In most accounts of realization of computational processes by physical mechanisms, it is presupposed that there is one-to-one correspondence between the causally active states of the physical process and the states of the computation. Yet such proposals either stipulate that only one model of computation is implemented, or they do not reflect upon the variety of models that could be implemented physically. In this paper, I claim that mechanistic accounts of computation should allow for a broad variation (...) of models of computation. In particular, some non-standard models should not be excluded a priori. The relationship between mathematical models of computation and mechanistically adequate models is studied in more detail. (shrink)

The Computational Theory of Mind (CTM) holds that cognitive processes are essentially computational, and hence computation provides the scientific key to explaining mentality. The Representational Theory of Mind (RTM) holds that representational content is the key feature in distinguishing mental from non-mental systems. I argue that there is a deep incompatibility between these two theoretical frameworks, and that the acceptance of CTM provides strong grounds for rejecting RTM. The focal point of the incompatibility is the fact that representational content (...) is extrinsic to formal procedures as such, and the intended interpretation of syntax makes no difference to the execution of an algorithm. So the unique 'content' postulated by RTM is superfluous to the formal procedures of CTM. And once these procedures are implemented in a physical mechanism, it is exclusively the causal properties of the physical mechanism that are responsible for all aspects of the system's behaviour. So once again, postulated content is rendered superfluous. To the extent that semantic content may appear to play a role in behaviour, it must be syntactically encoded within the system, and just as in a standard computational artefact, so too with the human mind/brain - it's pure syntax all the way down to the level of physical implementation. Hence 'content' is at most a convenient meta-level gloss, projected from the outside by human theorists, which itself can play no role in cognitive processing. (shrink)

Recently, Horsman et al. have proposed a new framework, Abstraction/Representation theory, for understanding and evaluating claims about unconventional or non-standard computation. Among its attractive features, the theory in particular implies a novel account of what is means to be a computer. After expounding on this account, I compare it with other accounts of concrete computation, finding that it does not quite fit in the standard categorization: while it is most similar to some semantic accounts, it is (...) not itself a semantic account. Then I evaluate it according to the six desiderata for accounts of concrete computation proposed by Piccinini. Finding that it does not clearly satisfy some of them, I propose a modification, which I call Agential AR theory, that does, yielding an account that could be a serious competitor to other leading account of concrete computation. (shrink)

This paper considers non-standard analysis and a recently introduced computational methodology based on the notion of ①. The latter approach was developed with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework and in all the situations requiring these notions. Non-standard analysis is a classical purely symbolic technique that works with ultrafilters, external and internal sets, standard and non-standard numbers, etc. In its turn, the ①-based methodology does not (...) use any of these notions and proposes a more physical treatment of mathematical objects separating the objects from tools used to study them. It both offers a possibility to create new numerical methods using infinities and infinitesimals in floating-point computations and allows one to study certain mathematical objects dealing with infinity more accurately than it is done traditionally. In these notes, we explain that even though both methodologies deal with infinities and infinitesimals, they are independent and represent two different philosophies of Mathematics that are not in a conflict. It is proved that texts :539–555, 2017; Gutman and Kutateladze in Sib Math J 49:835–841, 2008; Kutateladze in J Appl Ind Math 5:73–75, 2011) asserting that the ①-based methodology is a part of non-standard analysis unfortunately contain several logical fallacies. Their attempt to show that the ①-based methodology can be formalized within non-standard analysis is similar to trying to show that constructivism can be reduced to the traditional Mathematics. (shrink)

Internal sets and the Boolean algebras of the collection of the internal sets are of central importance in non-standard analysis. Boolean algebras are the algebraization of propositional logic while the logic applied in non-standard analysis (in non-standard stochastics) is the first order or the higher order logic (type theory). We present here a first order logic algebraization for the collection of internal sets rather than the Boolean one. Further, we define an unusual probability on this algebraization.

We give an elementary introduction to non-standard analysis and its applications to the theory of stochastic processes. This is based on a joint book with J. E. Fenstad, R. Høegh-Krohn and T. Lindstrøm. In particular we give a discussion of an hyperfinite theory of Dirichlet forms with applications to the study of the Hamiltonian for a quantum mechanical particle in the potential created by a polymer. We also discuss new results on the existence of attractive polymer measures in dimension (...) d ≤ 5, with applications to the (φ 1 2 φ 2 2 )d-mode1 of interacting quantum fields. (shrink)

Currently, there is widespread skepticism that higher cognitive processes, given their apparent flexibility and globality, could be carried out by specialized computational devices, or modules. This skepticism is largely due to Fodor’s influential definition of modularity. From the rather flexible catalogue of possible modular features that Fodor originally proposed has emerged a widely held notion of modules as rigid, informationally encapsulated devices that accept highly local inputs and whose opera- tions are insensitive to context. It is a mistake, however, to (...) equate such features with computational devices in general and therefore to assume, as Fodor does, that higher cognitive processes must be non-computational. Of the many possible non-Fodorean architectures, one is explored here that offers possible solutions to computational problems faced by conventional modular systems: an ‘enzymatic’ architecture. Enzymes are computational devices that use lock-and-key template matching to iden- tify relevant information (substrates), which is then operated upon and returned to a common pool for possible processing by other devices. Highly specialized enzymes can operate together in a common pool of information that is not pre-sorted by information type. Moreover, enzymes can use molecular ‘tags’ to regulate the operations of other devices and to change how particular substrates are construed and operated upon, allowing for highly interactive, context-specific processing. This model shows how specialized, modular processing can occur in an open system, and suggests that skepti- cism about modularity may largely be due to failure to consider alternatives to the standard model. (shrink)

278 non-freshman university students taking a l2-week critical thinking course in a large single-section class, with computer-assisted guided practice as a replacement for small-group discussion, and all testing in machine-scored multiple-choice format, improved their critical thinking skills, as measured by the California Critical Thinking Skills Test, by half a standard deviation, a moderate improvement. The improvement was more than that reported with a traditional format without computer-assisted instruction, but less than that reported with a format using both computer-assisted instruction (...) and essay-type assignments. Further studies are needed to test hypotheses suggested by these results. (shrink)

The computer engineers who refer to the education of computers do not have a definite idea of education and do not bother to justify the fuzzy ones to which they allude. Hence, they logically cannot specify the features a computer must have in order to be educable. This paper puts forth a non-standard, but not arbitrary, concept of education that determines such traits. The proposed concept is derived from the idea of education embedded in modern standard-English discourse. Because (...) the standard concept entails that an educable entity must be capable of consciousness and voluntary action, it cannot apply to computers. If, therefore, one is to have an idea of educable computers, one must drop the feature of consciousness and omit or modify that of voluntariness. The advanced concept leaves out consciousness, alters the ordinary notion of voluntariness, but keeps in tact the other criteria of the standard idea. Thereby, it provides continuity between those who talk about education in modern ordinary English and those who talk about it in the world of artificial intelligence. (shrink)

ObjectiveTo examine measurement agreement between a vocabulary test that is administered in the standardized manner and a version that is administered with a brain-computer interface.MethodThe sample was comprised of 21 participants, ages 9–27, mean age 16.7 years, 61.9% male, including 10 with congenital spastic cerebral palsy, and 11 comparison peers. Participants completed both standard and BCI-facilitated alternate versions of the Peabody Picture Vocabulary Test - 4. The BCI-facilitated PPVT-4 uses items identical to the unmodified PPVT-4, but each quadrant forced-choice (...) item is presented on a computer screen for use with the BCI.ResultsMeasurement agreement between instruments was excellent, including an intra-class correlation coefficient of 0.98, and Bland-Altman plots and tests indicating adequate limits of agreement and no systematic test version bias. The mean standard score difference between test versions was 2.0 points.ConclusionThese results demonstrate that BCI-facilitated quadrant forced-choice vocabulary testing has the potential to measure aspects of language without requiring any overt physical or communicative response. Thus, it may be possible to identify the language capabilities and needs of many individuals who have not had access to standardized clinical and research instruments. (shrink)

Computational properties, it is standardly assumed, are to be sharply distinguished from semantic properties. Specifically, while it is standardly assumed that the semantic properties of a cognitive system are externally or non-individualistically individuated, computational properties are supposed to be individualistic and internal. Yet some philosophers (e.g., Tyler Burge) argue that content impacts computation, and further, that environmental factors impact computation. Oron Shagrir has recently argued for these theses in a novel way, and gave them novel interpretations. In this (...) paper I present a conception of computation in cognitive science that takes Shagrir's conception as its starting point, but further develops it in various directions and strengthens it. I argue that the explanatory role of computational properties emerges from the idea that syntactical properties and the relevant external factors presented by cognitive systems compose wide computational properties. I also elaborate upon the notion of content that is in play, and argue that it is contents of the kind that are ascribed by transparent interpretations of content ascriptions that impact computation. This fact enables the thesis that external factors impact computation to rebuff the challenge which concerns the claim that psychology must be individualistic. (shrink)

Emotional facial expressions can inform researchers about an individual's emotional state. Recent technological advances open up new avenues to automatic Facial Expression Recognition (FER). Based on machine learning, such technology can tremendously increase the amount of processed data. FER is now easily accessible and has been validated for the classification of standardized prototypical facial expressions. However, applicability to more naturalistic facial expressions still remains uncertain. Hence, we test and compare performance of three different FER systems (Azure Face API, Microsoft; Face++, (...) Megvii Technology; FaceReader, Noldus Information Technology) with human emotion recognition (A) for standardized posed facial expressions (from prototypical inventories) and (B) for non-standardized acted facial expressions (extracted from emotional movie scenes). For the standardized images, all three systems classify basic emotions accurately (FaceReader is most accurate) and they are mostly on par with human raters. For the non-standardized stimuli, performance drops remarkably for all three systems, but Azure still performs similarly to humans. In addition, all systems and humans alike tend to misclassify some of the non-standardized emotional facial expressions as neutral. In sum, emotion recognition by automated facial expression recognition can be an attractive alternative to human emotion recognition for standardized and non-standardized emotional facial expressions. However, we also found limitations in accuracy for specific facial expressions; clearly there is need for thorough empirical evaluation to guide future developments in computer vision of emotional facial expressions. (shrink)

In the fifth version of our reply article [26] to Imamura's critique, we recall that Neutrosophic Non-Standard Logic was never used by the neutrosophic community in any application, that the quarter-century old (1995-1998) neutrosophic operators criticized by Imamura were never used as they were improved soon after, but omits to talk about their development, and that in real-world applications we need to convert/approximate the hyperreals, monads and bi-nads of Non-Standard Analysis to tiny intervals with the desired precision; otherwise (...) they would be inapplicable. We pointed out several errors and false statements by Imamura [21] regarding the inf/sup of nonstandard subsets, also Imamura's "rigorous definition of neutrosophic logic" is incorrect, as is his definition of nonstandard unit interval, and we showed that there is no total order in Neutrosophic Computing and Machine Learning , Vol. 23, 2022 Florentin Smarandache, Definición mejorada de la lógica neutrosófica no estándar e introducción a los hiperreales neutrosóficos (Quinta versión) 2 the set of hyperreals (due to the recently introduced Neutrosophic Hyperreals which are indeterminate), so the Transfer Principle from R to R* is questionable. After his critique, several reply posts on non-standard theoretical neutrosophy followed in 2018-2022. As such, I extended the Nonstandard Analysis by adding the right-closed left monad, the left-closed right monad, the punctured binad (which we introduced in 1998), and the nonpunctured binad - all in order to close the newly extended nonstandard space (R*) under nonstandard addition, nonstandard subtraction, nonstandard multiplication, nonstandard division, and nonstandard power operations [23, 24]. Improved definitions of the Nonstandard Unitary Interval and Nonstandard Neutrosophic Logic are presented, along with Nonstandard Neutrosophic Operators. (shrink)

This paper examines from a special perspective the problem of methodological limita­tions of the computational approach in the philosophy of mind and empirical sciences. The main goal is to consistently substantiate the dependence of philosophical “metaphori­cal dictionaries” on advances in the field of computer science, historical contexts of epis­temology, formal and methodological limitations of algorithmic and computational proce­dures. The key idea is that despite the success of computational models in empirical re­search, their conceptual level does not allow us to correctly (...) formulate the question of the ontology of consciousness. Computationalism in philosophical theories of con­sciousness is presented as a practice of word usage, which posits systems of consistent descriptions of the information properties of consciousness and cognitive processes within the framework of certain methodological rules. The limitations of the computa­tional approach are associated with the lack of a scientific theory of subjectivity, the fun­damental irreducibility of external properties of consciousness to internal states, and fun­damental restrictions on the completeness and consistency of computer mathematics. A classification of several anti-computational programs has been carried out. The article discusses various limitations of computational approaches, such as: the complexity of for­malizing nonlinear and hidden processes, the dependence of emotions and intuition on the situational context and individual differences, the difficulty of predicting the emerg­ing properties of autonomous and autopoietic systems, and the limitations associated with non-standard computational processes of quantum and dynamic phenomena. A special role is given to the problem of set-theoretic reductive realism within the framework of mathe­matical structuralism and some aspects of p-adic number systems as a possible alternative to a “universal language” for the computational philosophy of consciousness. (shrink)

It is conventionally understood that computers play a rather limited role in theoretical mathematics. While computation is indispensable in applied mathematics and the theory of computing and algorithms is rich and thriving, one does not, even today, expect to find computers in theoretical mathematics settings beyond the theory of computing. Where computers are used, by those studying combinatorics , algebra, number theory, or dynamical systems, the computer most often assumes the role of an automated and speedy theoretician, performing manipulations (...) and checking cases in a way assumed to be possible for human theoreticians, if only they had the time, the memory, and the precision. Automated proofs have become standard tools in mathematical logic, and it is often expected that proofs be published in a computer-checkable format. It is not surprising, then, that most philosophical work on computers in theoretical mathematics has been on computers' roles as supplementary mathematicians. Donald MacKenzie's 2001 book Mechanizing Proof demonstrates the rich potential for social and historical studies to complement the substantial analytic debate in this area of philosophy. But what of computers in theoretical mathematics behaving as computers, and not as mere mechanized mathematicians? Very little role is commonly assumed for computers working as supplements to mathematicians, rather than as supplementary mathematicians themselves. Accordingly, very little philosophy has attempted to grapple with theoretical mathematics in which computers play an essential but essentially non-theoretical role. My presentation will draw on work I conducted as a researcher in harmonic analysis on fractals at Cornell University. I will analyze the explicit and implicit conceptual apparatus employed in my and my fellow researchers' use of computers in the theoretical study of second order differential equations, such as those for sound and heat flow, on various fractal analogues of the Sierpinski gasket. Such gaskets are easy to visualize in very crude approximation in a low number of dimensions. As one increases the complexity of the gasket or the refinement of one's analysis, visualization and precise computation become impossible, and soon computers are unable to produce even approximate data to model differential equations in these situations. We thus had to carefully choose analytic approaches and methods to make our theoretical mathematics amenable to computer simulation. In my case, studying the transformation of the gaskets as they are expanded into increasingly high dimensions, computer simulation eventually required that the problem be reimagined entirely in terms of interlinked systems of parameters. This computer-approximation-driven theoretical orientation shaped my mathematical intuitions toward the problem and guided my fellow researchers and me in both theoretical and computational directions. We discovered both that computer approximation could be incredibly powerful as an aid to intuition, and that it can be incredibly difficult to transfer computer-oriented mathematics back into the purely theoretical standards of our area of specialty. I will address the philosophical implications of computer-driven theoretical mathematics, asking how computer experiments can shape both the content and standards of theoretical sciences. (shrink)

This dissertation is a contribution to formal and computational philosophy. -/- In the first part, we show that by exploiting the parallels between large, yet finite lotteries on the one hand and countably infinite lotteries on the other, we gain insights in the foundations of probability theory as well as in epistemology. Case 1: Infinite lotteries. We discuss how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. The solution boils down to the introduction (...) of infinitesimal probability values, which can be achieved using non-standard analysis. Our solution can be generalized to uncountable sample spaces, giving rise to a Non-Archimedean Probability (NAP) theory. Case 2: Large but finite lotteries. We propose application of the language of relative analysis (a type of non-standard analysis) to formulate a new model for rational belief, called Stratified Belief. This contextualist model seems well-suited to deal with a concept of beliefs based on probabilities ‘sufficiently close to unity’. -/- The second part presents a case study in social epistemology. We model a group of agents who update their opinions by averaging the opinions of other agents. Our main goal is to calculate the probability for an agent to end up in an inconsistent belief state due to updating. To that end, an analytical expression is given and evaluated numerically, both exactly and using statistical sampling. The probability of ending up in an inconsistent belief state turns out to be always smaller than 2%. (shrink)

We present a logical framework that enables us to define a formal theory of computational trust in which this notion is analysed in terms of epistemic attitudes towards the possible objects of trust and in relation to existing evidence in favour of the trustworthiness of these objects. The framework is based on a quantified epistemic and justification logic featuring a non-standard handling of identities. Thus, the theory is able to account for the hyperintensional nature of computational trust. We present (...) a proof system and a frame semantics for the logic, we prove soundness and completeness results and we introduce the syntactical machinery required to define a theory of trust. (shrink)

The study sets out to develop an online course for medical professionals who are not native Arabic speakers. The present study relied on a questionnaire developed by reviewing relevant theoretical literature and prior research in order to apply descriptive and analytical methods to accomplish the study's aims. The researcher sent an online questionnaire to a large number of healthcare workers, including doctors, nurses, lab techs, and radiology technicians. The objective of this survey is to learn about the linguistic communication needs (...) of healthcare workers and to find out when Arabic is useful for communicating with patients and meeting quality standards in healthcare. The study compiled a list of 36 linguistic needs pertaining to various medical settings (e.g., emergency rooms, outpatient clinics, hypnosis rooms, labs, and radiology departments), developed an electronic program to teach Arabic to non-native speakers, and made several suggestions and recommendations. (shrink)

There is currently much interest in bringing together the tradition of categorial grammar, and especially the Lambek calculus, with the recent paradigm of linear logic to which it has strong ties. One active research area is designing non-commutative versions of linear logic (Abrusci, 1995; Retoré, 1993) which can be sensitive to word order while retaining the hypothetical reasoning capabilities of standard (commutative) linear logic (Dalrymple et al., 1995). Some connections between the Lambek calculus and computations in groups have long (...) been known (van Benthem, 1986) but no serious attempt has been made to base a theory of linguistic processing solely on group structure. This paper presents such a model, and demonstrates the connection between linguistic processing and the classical algebraic notions of non-commutative free group, conjugacy, and group presentations. A grammar in this model, or G-grammar is a collection of lexical expressions which are products of logical forms, phonological forms, and inverses of those. Phrasal descriptions are obtained by forming products of lexical expressions and by cancelling contiguous elements which are inverses of each other. A G-grammar provides a symmetrical specification of the relation between a logical form and a phonological string that is neutral between parsing and generation modes. We show how the G-grammar can be oriented for each of the modes by reformulating the lexical expressions as rewriting rules adapted to parsing or generation, which then have strong decidability properties (inherent reversibility). We give examples showing the value of conjugacy for handling long-distance movement and quantifier scoping both in parsing and generation. The paper argues that by moving from the free monoid over a vocabulary V (standard in formal language theory) to the free group over V, deep affinities between linguistic phenomena and classical algebra come to the surface, and that the consequences of tapping the mathematical connections thus established can be considerable. (shrink)

The present paper concerns the Wittgenstein ontology project: an attempt to create a Semantic Web representation of Ludwig Wittgenstein’s philosophy. The project has been in development since 2006, and its current state enables users to search for information about Wittgenstein-related documents and the documents themselves. However, the developers have much more ambitious goals: they attempt to provide a philosophical subject matter knowledge base that would comprise the claims and concepts formulated by the philosopher. The current knowledge representation technology is not (...) well-suited for this task, and a non-standard approach is required. The creators of the Wittgenstein ontology project are aware of this fact; recently, they have been discussing conceptual devices adjusting the technology to their needs. The main goal of this paper is to present examples of a representation of philosophical content that make use of both the devices already proposed and some new inventions. The represented content comes from the Tractatus Logico-Philosophicus; more specifically, its theses concerning the problems in philosophy of mathematics. (shrink)

The purpose of this communication is to announce some recent results on the computably enumerable sets. There are two disjoint sets of results; the first involves invariant classes and the second involves automorphisms of the computably enumerable sets. What these results have in common is that the guts of the proofs of these theorems uses a new form of definable coding for the computably enumerable sets.We will work in the structure of the computably enumerable sets. The language is just inclusion, (...) ⊆. This structure is called ε.All sets will be computably enumerable non-computable sets and all degrees will be computably enumerable and non-computable, unless otherwise noted. Our notation and definitions are standard and follow Soare [1987]; however we will warm up with some definitions and notation issues so the reader need not consult Soare [1987]. Some historical remarks follow in Section 2.1 and throughout Section 3.We will also consider the quotient structure ε modulo the ideal of finite sets, ε*. ε* is a definable quotient structure of ε since “Χ is finite” is definable in ε; “Χ is finite” iff all subsets of Χ are computable. We use A* to denote the equivalent class of A under the ideal of finite sets. (shrink)

BackgroundThe current paper follows up on the results of an exploratory quantitative analysis that compared the publication and citation records of men and women researchers affiliated with the Faculty of Computing and Engineering at Dublin City University in Ireland. Quantitative analysis of publications between 2013 and 2018 showed that women researchers had fewer publications, received fewer citations per person, and participated less often in international collaborations. Given the significance of publications for pursuing an academic career, we used qualitative methods to (...) understand these differences and explore factors that, according to women researchers, have contributed to this disparity.MethodsSixteen women researchers from DCU’s Faculty of Computing and Engineering were interviewed using a semi-structured questionnaire. Once interviews were transcribed and anonymised, they were coded by both authors in two rounds using an inductive approach.ResultsInterviewed women believed that their opportunities for research engagement and research funding, collaborations, publications and promotions are negatively impacted by gender roles, implicit gender biases, their own high professional standards, family responsibilities, nationality and negative perceptions of their expertise and accomplishments.ConclusionsOur study has found that women in DCU’s Faculty of Computing and Engineering face challenges that, according to those interviewed, negatively affect their engagement in various research activities, and, therefore, have contributed to their lower publication record. We suggest that while affirmative programmes aiming to correct disparities are necessary, they are more likely to improve organisational culture if they are implemented in parallel with bottom-up initiatives that engage all parties, including men researchers and non-academic partners, to inform and sensitise them about the significance of gender equity. (shrink)

I examine a major objection to the mechanistic view of concrete computation, stemming from an apparent tension between the abstract nature of computational explanation and the tenets of the mechanistic framework: while computational explanation is medium-independent, the mechanistic framework insists on the importance of providing some degree of structural detail about the systems target of the explanation. I show that a common reply to the objection, i.e. that mechanistic explanation of computational systems involves only weak structural constraints, is not (...) enough to save the standard mechanistic view of computation—it trivialises the appeal to mechanism, and thus makes the account collapse into a purely functional view. I claim, however, that the objection can be put to rest once the account is appropriately amended: computational individuation is indeed functional, while mechanistic explanation plays a role in accounting for computational implementation. Since individuation and implementation are crucial elements in a satisfying account of computation in physical systems, mechanism keeps its central importance in the theory of concrete computation. Finally, I argue that my version of the mechanistic view helps to provide a convincing reply to a powerful objection against non-semantic theories of concrete computation: the argument from the multiplicity of computations. (shrink)

The Language of Thought program has a suicidal edge. Jerry Fodor, of all people, has argued that although LOT will likely succeed in explaining modular processes, it will fail to explain the central system, a subsystem in the brain in which information from the different sense modalities is integrated, conscious deliberation occurs, and behavior is planned. A fundamental characteristic of the central system is that it is “informationally unencapsulated” -- its operations can draw from information from any cognitive domain. The (...) domain general nature of the central system is key to human reasoning; our ability to connect apparently unrelated concepts enables the creativity and flexibility of human thought, as does our ability to integrate material across sensory divides. The central system is the holy grail of cognitive science: understanding higher cognitive function is crucial to grasping how humans reach their highest intellectual achievements. But according to Fodor, the founding father of the LOT program and the related Computational Theory of Mind (CTM), the holy grail is out of reach: the central system is likely to be non-computational (Fodor 1983, 2000, 2008). Cognitive scientists working on higher cognitive function should abandon their efforts. Research should be limited to the modules, which for Fodor rest at the sensory periphery (2000).1 Cognitive scientists who work in the symbol processing tradition outside of philosophy would reject this pessimism, but ironically, within philosophy itself, this pessimistic streak has been very influential, most likely because it comes from the most well-known proponent of LOT and CTM. Indeed, pessimism about centrality has become assimilated into the mainstream conception of LOT. (Herein, I refer to a LOT that appeals to pessimism about centrality as the “standard LOT”). I imagine this makes the standard LOT unattractive to those philosophers with a more optimistic approach to what cognitive science can achieve.. (shrink)

Contemporary methods of computational cognitive modeling have recently been criticized by Addyman and French (2012) on the grounds that they have not kept up with developments in computer technology and human–computer interaction. They present a manifesto for change according to which, it is argued, modelers should devote more effort to making their models accessible, both to non-modelers (with an appropriate easy-to-use user interface) and modelers alike. We agree that models, like data, should be freely available according to the normal standards (...) of science, but caution against confusing implementations with specifications. Models may embody theories, but they generally also include implementation assumptions. Cognitive modeling methodology needs to be sensitive to this. We argue that specification, replication and experimentation are methodological approaches that can address this issue. (shrink)

Moral reasoning traditionally distinguishes two types of evil: moral and natural. The standard view is that ME is the product of human agency and so includes phenomena such as war, torture and psychological cruelty; that NE is the product of nonhuman agency, and so includes natural disasters such as earthquakes, floods, disease and famine; and finally, that more complex cases are appropriately analysed as a combination of ME and NE. Recently, as a result of developments in autonomous agents in (...) cyberspace, a new class of interesting and important examples of hybrid evil has come to light. In this paper, it is called artificial evil and a case is made for considering it to complement ME and NE to produce a more adequate taxonomy. By isolating the features that have led to the appearance of AE, cyberspace is characterised as a self-contained environment that forms the essential component in any foundation of the emerging field of Computer Ethics. It is argued that this goes some way towards providing a methodological explanation of why cyberspace is central to so many of CE’s concerns; and it is shown how notions of good and evil can be formulated in cyberspace. Of considerable interest is how the propensity for an agent’s action to be morally good or evil can be determined even in the absence of biologically sentient participants and thus allows artificial agents not only to perpetrate evil but conversely to ‘receive’ or ‘suffer from’ it. The thesis defended is that the notion of entropy structure, which encapsulates human value judgement concerning cyberspace in a formal mathematical definition, is sufficient to achieve this purpose and, moreover, that the concept of AE can be determined formally, by mathematical methods. A consequence of this approach is that the debate on whether CE should be considered unique, and hence developed as a Macroethics, may be viewed, constructively, in an alternative manner. The case is made that whilst CE issues are not uncontroversially unique, they are sufficiently novel to render inadequate the approach of standard Macroethics such as Utilitarianism and Deontologism and hence to prompt the search for a robust ethical theory that can deal with them successfully. The name Information Ethics is proposed for that theory. It is argued that the uniqueness of IE is justified by its being non-biologically biased and patient-oriented: IE is an Environmental Macroethics based on the concept of data entity rather than life. It follows that the novelty of CE issues such as AE can be appreciated properly because IE provides a new perspective. In light of the discussion provided in this paper, it is concluded that Computer Ethics is worthy of independent study because it requires its own application-specific knowledge and is capable of supporting a methodological foundation, Information Ethics. (shrink)

Permutative logic is a non-commutative conservative extension of linear logic suggested by some investigations on the topology of linear proofs. In order to syntactically reflect the fundamental topological structure of orientable surfaces with boundary, permutative sequents turn out to be shaped like q-permutations. Relaxation is the relation induced on q-permutations by the two structural rules divide and merge; a decision procedure for relaxation has been already provided by stressing some standard achievements in theory of permutations. In these pages, we (...) provide a parallel procedure in which the problem at issue is approached from the point of view afforded by geometry of 2-manifolds and solved by making specific surfaces interact. (shrink)

Moral reasoning traditionally distinguishes two types of evil:moral (ME) and natural (NE). The standard view is that ME is the product of human agency and so includes phenomena such as war,torture and psychological cruelty; that NE is the product of nonhuman agency, and so includes natural disasters such as earthquakes, floods, disease and famine; and finally, that more complex cases are appropriately analysed as a combination of ME and NE. Recently, as a result of developments in autonomous agents in (...) cyberspace, a new class of interesting and important examples of hybrid evil has come to light. In this paper, it is called artificial evil (AE) and a case is made for considering it to complement ME and NE to produce a more adequate taxonomy. By isolating the features that have led to the appearance of AE, cyberspace is characterised as a self-contained environment that forms the essential component in any foundation of the emerging field of Computer Ethics (CE). It is argued that this goes someway towards providing a methodological explanation of why cyberspace is central to so many of CE's concerns; and it is shown how notions of good and evil can be formulated in cyberspace. Of considerable interest is how the propensity for an agent's action to be morally good or evil can be determined even in the absence of biologically sentient participants and thus allows artificial agents not only to perpetrate evil (and fort that matter good) but conversely to `receive' or `suffer from' it. The thesis defended is that the notion of entropy structure, which encapsulates human value judgement concerning cyberspace in a formal mathematical definition, is sufficient to achieve this purpose and, moreover, that the concept of AE can be determined formally, by mathematical methods. A consequence of this approach is that the debate on whether CE should be considered unique, and hence developed as a Macroethics, may be viewed, constructively,in an alternative manner. The case is made that whilst CE issues are not uncontroversially unique, they are sufficiently novel to render inadequate the approach of standard Macroethics such as Utilitarianism and Deontologism and hence to prompt the search for a robust ethical theory that can deal with them successfully. The name Information Ethics (IE) is proposed for that theory. Itis argued that the uniqueness of IE is justified by its being non-biologically biased and patient-oriented: IE is an Environmental Macroethics based on the concept of data entity rather than life. It follows that the novelty of CE issues such as AE can be appreciated properly because IE provides a new perspective (though not vice versa). In light of the discussion provided in this paper, it is concluded that Computer Ethics is worthy of independent study because it requires its own application-specific knowledge and is capable of supporting a methodological foundation, Information Ethics. (shrink)

The noisy computation hypothesis of developmental dyslexia (DD) is particularly appealing because it can explain deficits across a variety of domains, such as temporal, auditory, phonological, visual and attentional processes. A key prediction is that noisy computations lead to more variable and less stable word representations. A way to test this hypothesis is through repetition of words, that is, when there is noise in the system, the neural signature of repeated stimuli should be more variable. The hypothesis was tested (...) in an functional magnetic resonance imaging experiment with dyslexic and typical readers by repeating words twelve times. Variability measures were computed both at the behavioral and neural levels. At the behavioral level, we compared the standard deviation of reaction time distributions of repeated words. At the neural level, in addition to standard univariate analyses and measures of intra-item variability, we also used multivariate pattern analyses (representational similarity and classification) to find out whether there was evidence for noisier representations in dyslexic readers compared to typical readers. Results showed that there were no significant differences between the two groups in any of the analyses despite robust results within each group (i.e., high representational similarity between repeated words, good classification of words vs. non-words). In summary, there was no evidence in favor of the idea that dyslexic readers would have noisier neural representations than typical readers. (shrink)

Augmentative and alternative communication brain-computer interface systems are intended to offer communication access to people with severe speech and physical impairment without requiring volitional movement. As the field moves toward clinical implementation of AAC-BCI systems, research involving participants with SSPI is essential. Research has demonstrated variability in AAC-BCI system performance across users, and mixed results for comparisons of performance for users with and without disabilities. The aims of this systematic review were to describe study, system, and participant characteristics reported in (...) BCI research, summarize the communication task performance of participants with disabilities using AAC-BCI systems, and explore any differences in performance for participants with and without disabilities. Electronic databases were searched in May, 2018, and March, 2021, identifying 6065 records, of which 73 met inclusion criteria. Non-experimental study designs were common and sample sizes were typically small, with approximately half of studies involving five or fewer participants with disabilities. There was considerable variability in participant characteristics, and in how those characteristics were reported. Over 60% of studies reported an average selection accuracy ≤70% for participants with disabilities in at least one tested condition. However, some studies excluded participants who did not reach a specific system performance criterion, and others did not state whether any participants were excluded based on performance. Twenty-nine studies included participants both with and without disabilities, but few reported statistical analyses comparing performance between the two groups. Results suggest that AAC-BCI systems show promise for supporting communication for people with SSPI, but they remain ineffective for some individuals. The lack of standards in reporting outcome measures makes it difficult to synthesize data across studies. Further research is needed to demonstrate efficacy of AAC-BCI systems for people who experience SSPI of varying etiologies and severity levels, and these individuals should be included in system design and testing. Consensus in terminology and consistent participant, protocol, and performance description will facilitate the exploration of user and system characteristics that positively or negatively affect AAC-BCI use, and support innovations that will make this technology more useful to a broader group of people.Clinical trial registrationhttps://www.crd.york.ac.uk/prospero/display_record.php?ID=CRD42018095345, PROSPERO: CRD42018095345. (shrink)

We conducted two eye-tracking experiments investigating the processing of the Mandarin reflexive ziji in order to tease apart structurally constrained accounts from standard cue-based accounts of memory retrieval. In both experiments, we tested whether structurally inaccessible distractors that fulfill the animacy requirement of ziji influence processing times at the reflexive. In Experiment 1, we manipulated animacy of the antecedent and a structurally inaccessible distractor intervening between the antecedent and the reflexive. In conditions where the accessible antecedent mismatched the animacy (...) cue, we found inhibitory interference whereas in antecedent-match conditions, no effect of the distractor was observed. In Experiment 2, we tested only antecedent-match configurations and manipulated locality of the reflexive-antecedent binding (Mandarin allows non-local binding). Participants were asked to hold three distractors (animate vs. inanimate nouns) in memory while reading the target sentence. We found slower reading times when animate distractors were held in memory (inhibitory interference). Moreover, we replicated the locality effect reported in previous studies. These results are incompatible with structure-based accounts. However, the cue-based ACT-R model of Lewis and Vasishth ( 2005 ) cannot explain the observed pattern either. We therefore extend the original ACT-R model and show how this model not only explains the data presented in this article, but is also able to account for previously unexplained patterns in the literature on reflexive processing. (shrink)

A version of the Church-Turing Thesis states that every effectively realizable physical system can be simulated by Turing Machines (‘Thesis P’). In this formulation the Thesis appears to be an empirical hypothesis, subject to physical falsification. We review the main approaches to computation beyond Turing definability (‘hypercomputation’): supertask, non-well-founded, analog, quantum, and retrocausal computation. The conclusions are that these models reduce to supertasks, i.e. infinite computation, and that even supertasks are no solution for recursive incomputability. This yields (...) that the realization of hypercomputing devices is implausible, and that Thesis P is not essentially different from the standard Church-Turing Thesis. (shrink)

Cellular automata (henceforth: CA) are discrete, abstract computational systems that have proved useful both as general models of complexity and as more specific representations of non-linear dynamics in a variety of scientific fields. Firstly, CA are (typically) spatially and temporally discrete: they are composed of a finite or denumerable set of homogeneous, simple units, the atoms or cells. At each time unit, the cells instantiate one of a finite set of states. They evolve in parallel at discrete time steps, following (...) state update functions or dynamical transition rules: the update of a cell state obtains by taking into account the states of cells in its local neighborhood (there are, therefore, no actions at a distance). Secondly, CA are abstract, as they can be specified in purely mathematical terms and implemented in physical structures. Thirdly, CA are computational systems: they can compute functions and solve algorithmic problems. Despite functioning in a different way from traditional, Turing machine-like devices, CA with suitable rules can emulate a universal Turing machine, and therefore compute, given Turing's Thesis, anything computable.... (shrink)

Multialgebras have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap structures are given. (...) Specifically, a formal study of swap structures for LFIs is developed, by adapting concepts of universal algebra to multialgebras in a suitable way. A decomposition theorem similar to Birkhoff’s representation theorem is obtained for each class of swap structures. Moreover, when applied to the 3-valued algebraizable logics J3 and Ciore, their classes of algebraic models are retrieved, and the swap structures semantics become twist structures semantics. This fact, together with the existence of a functor from the category of Boolean algebras to the category of swap structures for each LFI, suggests that swap structures can be seen as non-deterministic twist structures. This opens new avenues for dealing with non-algebraizable logics by the more general methodology of multialgebraic semantics. (shrink)

Conceptual models are descriptions of our ideas about a problem, used to shape the implementation of a solution to it. Everyone who builds complex information systems uses such models - be they requirements analysts, knowledge modellers or software designers - but understanding of the pragmatics of model design tends to be informal and parochial. Lightweight uses of logic can add precision without destroying the intuitions we use to interpret our descriptions. Computing with logic allows us to make use of this (...) precision in providing automated support tools. Modern information scientists need to know what these methods are for and may need to build their own. This book gives you a place to begin. Where do you start when building models in a precise language like logic? One way is by following standard paradigms for design and adapting these to your needs. Some of these come from an analysis of existing informal notations. Others are from within logic itself. We take you through a sample of these, from more commonplace styles of formal modelling to non-standard methods such as techniques editing and argumentation. Each of these provides a window onto broader areas of applied logic and gives you a basis for adapting the method to your own needs. (shrink)

In this paper we develop what we can describe as a “dual two-sided” cut-free sequent calculus system for the non-classical logics of truth lp, k3, stt and a non-reflexive logic ts which is, arguably, more elegant than the three-sided sequent calculus developed by Ripley for the same logics. Its elegance stems from how it employs more or less the standard sequent calculus rules for the various connectives and truth, and the fact that it offers a rather neat connection between (...) derivable sequents and validity in comparison to the calculus developed by Ripley. (shrink)

A true Turing machine (TM) requires an infinitely long paper tape. Thus a TM can be housed in the infinite world of Newtonian spacetime (the spacetime of common sense), but not necessarily in our world, because our world-at least according to our best spacetime theory, general relativity-may be finite. All the same, one can argue for the "existence" of a TM on the basis that there is no such housing problem in some other relativistic worlds that are similar ("close") to (...) our world. But curiously enough-and this is the main point of this paper-some of these close worlds have a special spacetime structure that allows TMs to perform certain Turing unsolvable tasks. For example, in one kind of spacetime a TM can be used to solve first-order predicate logic and the halting problem. And in a more complicated spacetime, TMs can be used to decide arithmetic. These new computers serve to show that Church's thesis is a thoroughly contingent claim. Moreover, since these new computers share the fundamental properties of a TM in ordinary operation (e.g. intuitive, finitely programmed, limited in computational capability), a computability theory based on these non-Turing computers is no less worthy of investigation than orthodox computability theory. Some ideas about this new mathematical theory are given. (shrink)

An attempt to survey all non-western AI ethics guidelines that are available either in English or in Thai was made to find out whether there are any cultural elements within them that could shed light on how we understand their backgrounds and how these elements could advance the discussion on intercultural ethics of technology. The cultural elements are found to be superficially universal in that they retain the language used in the guidelines found in the west but contain interestingly unique (...) cultural elements when probed deeper. For example, many non-western guidelines have an injunction “Be ethical” without specifying the content of the ethical in question. We present an analysis of this and other unique aspects of the non-western guidelines in terms of broad cultural traditions that inform the guidelines and their drafters. This leads to a normative argument that what is understood to be universal in intercultural ethics is in fact based on the desire of many cultures to live and work together, and not, as ethical universalists seem to argue, on some culture-transcendent standard of morality. (shrink)

The aim of this book is to present the fundamental theoretical results concerning inference rules in deductive formal systems. Primary attention is focused on: admissible or permissible inference rules the derivability of the admissible inference rules the structural completeness of logics the bases for admissible and valid inference rules. There is particular emphasis on propositional non-standard logics (primary, superintuitionistic and modal logics) but general logical consequence relations and classical first-order theories are also considered. The book is basically self-contained and (...) special attention has been made to present the material in a convenient manner for the reader. Proofs of results, many of which are not readily available elsewhere, are also included. The book is written at a level appropriate for first-year graduate students in mathematics or computer science. Although some knowledge of elementary logic and universal algebra are necessary, the first chapter includes all the results from universal algebra and logic that the reader needs. For graduate students in mathematics and computer science the book is an excellent textbook. (shrink)

The standard view of classical cognitive science stated that cognition consists in the manipulation of language-like structures according to formal rules. Since cognition is ‘linguistic’ in itself, according to this view language is just a complex communication system and does not influence cognitive processes in any substantial way. This view has been criticized from several perspectives and a new framework (Embodied Cognition) has emerged that considers cognitive processes as non-symbolic and heavily dependent on the dynamical interactions between the cognitive (...) system and its environment. But notwithstanding the successes of the embodied cognitive science in explaining low-level cognitive behaviors, it is still not clear whether and how it can scale up for explaining high-level cognition. In this paper we argue that this can be done by considering the role of language as a cognitive tool: i.e. how language transforms basic cognitive functions in the high-level functions that are characteristic of human cognition. In order to do that, we review some computational models that substantiate this view with respect to categorization and memory. Since these models are based on a very rudimentary form of non-syntactic ‘language’ we argue that the use of language as a cognitive tool might have been an early discovery in hominid evolution, and might have played a substantial role in the evolution of language itself. (shrink)

We investigate two large families of logics, differing from each other by the treatment of negation. The logics in one of them are obtained from the positive fragment of classical logic (with or without a propositional constant ff for “the false”) by adding various standard Gentzen-type rules for negation. The logics in the other family are similarly obtained from LJ+, the positive fragment of intuitionistic logic (again, with or without ff). For all the systems, we provide simple semantics which (...) is based on non-deterministic four-valued or three-valued structures, and prove soundness and completeness for all of them. We show that the role of each rule is to reduce the degree of non-determinism in the corresponding systems. We also show that all the systems considered are decidable, and our semantics can be used for the corresponding decision procedures. Most of the extensions of LJ+ (with or without ff) are shown to be conservative over the underlying logic, and it is determined which of them are not. (shrink)

This essay argues that the "classical" or "standard" computation model of an enviroment of thought may hamstring the nascent cognitive science of religion by masking the ways in which the bare biological brain is prosthetically extended and embedded in the surrounding landscape. The motivation for distinsuishing between the problem-solving profiles of the basic brain and the brain-plus-scaffolding is that in many domains non-biological artifacts support and augment biological modes of computation - often allowing us to overcome some (...) of the brain's native computation limitations. The recognition that in some contexts not all of the relevant computational machinery fits inside the head suggests that we should reconsider the possible role and significance of material culture in religious cognition. More specifically, the broad spectrum of rituals, music, relics, scriptures, statues and buildings typically associated with religious traditions may be more than quaint ethnographic window dressing. Rather than thin cultural wrap arounds that decorate the real cognitive processes going on underneath, these elements could represent central components of the relevant machinery of religious thought. By introducing tangible features of the world that can be physically manipulated and tracked in real-time, for example, the cognitive scaffolding that religious material culture affords seems tailor-made for allowing people to exchange the intricate "off-line" problems that arise from dealing with invisible, counter-intuitive supernatural agents for the kinds of "on-line" cognitive tasks they are naturally good at doing. (shrink)

It is commonly held that the natural numbers sequence 0, 1, 2,... possesses a unique structure. Yet by a well known model theoretic argument, there exist non-standard models of the formal theory which is generally taken to axiomatize all of our practices and intentions pertaining to use of the term “natural number.” Despite the structural similarity of this argument to the influential set theoretic indeterminacy argument based on the downward L ̈owenheim-Skolem theorem, most theorists agree that the number theoretic (...) version does not have skeptical consequences about the reference of “natural number” analogous to the ‘relativity’ Skolem claimed pertains to notions such as “uncountable” and “cardinal.” In this paper I argue that recent proposals by Shapiro, Lavine, McGee and Field which aim to distinguish the number and set theoretic indeterminacy arguments by locating extra-mathematical constraints on the interpretation of our number theoretic vocabulary are inadequate. I then suggest that if we consider the manner in which the natural numbers figure in our computational practices – e.g. in characterizing how we compute sums and products or determine prime factorizations – it follows that our application of computational terms such as “computable function” and “tractable computational problem” indirectly uniquely determines their structure. (shrink)

Computably enumerable equivalence relations received a lot of attention in the literature. The standard tool to classify ceers is provided by the computable reducibility \. This gives rise to a rich degree structure. In this paper, we lift the study of c-degrees to the \ case. In doing so, we rely on the Ershov hierarchy. For any notation a for a non-zero computable ordinal, we prove several algebraic properties of the degree structure induced by \ on the \ equivalence (...) relations. A special focus of our work is on the existence of infima and suprema of c-degrees. (shrink)

Traditional logic as a part of philosophy is one of the oldest scientific disciplines. Mathematical logic, however, is a relatively young discipline and arose from the endeavors of Peano, Frege, Russell and others to create a logistic foundation for mathematics. It steadily developed during the 20th century into a broad discipline with several sub-areas and numerous applications in mathematics, informatics, linguistics and philosophy. While there are already several well-known textbooks on mathematical logic, this book is unique in that it is (...) much more concise than most others, and the material is treated in a streamlined fashion which allows the professor to cover many important topics in a one semester course. Although the book is intended for use as a graduate text, the first three chapters could be understood by undergraduates interested in mathematical logic. These initial chapters cover just the material for an introductory course on mathematical logic combined with the necessary material from set theory. This material is of a descriptive nature, providing a view towards decision problems, automated theorem proving, non-standard models and other subjects. The remaining chapters contain material on logic programming for computer scientists, model theory, recursion theory, Godel’s Incompleteness Theorems, and applications of mathematical logic. Philosophical and foundational problems of mathematics are discussed throughout the text. The author has provided exercises for each chapter, as well as hints to selected exercises. About the German edition: …The book can be useful to the student and lecturer who prepares a mathematical logic course at the university. What a pity that the book is not written in a universal scientific language which mankind has not yet created. - A.Nabebin, Zentralblatt. (shrink)

The first part (“Is there a future?”), discusses the idea of the future in the context of Carl Schmitt’s vision for the spatial revolutions of modernity, and then the idea of Anthropocene, as a synonym for an environmental crisis endangering the very survival of humankind. From this point of view, the conquest of space and the colonization of Mars at the center of futuristic and technocratic visions appear to be an attempt to escape from human responsibilities on Earth. The second (...) part (“AI and other hyperobjects”) discusses the extent of intellectual hubris expressed in computation, AI (Garvin Minsky e Ray Kurzweil), and the philosophy of computing and information (Eric Fredkin), involved in the elaboration of new theoretical assessments on the ultimate nature of reality. Their vision is then contrasted and made to interact with that of philosopher Timothy Morton. He has taken the perspective of global warming and the possibility of ecological catastrophe seriously, avoiding all the futuristic enthusiasms and instead emphasizing the radical nature of the transformations that humans experience in the present. In this perspective, AI becomes one of the “hyperobjects,” like the Internet or climate change, in which humans are immersed. Morton’s hyperobjects delineate an uncanny view of the future; this uncanniness is not related to the supernatural but to the environment. The third section (“More-than-human-humanism”) further reflects on the “uncanniness” that human perceive in the encounters with the manifestations of hyperobjects. It also seeks to understand the human position in the face of the radical technological transformations induced by cybernetics and AI. This section discusses Anti-humanism, Transhumanism, and Posthumanism within the broader category of more-than-human thought, which seems to be a more appropriate term to clarify the possible misunderstandings induced by the word “posthuman” and “transhuman.” The central question is not to empower (Transhumanism) or disempower (Posthumanism) humans, but to see them in relation to what is not human, including other animals, the environment, and the machine. The analysis considers the works of Cary Wolfe, Jane Bennet, Bryant Levi, among others, and introduces ethical debates on cyborgs, robots, and Autonomous weapons systems (AWS). The fourth section (“Ethical Perspectives”) continues this inquiry, concentrating on the non-standard ethical theories of Luciano Floridi (Computer and Information Ethics) and David Gunkel (The question of the Machine). It examines the opportunity and feasibility of including in the discussion on the ethics of our time - characterized by the pervasiveness of AI - the notions of consciousness as theorized by Emmanuel Levinas’s Humanism of the Other and Paul Ricoeur’s Oneself as Another. Finally, the last section (“The time of the end?”) reflects on how the hyperobject, Anthropocene, re-establishes a sense of limits in human history and confirms the special responsibility of human beings, and supports the need for a more-than-human-humanism. The latter, in other words, means intertwining ourselves with a unique ecosystem which cannot be overlooked and which restores meaning to our relationship with the past, present, and future. The awareness of the current challenges of technology can and must express itself in different forms of resistance to the adverse effects of AI in our lives. The ethical approach based on the persisting role of human consciousness is essential, but it must be coupled with human decision-making and political action. (shrink)

We give a constructive analysis of learning as it arises in various computational interpretations of classical Peano Arithmetic, such as Aschieri and Berardi learning based realizability, Avigad’s update procedures and epsilon substitution method. In particular, we show how to compute in Gödel’s system T upper bounds on the length of learning processes, which are themselves represented in T through learning based realizability. The result is achieved by the introduction of a new non standard model of Gödel’s T, whose new (...) basic objects are pairs of non standard natural numbers and moduli of convergence, where the latter are objects giving constructive information about the former. As a foundational corollary, we obtain that that learning based realizability is a constructive interpretation of Heyting Arithmetic plus excluded middle over Σ10 formulas and of all Peano Arithmetic when combined with Gödel’s double negation translation. As a byproduct of our approach, we also obtain a new proof of Avigad’s theorem for update procedures and thus of the termination of the epsilon substitution method for PA. (shrink)

This book stands at the intersection of two topics: the decidability and computational complexity of hybrid logics, and the deductive systems designed for them. Hybrid logics are here divided into two groups: standard hybrid logics involving nominals as expressions of a separate sort, and non-standard hybrid logics, which do not involve nominals but whose expressive power matches the expressive power of binder-free standard hybrid logics.The original results of this book are split into two parts. This division reflects (...) the division of the book itself. The first type of results concern model-theoretic and complexity properties of hybrid logics. Since hybrid logics which we call standard are quite well investigated, the efforts focused on hybrid logics referred to as non-standard in this book. Non-standard hybrid logics are understood as modal logics with global counting operators ) whose expressive power matches the expressive power of binder-free standard hybrid logics. The relevant results comprise: 1. Establishing a sound and complete axiomatization for the modal logic K with global counting operators ), which can be easily extended onto other frame classes, 2. Establishing tight complexity bounds, namely NExpTime-completeness for the modal logic with global counting operators defined over the classes of arbitrary, reflexive, symmetric, serial and transitive frames ), MT), MD), MB), MK4) with numerical subscripts coded in binary. Establishing the exponential-size model property for this logic defined over the classes of Euclidean and equivalential frames ), MS5).Results of the second type consist of designing concrete deductive systems for standard and non-standard hybrid logics. More precisely, they include: 1. Devising a prefixed and an internalized tableau calculi which are sound, complete and terminating for a rich class of binder-free standard hybrid logics. An interesting feature of indicated calculi is the nonbranching character of the rule, 2. Devising a prefixed and an internalized tableau calculi which are sound, complete and terminating for non-standard hybrid logics. The internalization technique applied to a tableau calculus for the modal logic with global counting operators is novel in the literature, 3. Devising the first hybrid algorithm involving an inequality solver for modal logics with global counting operators. Transferring the arithmetical part of reasoning to an inequality solver turned out to be sufficient in ensuring termination.The book is directed to philosophers and logicians working with modal and hybrid logics, as well as to computer scientists interested in deductive systems and decision procedures for logics. Extensive fragments of the first part of the book can also serve as an introduction to hybrid logics for wider audience interested in logic.The content of the book is situated in the areas of formal logic and theoretical computer science with some elements of the theory of computational complexity. (shrink)

This paper outlines a formal recursive wager resolution calculus (WRC) that provides a novel conceptual framework for sentential logic via bridge rules that link wager resolution with truth values. When paired with a traditional truth-centric criterion of logical soundness WRC generates a sentential logic that is broadly truth-conditional but not truth-functional, supports the rules of proof employed in standard mathematics, and is immune to the most vexing features of their traditional implementation. WRC also supports a novel probabilistic criterion of (...) logical soundness, the fair betting probability criterion (FBP). It guarantees that the conclusion of an FBP-valid argument is at least as credible as a conjunction of premises, and also that the conclusion is true if the premises are. In addition, WRC provides a platform for a novel non-probabilistic, computationally simpler criterion of logical soundness – the criterion of Super-validity - that issues the same logical appraisals as FBP, and hence the same guarantees. (shrink)