the persuasion that any rigorous approach to mental phenomena must conform to the criteria of scientificity applied by the natural sciences, i.e. its investigations and results must be intersubjectively and publicly controllable. In Ryle’s view, (...) philosophy of mind needs to adopt an antimentalist stance to achieve this aim. Antimentalism not only definitively rejects the idea that mind is a substance separated from the body, it also denies that mental phenomena radically differ from physical phenomena by virtue of several unique features. Most problematically, mental phenomena have a conscious character (mental states are related to specific qualitative feelings) and are accessible only to the first-person (only the subject knows directly what s/he is experiencing inside his/her mind). Ryle takes a strong stance on antimentalism going so far as to maintain that an approach to mind which aims to meet the criteria of scientificity set by the natural sciences must avoid any reference to internal, unobservable mental states. In his view (which is considered a specifically philosophical version of psychological behaviorism and also addresses questions put forward in psychological research), mental states can be redescribed in terms of behavioral dispositions. In this chapter, we address the historical roots of the antimentalist view and analyze its relation to the later tradition of research on mind. We show that, compared to the antimentalist stance, functionalism and cognitivism take a step back when they maintain that direct reference to mental states is necessary since mental states cause and therefore explain human behavior. This step backwards is often interpreted as a return to mentalism. However, this is only partially true. Indeed, we suggest that these later traditions retain one important element of Ryle’s antimentalism, i.e. the idea that mental states must be uniquely identified using external and publicly observable criteria, while excluding any reference to introspection and those qualitative dimensions of a mental state, which are accessible only to the first-person. According to the perspective we put forward, this epistemological stance has continued to influence contemporary research on mind and current philosophical and psychological theories which both tend to exclude the subjective qualities of human experience from their accounts of how the mind works. The issue we raise here is whether this is legitimate or whether subjective qualities do play a role with respect to the way our mind works. The conclusion of this chapter anticipates the argument the book makes in in favor of this latter position, starting from a particular angle, i.e. the problem of how we categorize concepts related to our internal states. -/- Chapter 2 The Misleading Aspects of the Mind/Computer Analogy. The Grounding Problem and the Thorny Issue of Propriosensitive Information -/- Abstract. After the crisis of behaviorism, cognitivism and functionalism became the predominant models in the field of psychology and of philosophy, respectively. Their success is mainly due to the new key they use for interpreting mental processes: the mind/computer analogy. On the basis of this analogy, mental operations are seen as cognitive processes based on computations, i.e. on manipulations of abstract symbols which are in turn understood as informational unities (representations). This chapter identifies two main problems with this model. The first is how these symbols can relate to and communicate with perception and thus allow us to identify and classify what we perceive through the senses. Here we limit ourselves to presenting this issue in relation to the classical symbol grounding problem originally put forward by Harnad on the basis of Searle’s Chinese room argument. An attempt to address the problem raised here will be made in chap. 3. The second point we discuss in relation to the mind/computer analogy concerns the idea of information it fosters. Indeed, following this analogy, information is something available in the external world which can be captured by the senses and transmitted to the central system without being influenced or modified by the procedures of transmission. This perspective does not take into account that – unlike computers – in living beings information is acquired by means of the body. As Ulric Neisser has already pointed out, the body is itself an informational source that provides us with additional sensory experience that influences (modifies or complements) the information extracted from the external world by the senses. To develop this line of analysis and to determine exactly what information is provided by the body and how this might influence cognition, we examine Sherrington’s and Gibson’s positions. Moving on from their views, we qualify bodily information in terms of ‘proprioception’. We use ‘proprioception’ in a broad sense to describe any kind of experience we have of our internal states (including postural information as well as sensations related to the general state of the body and its parts). Following Damasio’s and Craig’s studies, we further elaborate this position, arguing that living beings are equipped with an internal propriosensitive monitoring system which maps all the changes that constantly occur in our body and that give us perceptual (‘proprioceptive’ or propriosensitive) information about what happens inside us. Moreover, relying on Goldie’s and Ratcliffe’s view, we show that emotional information can also be considered as a form of ‘proprioception’ which contributes to determining everything we perceive. This analysis leads us to the second main thesis of this book: ‘proprioception’ is a form of internal perception and it is an essential component of the sensory information we can access and use for all cognitive purposes. -/- Chapter 3 Semantic Competence from the Inside: Conceptual Architecture and Composition -/- Abstract. Concepts are essential constituents of thought: they are the instruments we use to categorize our experience, i.e. to classify things and group them together in homogeneous sets. Here we define concepts as the internal mental information (representations) that allows us, among other things, to master words in natural language. By analyzing the way in which individuals master word meanings we explore a number of hypotheses regarding the nature of concepts. Following Diego Marconi’s research, we differentiate between two kind of abilities that underpin lexical competence – so-called ‘referential’ and ‘inferential competence’ – and we suggest that, in order to support these abilities, concepts must also include two corresponding kinds of information, i.e. inferential and referential information. We point out that the most widely used and acknowledged theories of concepts do not make this distinction, instead broadly characterizing the information used for categorization in terms of propositionally described feature lists. However, we show that while feature lists can explain inferential competence, they do not account for referential competence. To address the issue of referential competence we examine Ray Jackendoff’s hypothesis that to account for the possibility of linking perceptual and conceptual information we need to assume the existence of a (visual) representation that encodes the geometric and topological properties of objects and bridges the gap between the percept and the concept. Furthermore, we analyze the extension of this work by Jesse Prinz who introduced the notion of a proxytype, a perceptual representation of a class of objects that incorporates structural and parametric information related to their appearance. However, as we point out, proxytypes can only explain the relationship between perception and concepts with respect to instances that can be perceived through the senses and that belong to the same class by virtue of their physical similarity. We suggest that this notion be extended to include larger conceptual classes. To accomplish this, we further develop Mark Johnson, George Lakoff and Jean Mandler’s idea of a schematic image and argue that conceptual representations include a perceptual schema. Perceptual schemata are non-linguistic, structured experiential gestalts (patterns or maps) that make use of information taken from all sensory modalities, including body perception. They accomplish a quasi-conceptual function: they allow us to recognize and to classify different instances. In this work, we hypothesize that perceptual schemata are an essential component of concepts, but not identical to them. Instead, we suggest that concepts include both perceptual and propositional information with perceptual schemata providing the ‘perceptual core concept’ that grounds related propositional information. -/- Chapter 4 In the Beginning There Were Categories. The Bodily Origin of Prelinguistic Categorical Organization: The Example of Folkbiological Taxonomies -/- Abstract. Studies of categorization in psychology and the cognitive sciences have made use of the notions of ‘category’ and ‘concept’ without precisely defining what is meant by either; in fact, often these terms have been used as synonyms, making it difficult to address specific issues related to conceptual development. This chapter begins by discussing the definitions of, as well as the distinctions between, ‘categories’ and ‘concepts’ in the classical philosophical tradition (Aristotle, Kant and Husserl). We introduce our view of categories with reference to Husserl. Categorization is defined as the way in which our experience is originally (pre-linguistically) organized in a passive and fully unconscious manner on the basis of universal structuring principles. Conceptualization is explained as a later process in which the earlier categorical macro-classes are further subdivided into more specific and detailed sets; this later process also relies on linguistic learning and exposure to culture. On the basis of Ray Jackendoff, Jean Mandler, George Lakoff and Mark Johnson’s work, we hypothesize that categorization is a two-step process that begins with the formation of homogeneous sets of entities partitioned into regions that describe the ontological boundaries of the objects that humans perceive (categories) and continues at a later stage with the development of more specific classifications (concepts). In this chapter, we mainly address three related issues: Why should we assume that there is categorical organization which precedes the development of a conceptual system? How do categories and concepts relate to each other? Shall we hypothesize that categories are innate or that they are formed before concepts on the basis of information and organizational structure available at a very early developmental stage? We show that categorical partitions are necessary for categorization and, following Mandler, that the general categories we form at an early age do not match our adult superordinate concepts. As for the third issue, we argue that there might be no need to assume that categories are innately present in the human mind, since their formation can be explained – at least in certain cases – by basic mechanisms that work on body (propriosensitive) information. This hypothesis will not be discussed in general, but in relation to a particularly relevant example of categorical partition, i.e. the folk-biological dichotomy between ANIMATE/INANIMATE. This is compared with other dichotomies that derive from it, but are not directly categorical such as LIVING/NON-LIVING and BIOLOGICAL/NON-BIOLOGICAL. -/- Chapter 5 Internal States: From Headache to Anger. Conceptualization and Semantic Mastery -/- Abstract. Here we ask if we can also apply the distinction between referential and inferential competence we introduced in Chapter 3 to words that do not refer to things that are perceived using the external senses, especially to words/concepts that denote bodily experiences (such as pain, thirst, hunger, etc.) or emotions. We introduce and discuss the hypothesis that – even though such words/concepts do not refer to intersubjectively identifiable entities in the external world – they do have a kind of referent that can be accessed via direct perception, more specifically ‘proprioception’, as we have defined it in terms of all propriosensitive information we can consciously access. In the first part of the chapter, we specifically consider terms denoting bodily experiences such as ‘pain’ or ‘hunger’ and argue that their referents are identified and classified from a first-personal point of view on the basis of four main characteristics: their specific intensity, their localization in the body, their co-occurrence with other signals and above all their specific qualitative sensations. Emotions are addressed in the second part of the chapter. We suggest that there is a continuity between bodily experiences and emotions. In particular, we argue for a perceptual theory of emotions in line with that proposed by James and Lange at the end of the 19th century and developed more recently by authors such as Damasio (see also chap. 2§5, §6). The hypothesis we put forward is that the referential information that supports the categorization of emotions and therefore also our mastery of terms referring to emotions consists in the perception (i.e. the ‘proprioception’) of those bodily states and changes in bodily states which constitute our emotional experience. In the context of this discussion we examine some objections to this line of reasoning that arise from a cognitivist perspective and following authors such as Oatley, Johnson-Laird and Frijda, we distinguish between basic emotions that can be identified and classified solely on the basis on how they feel and complex emotions whose identification and classification additionally depends on cognitive factors. To describe how emotions are identified and classified on the basis of how they feel, we rely on Marcel and Lambie’s distinction between an ‘emotion state’ and an ‘emotion experience’. Both notions indicate kinds of feelings that we consciously experience. However, they describe first-order and second order emotion awareness respectively. The emotion state is the feeling we have of the bodily states and changes that occur when we are experiencing an emotion, while the emotion experience is the fully developed and integrated emotion we both experience and are, with reflection, aware of experiencing. On the basis of this differentiation, we also show that the same characteristics that aid in the identification and classification of bodily experiences (specific qualitative sensations; somatic localization; specific intensity; presence/absence of specific concomitant sensations) can also be used for the identification and classification of emotions – at least basic emotions. In the last two sections of the chapter we present some clinical evidence on the semantic competence of people who suffer from Alexithymia and Autism Spectrum Disorder which supports the conclusions of our preceding analyses. -/- Chapter 6 The ‘Proprioceptive’ Component of Abstract Concepts -/- Abstract. In this chapter, we address the issue of whether the mastery of abstract words requires only inferential knowledge and thus, if the concepts that support the mastery of abstract words include only linguistic information. We start by differentiating the notions of ‘abstract’ and ‘general’ which are often erroneously confused. We then identify a strict definition of abstract, as contrasted with ‘concrete’, that applies to words or concepts whose referent cannot be experienced by the senses. We argue that abstract words/concepts would be better described as theoretical, because they are usually conceived as structured sets of inferential knowledge expressed linguistically; that is, as small theories. Pointing out parallels with Carnap’s analysis of this issue in philosophy of science, we hypothesize that words/concepts denoting non-observable entities are not all ‘equally theoretical’, because their link to sensory experience can be stronger or weaker. We revive the distinction, inspired by Quine, between theoretical and intertheoretical concepts/words. This distinction relies on the fact that the former – unlike the latter – retains a strong, although indirect, connection with perception. In Quine’s discussion, perception is understood uniquely in terms of observability, i.e. of external sensory experience. Here we argue, however, that bodily, ‘proprioceptive’ (i.e. propriosensitive) experience can also serve to referentially ground theoretical (i.e. abstract) concepts/words. We frame this issue using the example of the theoretical concept ‘freedom’ and Lakoff’s hypothesis that this concept is developed on the basis of bodily information. We contrast this with the example of ‘democracy’ which more closely resembles an intertheoretical concept/word. Furthermore, we show that one of the classical views put forward in psycholinguistic research to explain how abstract concepts are mentally represented – i.e. Paivio’s Dual Coding Theory – points in the same direction as our analysis. The same is true of Barsalou’s work suggesting that we use internal information to understand at least some abstract words. To sustain this position, we put forward two lines of evidence: the first comes from psycholinguistic studies while the second examines deficits of semantic competence exhibited by people with Autism Spectrum Disorder. On the basis of our analysis, we put forward a classification that distinguishes between different kinds of concreteness and different degrees of abstraction: concepts/words referring to body experiences and basic emotions are described as analogous to concrete concepts/words because they are grounded in perceptual (i.e. propriosensitive) experience, while abstract concepts/words are considered more or less abstract depending on whether they are intratheoretical (and rely entirely on inferential information) or theoretical (and are partially grounded in perceptual – or more often in propriosensitive perceptual – information). In the last section of the chapter we consider two scales that have been used in psycholinguistic research to measure the degree of concreteness vs. abstractness of words and we show that – used conjointly – they can provide a measure of the internal vs. external grounding of specific words. (shrink)

As an undergraduate I was taught to multiply two numbers with the help of log tables, using the formulaHaving graduated to teach calculus to Engineers, I learned that log tables were to be replaced by slide rules. It was then that Imade the fateful decision that there was no need for me to learn how to use this tedious device, as I could always rely on the students to perform the necessary computations. In the course of time, (...) slide rules were replaced by pocket calculators and personal computers, but I stuck to my original decision.My computer phobia did not prevent me from taking an interest in the theoretical question: what is a computation? This question goes back to Hilbert's 10th problem, which asks for an algorithm, or computational procedure, to decide whether any given polynomial equation is solvable in integers. It quickly leads to the related question: which numerical functionsf: ℕn→ ℕ are computable?While Hilbert's 10th problem was only resolved in 1970, this related question had some earlier answers, of which I shall single out the following three:f is recursive,f is computable on an abstract machine,f is definable in the untyped λ-calculus.These tentative answers were shown to be equivalent by Church [1936] and Turing [1936–7].I shall discuss here some of the more recent developments of these notions of computability and their relevance to linguistics and logic. I hope to be forgiven for dwelling on some of the work I have been involved with personally, with greater emphasis than is justified by its historical significance. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Anthropological Perspectives in Psychiatric NosologyJuan J. López-Ibor Jr. (bio) and María-Inés López-Ibor (bio)KeywordsDSM, etiology, Aristotelian causes, social dramasPsychiatry and clinical psychology, as we learn in this paper, are disciplines in need of an ontological perspective. Very few branches of contemporary learning share this characteristic. Probably only theoretical physic and theology—as the rest have long ago given up trying to define and understand the essence of their object, for example, (...) life in the case of biology or mind in psychology. Consequently, the paper by Pérez-Álvarez, Sass and García-Montes, “The Ontology of Mental Disorders in Constructivist Perspective,” (2008) should be welcomed and indeed included in the reading lists for trainees in psychiatry and clinical psychology.The authors propose an approach to the understanding of mental disorders that is extremely attractive and well articulated, and which also has practical implications for clinicians. It is not just another “philosophical divertimento” devoid of scientific and practical importance. Let us analyze the article in an orderly way.Less DsmThe authors of the target paper disapprove of the Diagnostic and Statistical Manual of Mental Disorders (DSM)-III/IV approach to defining illnesses by starting from the symptoms that are present—on the grounds that this may lead clinicians to assume that their sole role is to identify, fight, and suppress the symptoms by whichever procedure. They propose an alternative that is dear to myself because it follows the path of the so-called “anthropological” psychiatry of Binswanger, von Gebsattel, Erwin Strauss, Zutt, López-Ibor, Sr., and others. In essence, this is a phenomenological approach to the meaning of mental diseases, one that emphasizes how the illness is revealed to the patient him- or herself.The target article’s criticism of DSM should be considered in the context of the abuses committed on its behalf. The DSM is not a textbook of psychiatric disorders, nor does it contain a definition of the diseases. The DSM does not tell what a disease is (Klerman et al. 1984)—something that is impossible with a classification system based on the manifestations of the diseases, the signs and symptoms. The DSM, as its title states, is just a diagnostic and statistical manual, which does not contain anything about the origin of [End Page 259] any disease nor an explanation of why it exists or what it means. The DSM is, in fact, just a tool to determine whether a disease is present, and therefore to facilitate communication between professionals and with other individuals, without saying anything about the disease’s aitia—a key term (associated with notions of essence as well as cause) to be discussed below. In theory, most clinicians should understand these limitations; it may be, however, that this is not really the case for many who read or use the DSM. In the world there are around 200,000 psychiatrists; since 1980 the number of DSM copies sold is in the order of several hundred thousand.The misuse of a classification system is even more noticeable in the International Classification of Diseases (ICD)-10 Research Version. The instructions for the use of this version recommend that the first step is to make an inventory of all the symptoms present, and then to construct a diagnosis based on them. This how all computer-assisted systems work. This procedure can, however, only be valid if the clinician has already reached a diagnostic conclusion by other means—a diagnosis then to be confirmed for research purposes. It may be that this is one of the reasons why the ICD-10 Research Version has almost never actually been used for research.Furthermore, the concept of symptoms in psychiatry applies only to organic mental disorders (Schneider 1959), conditions in which the patient’s attitude and way of experiencing the symptoms do not play the kind of role that they play in schizophrenia and other mental disorders. The quotation from the important paper by Sass and Parnas in this context is most appropriate. It is indeed that case that “subjective experience can play an important causal role in the progressive experiential transformations of a developing schizophrenic illness... (shrink)

When computing is defined as the causal implementation of algorithms and algorithms are defined as effective decision procedures, human thought is mental computation only if it is governed by mental algorithms. An examination of ordinary thinking, however, suggests that most human thought processes are non-algorithmic. Digital machines, moreover, are mark-manipulating or string-processing systems whose marks or strings do not stand for anything for those systems, while minds are semiotic (or “signusing”) systems for which signs stand for other (...) things for those systems. Computing, at best, turns out to be no more than a special kind of thinking. (shrink)

Recent studies have shown that self‐explanation is an effective metacognitive strategy, but how can it be leveraged to improve students' learning in actual classrooms? How do instructional treatments that emphasizes self‐explanation affect students' learning, as compared to other instructional treatments? We investigated whether self‐explanation can be scaffolded effectively in a classroom environment using a Cognitive Tutor, which is intelligent instructional software that supports guided learning by doing. In two classroom experiments, we found that students who explained (...) their steps during problem‐solving practice with a Cognitive Tutor learned with greater understanding compared to students who did not explain steps. The explainers better explained their solutions steps and were more successful on transfer problems. We interpret these results as follows: By engaging in explanation, students acquired better‐integrated visual and verbal declarative knowledge and acquired less shallow procedural knowledge. The research demonstrates that the benefits of self‐explanation can be achieved in a relatively simple computer‐based approach that scales well for classroom use. (shrink)

In [5] it has been shown that for first-order definability over the reals there exists an effective procedure which by a finite formula with equality defining an open set produces a finite formula without equality that defines the same set. In this paper we prove that there exists no such procedure for Σ-definability over the reals. We also show that there exists even no uniform effective transformation of the definitions of Σ-definable sets into new (...) definitions of Σ-definable sets in such a way that the results will define open sets, and if a definition defines an open set, then the result of this transformation will define the same set. These results highlight the important differences between Σ-definability with equality and Σ-definability without equality. (shrink)

In this paper we argue that Revision Rules, introduced by Anil Gupta and Nuel Belnap as a tool for the analysis of the concept of truth, also provide a useful tool for defining computable functions. This also makes good on Gupta's and Belnap's claim that Revision Rules provide a general theory of definition, a claim for which they supply only the example of truth. In particular we show how Revision Rules arise naturally from relaxing and generalizing a classical (...) construction due to Kleene, and indicate how they can be employed to reconstruct the class of the general recursive functions. We also point at how Revision Rules can be employed to access non-minimal fixed points of partially defined computing procedures. (shrink)

We examine the degree structure $\operatorname {\mathrm {\mathbf {ER}}}$ of equivalence relations on $\omega $ under computable reducibility. We examine when pairs of degrees have a least upper bound. In particular, we show that sufficiently incomparable pairs of degrees do not have a least upper bound but that some incomparable degrees do, and we characterize the degrees which have a least upper bound with every finite equivalence relation. We show that the natural classes of finite, light, and (...) dark degrees are definable in $\operatorname {\mathrm {\mathbf {ER}}}$. We show that every equivalence relation has continuum many self-full strong minimal covers, and that $\mathbf {d}\oplus \mathbf {\operatorname {\mathrm {\mathbf {Id}}}_1}$ needn’t be a strong minimal cover of a self-full degree $\mathbf {d}$. Finally, we show that the theory of the degree structure $\operatorname {\mathrm {\mathbf {ER}}}$ as well as the theories of the substructures of light degrees and of dark degrees are each computably isomorphic with second-order arithmetic. (shrink)

The Kantian idea that some judgments are synthetic even in the area of a priori judgments cannot be accepted in its original version, but a modification of the notions analytic' and 'synthetic' discovers a rational core of that idea. The new definition of 'analytic' concerns concepts and makes it possible to distinguish between analytic concepts, which are effective ways of computing recursive functions, and synthetic concepts, which either define non-recursive functions, or define recursive functions in an ineffective way. (...) To justify this claim we have to construe concepts as abstract procedures not reducible to set-theoretical entities. (shrink)

Context: The advent of a general artificial intelligence mechanism that learns like humans do would represent the realization of an old and major dream of science. It could be achieved by an artifact able to develop its own cognitive structures following constructivist principles. However, there is a large distance between the descriptions of the intelligence made by constructivist theories and the mechanisms that currently exist. Problem: The constructivist conception of intelligence is very powerful for explaining how cognitive development (...) takes place. However, until now, no computational model has successfully demonstrated the underlying mechanisms necessary to realize it. In other words, the artificial intelligence (AI) community has not been able to give rise to a system that convincingly implements the principles of intelligence as postulated by constructivism, and that is also capable of dealing with complex environments. Results: This paper presents the constructivist anticipatory learning mechanism (CALM), an agent learning mechanism based on the constructivist approach of AI. It is designed to deal dynamically and interactively with environments that are at the same time partially deterministic and partially observable. CALM can model the regularities experienced in the interaction with the environment, on the sensorimotor level as well, as by constructing abstract or high-level representational concepts. The created model provides the knowledge necessary to generate the agent behavior. The paper also presents the coupled agent environment system (CAES) meta-architecture, which defines a conception of an autonomous agent, situated in the environment, embodied and intrinsically motivated. Implications: The paper can be seen as a step towards a computational implementation of constructivist principles, on the one hand suggesting a further perspective of this refreshing movement on the AI field (which is still too steeped in a behaviorist influence and dominated by probabilistic models and narrow applied approaches), and on the other hand bringing some abstract descriptions of the cognitive process into a more concrete dimension, in the form of algorithms. Constructivist content: The connection of this paper with constructivism is the proposal of a computational and formally described mechanism that implements important aspects of the subjective process of knowledge construction based on key ideas proposed by constructivist theories. (shrink)

This paper brings the intellectual tools of cognitive science to bear on resolving the “paradox of the active user” [Interfacing Thought: Cognitive Aspects of Human–Computer Interaction, Cambridge, MIT Press, MA, USA]—the persistent use of inefficient procedures in interactive tasks by experienced or even expert users when demonstrably more efficient procedures exist. The goal of this paper is to understand the roots of this paradox by finding regularities in these inefficient procedures. We examine three very different data sets. For each data (...) set, we first satisfy ourselves that the preferred procedures used by some subjects are indeed less efficient than the recommended procedures. We then amass evidence, for each set, and conclude that when a preferred procedure is used instead of a more efficient, recommended procedure, the preferred procedure tends to have two major characteristics: (1) the preferred procedure is a well‐practiced, generic procedure that is applicable either within the same task environment in different contexts or across different task environments, and (2) the preferred procedure is composed of interactive components that bring fast, incremental feedback on the external problem states. The support amassed for these characteristics leads to a new understanding of the paradox. In interactive tasks, people are biased towards the use of general procedures that start with interactive actions. These actions require much less cognitive effort as each action results in an immediate change to the external display that, in turn, cues the next action. Unfortunately for the users, the bias to use interactive unit tasks leads to a path that requires more effort in the long run. Our data suggest that interactive behavior is composed of a series of distributed choices; that is, people seldom make a once‐and‐for‐all decision on procedures. This series of biased selection of interactive unit tasks often leads to a stable suboptimal level of performance. (shrink)

The book is about logical analysis of natural language. Since we humans communicate by means of natural language, we need a tool that helps us to understand in a precise manner how the logical and formal mechanisms of natural language work. Moreover, in the age of computers, we need to communicate both with and through computers as well. Transparent Intensional Logic is a tool that is helpful in making our communication and reasoning smooth and precise. It deals (...) with all kinds of linguistic context in a fully compositional and anti-contextual way. (shrink)

Arthur Kaufmann is one of the most prominent figures among the contemporary philosophers of law in German speaking countries. For many years he was a director of the Institute of Philosophy of Law and Computer Sciences for Law at the University in Munich. Presently, he is a retired professor of this university. Rare in the contemporary legal thought, Arthur Kaufmann's philosophy of law is one with the highest ambitions — it aspires to pinpoint the ultimate foundations of law by explicitly (...) proposing an ontology, a general theory of knowledge and concept of a person. Kaufmann's work derives, first of all, from the thinking of Gustav Radburch, his teacher, and then from ideas of Karl Engish and Hans-Georg Gadamer. The philosophy undertakes to pursue the ultimate foundation of law, law which is understood by Kaufmann, first of all, as a "concrete judgement" that is, what is right in a concrete situation. Justice belongs to the essence of law and "unjust law" is contradictio in adiectio. Kaufmann opposes all those theories, which as the only foundation for establishing just law (Recht) adopt legal norms (Gesetz). In Kaufmann's opinion , such theories are powerless in the face of all types of distortions of law rendered by political forces. He suggests that the basic phenomenon which needs to be explained and which cannot be disregarded by a philosopher of law is so-called "legal lawlessness" ("Gestzliches Unrecht"). "Legal lawlessness" which forms a part of life experience for the people of twentieth century totalitarian states. It proved "with the accuracy of scientific experiment" that the reality of law consists of something more than bare conformity with legal norms. The existence of lex corrupta indicates that law contains something "non-dispositive" which requires acknowledgment of both law-maker and judge. Kaufmann, accepting the convergent concept of truth and cognition, assumes that "non-dispositive" content, emerging as the conformity of a number of cognitive acts of different subjects (inter-subjective communicativeness and verifiability), indicates the presence of being in this cognition. The questions "What is law?" and "What are the principles of a just solution?" lead straight to the ontology of law, to the question about the ontological foundations of law. Kaufmann discerns the ontological foundations of law in the specifically understood "nature of things" and, ultimately, in a "person". He proposes a procedural theory of justice, founded on a "person". In my work, I undertake to reconstruct the train of thought which led Kaufmann to the recognition of a "person" as the ontological foundation of law. In the first part, the conception of philosophy adopted by Kaufmann, initial characteristics of law — of reality which is the subject of analysis, as well as, the requirements for proper philosophical explanation of law posed by Kaufmann are introduced. In the second, Kaufmann's reconstruction of the process of the realisation of law is presented. Next, the conception of analogy which Kaufmann uses when explaining law is analyzed. In the fourth part, Kaufmann's conception of ontological foundations of law is discussed. A critical analysis is carried out in which I demonstrate that the theory of the ontological foundation of law proposed by Kaufmann and the concept of a person included in it do not allow a satisfac¬tory explanation of the phenomenon of "legal lawlessness" and lead to a number of difficulties in the philosophical explanation of law. Finally, the perspectives of a proper formulation of the issue of the ontological foundations of law are drafted in the context of the analyzed theory. My interest is centered on the conception of philosophy adopted by Kaufmann, according to which the existence of the reality is inferred on the basis of a certain configuration of the content of consciousness, whereas at the point of departure of philosophy of law, the data to be explained is a certain process, which is, basically, a process of cognition, while the reality appears only as a condition for the possibility of the occurrence of the process. I wish to argue that the difficulties which appear in the explanation of law are a consequence of the assumed fundamental philosophical solu¬tions, which seem to be characteristic, though usually not assumed explicitly, in philoso¬phy and theory of law dominant at present in continental Europe. Thereby, I wish to show the significance of ontological and epistemological solutions to the possibility of a proper formulation of the problems posed by philosophy and theory of law. Kaufmann proclaims himself in favour of a philosophy which poses questions about the ultimate foundations of understanding of the reality. In epistemology, he assumes that answers to the questions "What is reality like?" and ultimately "What is real?" are inferred on the basis of uniformity of a cognitive acts of different subjects. Cognition of the reality is accomplished exclusively through the content of conceptual material. The two fundamental questions posed by philosophy of law are "What is just law?" and "How is the just law enacted?" The latter is a question about the process of achieving a solution to a concrete case. Since, in Kaufmann's opinion, law does not exist apart from the process of its realisation, an answer to the question about the manner of realisation of law is of fundamental significance to answering the question: "What is law?" and to the explanation of the question about the ontological grounding of law, which is, as well, the foundation of justice. The proper solution has to take into account the moment of "non-dispositive" content of law; its positiveness understood as the reality and, at the same time, it has to point to the principles of the historical transformation of the content. Law, in the primary meaning of the word, always pertains, in Kaufmann's opinion, to a concrete case. A legal norm is solely the "possibility" of law and the entirely real law is ipsa res iusta, that which is just in a given situation. Determination of what is just takes place in a certain type of process performed by a judge (or by man confronted with a choice). Kaufmann aims to reconstruct this process. A question about the ontological foundation of law is a question about the ontological foundations of this process. In the analyzed theory it is formulated as a question about the transcendental conditions, necessary for the possibility of the occurrence of the process: how the reality should be thought to make possible the reconstructed process of the realisation of law. Kaufmann rejects the model for finding a concrete solution based on simple subsump¬tion and proposes a model in which concrete law ensues, based on inference by analogy, through the process of "bringing to conformity" that which is normative with that which is factual. Kaufmann distinguishes three levels in the process of the realisation of law. On the highest level, there are the fundamental legal principles, on the second legal norms, on the third — concrete solutions. The fundamental principles of law are general inasmuch as they cannot be "applied" directly to concrete conditions of life, however, they play an important part in establishing norms. A judge encounters a concrete situation and a system of legal norms. A life situation and norms are situated on inherently different levels of factuality and normativeness. In order to acquire a definite law both a norm (system of norms) and a life situation (Lebenssachverhalt) should undergo a kind of "treatment" which would allow a mutual conformity to be brought to them. Legal norms and definite conditions of life come together in the process of analogical inference in which the "factual state" ("Tatbestand") — which represents a norm, and in the "state of things" ("Sachverhalt") — which represents a specific situation are constructed. A "factual state" is a sense interpreted from a norm with respect to specific conditions of life. The "state of things" is a sense constructed on the basis of concrete conditions of life with respect to norms (system of norms). Legal norms and concrete conditions of life meet in one common sense established during the process of realisation of law. Mutatis mutandis the same refers to the process of composition of legal norms: as the acquisition of concrete law consists in a mutual "synchronization" of norms and concrete conditions of life, so acquisition of legal norms consists of bringing to conformity fundamental principles and possible conditions of life. According to Kaufmann, both of these processes are based on inference through analogy. As this inference is the heart of these processes it is simultaneously a foundation finding just law and justice. How does Kaufmann understand such an inference? As the basis for all justice he assumes a specifically interpreted distributive justice grounded on proportionality. Equality of relations is required between life conditions and their normative qualification. Concrete conditions of life are ascribed normative qualification not through simple application of a general norm. More likely, when we look for a solution we go from one concrete normative qualified case to another, through already known "applications" of norms to a new "application". The relation between life conditions and their normative qualifica¬tion has to be proportional to other, earlier or possible (thought of) assignments of that which is factual to that which is normative. Law as a whole does not consist of a set of norms, but only of a unity of relations. Since law is a, based on proportion, relative unity of a norm and conditions of life, in order to explain law in philosophical manner, the question about ontological base of this unity has to be asked. What is it that makes the relation between a norm and conditions of life "non-dispositive"? What is the basis for such an interpretation of a norm and case which makes it possible to bring a norm and conditions of life into mutual "conformity"? This is a question about a third thing (next to norms and conditions of life), with respect to which the relative identity between a norm and conditions of life occurs, about the intermediary between that which is normative and that which is factual and which provides for the process of establishing of norms, as well as, finding solutions. It is the "sense" in which the idea of law or legal norm and conditions of life have to be identical to be brought to mutual "conformity". In Kaufmann's opinion such a sense is nothing else but the "nature of things" which determines the normative qualification of the reality. Since establishment of this "sense" appears to be "non-dispositive" and controlled inter-subjectively (namely, other subjects will reach a similar result) so, in conformity with the convergent concept of truth, the "nature of things" must be assigned a certain ontological status. According to Kaufmann this is a real relation which occurs between being and obligation, between the conditions of life and normative quality. However, it should be underlined that from the point of view of the analyzed system the "nature of things" is a correlate of constructed sense, a result of a construction which is based on the principle of consistent understanding of senses ("non-normative" and "normative") and is not a reality which is transcendent against the arrangement of senses. In Kaufmann's theory, inference from analogy appears to be a process of reshaping the concepts (senses) governed by tendency to understand the contents appearing in relations between that which is factual and that which is normative in a consistent way. The analogical structure of language (concepts) and recognition of being as composed of an essence and existence is an indispensable requirement for the possibility of the realisation of law, based on specifically understood inference from analogy. It is necessary to assume a moment of existence without content which ensures unity of cognition. Existence emerges thus as a condition of the possibility of cognition. According to Kaufmann, the "nature of things" is the heart of inference through analogy and the basis for establishment of finding of law. Inference from the "state of things" to a norm or from a norm to the "state of things" always means inference through the "nature of things". The "nature of things" is the proper medium of objective legal sense sought in every cognition of law. In Kaufmann's view, the question whether the "nature of things" is ultima ratio of interpretation of law or is only a means of supplement gaps in law or whether it is one of the sources of law, is posed wrongly. The "nature of things" serves neither to supplement the gaps nor is it a source of law as, for example, a legal norm may be. It is a certain kind of "catalyst" necessary in every act of making law and solving a concrete case. Owing to "nature of things" it is possible to bring to a mutual conformity the idea of law and possible conditions of life or legal norms and concrete conditions of life. In Kaufmann's conception the "nature of things" is not yet the ultimate basis for understanding the "non-dispositiveness" of law. The relation between obligation and being is determined in the process of the realisation of law. Both the process itself and that which is transformed in this process are given. A question about the ontological bases of "material" contents undergoing "treatment" in the process of the realisation of law and about being which is the basis of regularity of the occurrence of the process arises. Only this will allow an explanation that the result of the process is not optional. Thus, a question about reality to which law refers and about the subject realising the law has to be formed. To this, Kaufmann gives the following answer: that which is missing is man but not "empirical man" but man as a "person". A "person" understood as a set of relations between man and other people and things. A "person" is the intermediary between those things which are different — norm and case are brought to conformity. A "person" is that which is given and permanent in the process of the realisation of law. It determines the content of law, is "subject" of law; this aspect is described by Kaufmann as the "what" of the process of realisation of law. A "person" consists of precisely just these relations which undergo "treatment" in the process. On the other hand, a "person" is "a place" in which the processes of realisation of law occur, it is the "how" of normative discourse, a "person" is that which determines the procedure of the process, being "outside" of it. This aspect of a "person" is connected with the formal moment of law. A "person" being, at the same time, the "how" and the "what" of the process of the realisation of law, is also, to put it differently, a structural unity of relation and that which constitutes this relation (unity of relatio and relata). According to this approach a "person" is neither an object nor a subject. It exists only "in between". It is not substance. Law is the relation between being and obligation. That which is obligatory is connected with that which is general. That which is general does not exist on its own, it is not completely real. Accordingly, a "person" as such is also not real. It is relational, dynamic and historical. A "person" is not a state but an event. In Kaufmann's opinion, such a concept of a "person" helps to avoid the difficulties connected with the fungibility of law in classical legal positivism. A "person" is that which is given, which is not at free disposal and secures the moment of "non-dispositiveness" of law. Kaufmann concludes: "The idea (»nature«) of law is either the idea of a personal man or is nothing". Theory points at the structure of realising law and explains the process of adoption of general legal norms for a concrete situation. The analysis has shown however, that in this theory a satisfactory answer to the question about the ultimate foundations of law is not given. It seems that in the analyzed theory the understanding of human being takes place through understanding of law. What is good for man as a "person", what is just, what a "person" deserves may be determined only against the existing system of law. A "per¬son" adopted as a basis of law is the reality postulated in the analysis of the process of the realisation of law. It is a condition of possibility of this process ( explaining, on one hand, its unity and, on the other hand, the non-dispositive moments stated in this process). A "person" in the discussed theory is entirely defined by the structure of law, it can be nothing more than that which is given in law, what law refers to, what law is about. Being, which is a "person", is constituted by relations between people and objects, the relations which are based on fundamental links between norms and conditions of life established in a process of bringing them to conformity. It has to be assumed that man as a "person" is a subject of law only as far as realising law "treats" given senses according to their current configuration. The system of law is a starting point and it describes in content what man is as a "person". Moreover, being a "person" is the condition for entering legal relations. Consistently, Kaufmann writes that "empirical man" is not the subject of law, man is not "out of nature" a "person". People become "persons" due to the fact that they acknowledge each other as "persons" — acknowledging, at the same time, law. This acknowledgement is a con¬dition of existence, of the possibility of the occurrence of process of realisation of law and of constituting legal relations which ultimately constitute a "person". Kaufmann assumes, that law tends towards a moral aim: it may and must create an external freedom, without which the internal freedom to fulfil moral obligations cannot develop. However, this postulate is not based on the necessary structure of human being. From the point of view of his system, it is nothing more than only a condition for the possibility of the occurrence of the process of the realisation of law — lack of freedom would destroy the "how" of this process. Thus, the postulate to protect the freedom of personal acts has to be interpreted, in accordance with the analyzed theory, as a postulate, the fulfilment of which aims ultimately at the accomplishment of the very same process of realisation of law itself and not the realisation of a given man. Kaufmann considers a "person" to be an element which unites the system of law as a whole. Law is a structure of relations, which are interdependent and inter-contingent. Consequently, a "person" which is to form the ontological basis of law has to be entity consisting of all relations. Being also the "how" of the process of realisation of law, if a "person" is to warrant its unity, it has to be a common source for all procedures. Hence, a single "person" would constitute a subject of law. Man appears to be only a moment of a certain entirety, realisation of which should be an aim of his actions. Law, creating a "person" as an object and subject of law becomes a primary entity. In the analyzed theory, the basis for determination of aims which law sets to man is not the allocation of man-subject to something which improves him but rather, such relation is only just constituted by law. A question appears, why should aims set in law also be the aims of "empirical man"? Why is this "empirical man" to be punished in the name of a "person" understood in such a way? If, however, it is assumed that what is man is determined by a system which is superior to him, then man has to be understood only as a part of a whole and there are no grounds to prohibit istrumental treatment of man and so the road to all aspects of totalitarianism might be opened. A problem of the application of created theory to the reality arises, the reality which the theory pretends to explain. Ultimately in his theory Kaufmann does not give any systemic grounds for a radical questioning of the validity of any legal norms. Every new norm becomes an equal part of system of norms. It is only its interpretation and application to given conditions of life that may be disputable, however, this refers to all norms without exception. Cohesive inter-pretation of norms and applications is necessary and sufficient for the acquisition of just law. New norms have to be interpreted in the light of others, correspondingly, the other norms require reinterpretation in the light of the new ones. Contradiction in interpretation of a norm does not form a basis for questioning norms but may serve only to question the manner of their interpretation (understanding). Therefore, no grounds exist to assume any legal norm as criminal or unjust, and in consequence, to question any consistently realised system based on formally, properly established norms, as "legal lawlessness". As law and a "person" do not exist without the process of realisation of law, the role of legal safety becomes crucial as the condition for the possibility of the occurrence of the process of realisation of law. Denying legal safety would be tantamount to negation of law in general (also of moral law) as negation of safety takes away, at the same time, the basis for occurrence of the process of realisation of law. Moreover, any lack of legal safety would also mean lack of a basis for the existence of man as a "person". Kaufmann's thesis, that civil disobedience is legalized only when it has a chance to lead to success, consistent with his concept of the foundations of law, seems to point directly to conclusions which deny the facts taken under consideration and doubtlessly Kaufmann's own intentions, since it would have to be assumed that accordingly there are no grounds to question a legal system in force based on violence which secures its operation. Force finally seems to determine which one of the mutually irreconcilable normative systems constitute law and which does not. A legitimate position is one which leads to success, it is the weaker system which is negated. If so, then basically violent imposition of law is not an act directed against the law in force but, to the contrary, realisation of law. In the context of the new system the former system of law may be talked about as unjust solely in the sense of being incapable of being consistently united with the new. However, at the base, ultimately, lies force which reaffirms differences and excludes from the process of realisation of law certain norms and their interpretations. Kaufmann was aiming at grounding of that which is "non-dispositive" in a certain given framework of interpretation. Nevertheless, he does not provide foundations for the understanding of phenomena, which he undertakes to explain at a point of departure. Instead of explaining them the theory negates the possibility of their existence. The reality postulated in regard to "non-dispositive" moments of the reconstructed process of acquiring law consist of a specifically understood "person", which appears in Kaufmann's conceptions as a condition of the possibility of the realisation of law. According to this approach understanding of a "person" may be only a function of law. To understand "legal lawlessness" and foundations of justice it is necessary to look for such theory of law in which understanding of man as a "person" and being is not a function of understanding of law (in which a "person" is not only a condition for possibility of reconstructed process of realisation of law; for possibility of cognition processes). It seems necessary to start from theory of being and a "person" based on broader experience than the one assumed by Kaufmann and reconstruct the ontological foundations of the process of realisation of law only in such perspective. Kaufmann points out that that to which law refers is ipsa res iusta a concrete relation of man to other people and things. This relation, in his theory, appears to be basically only just constituted by law (normative senses "applied" to conditions of life). Therefore, understanding the relation between a given man and other people and things which constitute the aim of his actions, that is understanding of good, is enacted against the background of constitution of senses; constitution which is a result of a process aiming towards consistent understanding of particular contents (of nor¬mative and non-normative senses). "Being" is secondary towards constructed senses it is only their correlate. The primary relation consists of relation of a man to law (system of norms), while the secondary relation is one of man to something which is the aim of his action (relation between man and good). Considering such approach it is difficult to envision a satisfying answer to the fundamental question: why does law put concrete man under any obligation to obey it? The source of this problem can be seen in reduction of the base for understanding good to content of obligation formulated in auto-reflection. Such reduction seems to be a consequence of Kaufmann's adoption of "convergent concept of truth" and in con¬sequence his recognition of indirect, essentialistic grasp of reality formulated in concepts as the basic and only foundation of theory of being and of law. In view of such an approach, analogy of law, concepts and being is the condition for the possibility of the process of transformation of senses which aims at consistent interpretation of all law. Existence is postulated with respect to the possibility of unity of experience and cognition. However, also a different approach to understanding of the problem of being and good is possible. In spontaneous cognition being is affirmed, first of all, not as a certain, non-contradictory, determined content, but as something existing. Together with a cer¬tain content (passed indirectly through notions) existence of being is co-given. The basis for unity of being is not formed by the consistence of content, as it is in the case of the theories departing from the analysis of cognition processes, but by an act of existence realising content (essence). Such an approach makes it also possible to go beyond the convergent concept of truth. It is worth mentioning that allocation of an agent to good is realised not only by the content of duty. A statement that something is good is primary with respect to determination of this good in content. The recognised good always bears some content, however, there are no reasons to base the concept of good exclusively on indirect, formulated in concepts cognition. As primary, can be adopted the relation of man to good and not of man to law. Determination in content appears to be only an articulation of aspectual cognition of being, as an object of action. In such a case the basis for relative unity of norm and conditions of life is not the "nature of things" understood as correlate of sense but it is relation to good based on internal constitution of man as potential, not self-sufficient being. It does not mean, that the moments of the process of realisation of law singled out by Kaufmann are not important to determination of what is just. He, quite rightly, points to significant role played by norms in the evaluation of concrete situations, in man's search for closer specification in content of good innate to him. The structure of process of determining law for a concrete situation, to a great degree corresponds to the processes of determining law which take place not only in the legal sciences. Kaufmann's analyses of the process of realisation of law show the complexity of the structure of these processes and point towards important moments allowing a better understanding of law and man. Nevertheless, these analyses cannot be a basis for construction of philosophical theory of law, theory which hopes to point out the ultimate, ontological foundations for understanding law. Kaufmann's results may become fully valid only in a more general perspective including broader experience at the point of departure. (shrink)

ABSTRACT In this paper we present a new semantic approach for propositional linear temporal logic with discrete time, strongly based in the well-order of IN (the set of natural numbers). We consider temporal connectives which express precedence, posteriority and simultaneity, and they provide a family of expressively complete temporal logics. The selection of the new semantics and connectives used in this work was principally to obtain a suitable executable temporal logic, which can be used for the specification and control (...) of process behaviour in discrete time in a similar way to thai presented by D. Gabbay in [GAB 89], Our new approach has two advantages: firstly, the connectives are defined intuitively so that they have interpretations which relate to properties of interest in real systems; secondly, it provides a new semantics that facilitates simpler proofs of many valid formulas and metatheorems. To confirm this second advantage, we use our semantics to give a formal proof of the Separation Theorem for one of these logics (specifically LN3). The great interest of this Separation Theorem for the executable temporal logic is emphasised by D. Gabbay in [GAB 89], [GAB 88]. (shrink)