Bayes’ formula is a fundamental statistical method for inference judgments in uncertain situations used by both laymen and professionals. However, since people often fail in situations where Bayes’ formula can be applied, how to improve their performance in Bayesian situations is a crucial question. We based our research on a widely accepted beneficial strategy in Bayesian situations, representing the statistical information in the form of natural frequencies. In addition to this numerical format, we used five visualizations: a 2×2-table, a unit (...) square, an icon array, a tree diagram, and a double-tree diagram. In an experiment with 688 undergraduate students, we empirically investigated the effectiveness of three graphical properties of visualizations: area-proportionality, use of discrete and countable statistical entities, and graphical transparency of the nested-sets structure. We found no additional beneficial effect of area-proportionality. In contrast, the representation of discrete objects seems to be beneficial. Furthermore, our results show a strong facilitating effect of making the nested-sets structure of a Bayesian situation graphically transparent. Our results contribute to answering the questions of how and why a visualization could facilitate judgment and decision making in situations of uncertainty. (shrink)

Complex fuzzy sets are the novel extension of Zadeh’s fuzzy sets. In this paper, we comprise the introduction to the concept of ξ -complex fuzzy sets and proofs of their various set theoretical properties. We define the notion of α, δ -cut sets of ξ -complex fuzzy sets and justify the representation of an ξ -complex fuzzy set as a union of nested intervals of these cut sets. We also apply this newly defined (...) concept to a physical situation in which one may judge the performance of the participants in a given task. In addition, we innovate the phenomena of ξ -complex fuzzy subgroups and investigate some of their fundamental algebraic attributes. Moreover, we utilize this notion to define level subgroups of these groups and prove the necessary and sufficient condition under which an ξ -complex fuzzy set is ξ -complex fuzzy subgroup. Furthermore, we extend the idea of ξ -complex fuzzy normal subgroup to define the quotient group of a group G by this particular ξ -complex fuzzy normal subgroup and establish an isomorphism between this quotient group and a quotient group of G by a specific normal subgroup G A ξ. (shrink)

Many named entities contain other named entities inside them. Despite this fact, the field of named entity recognition has almost entirely ignored nested named entity recognition, but due to technological, rather than ideological reasons. In this paper, we present a new technique for recognizing nested named entities, by using a discriminative constituency parser. To train the model, we transform each sentence into a tree, with constituents for each named entity (and no other syntactic structure). We present results (...) on both newspaper and biomedical corpora which contain nested named entities. In three out of four sets of experiments, our model outperforms a standard semi-CRF on the more traditional top-level entities. At the same time, we improve the overall F-score by up to 30% over the flat model, which is unable to recover any nested entities. (shrink)

The general principle behind the effects of nested sets on the use of base rates, we believe, is that the mind is prepared to take in Without any need to assume two cognitive systems, this principle explains how the proper use of base rates can be facilitated and also accounts for occasions when base rates are overused.

This article introduces finitist set theory (FST) and shows how it can be applied in modeling finite nested structures. Mereology is a straightforward foundation for transitive chains of part-whole relations between individuals but is incapable of modeling antitransitive chains. Traditional set theories are capable of modeling transitive and antitransitive chains of relations, but due to their function as foundations of mathematics they come with features that make them unnecessarily difficult in modeling finite structures. FST has been designed to function (...) as a practical tool in modeling transitive and antitransitive chains of relations without suffering from difficulties of traditional set theories, and a major portion of the functionality of discrete mereology can be incorporated in FST. This makes FST a viable collection theory in ontological modeling. (shrink)

Jones argues that extending Seneca kin terms to second cousins requires a revised version of Optimality Theoretic grammar. I extend Seneca terms using three constraints on expression of markers in nested binary classification trees. Multiple constraint rankings on a nested set coupled with local parity checking determines how a given kin classification grammar marks structural endogamy.

People often struggle with Bayesian reasoning. However, research showed that people’s performance (and rationality) can be supported by the way of representing the statistical information. First, research showed that using natural frequencies instead of probabilities as format of statistical information increases people’s performance in Bayesian situations thoroughly. Second, research also yielded that people’s performance increases through using visualization. We build our paper on existing research in this field. The main aim is to analyse people’s strategies in Bayesian situations that are (...) still erroneous although statistical information is represented by natural frequencies and visualizations. In particular, we compare two pairs of visualization with similar numerical information (tree diagram vs. unit square and double-tree diagram vs. 2x2-table) concerning their impact on people’s erroneous strategies in Bayesian situations. For this aim, we conducted an experiment with 540 university students. The students were randomly assigned to four conditions that are defined by the four different visualizations of statistical information. The students were asked to indicate a fraction as response in four Bayesian situations. We documented the numerator and the denominator of the students’ responses representing a basic set and a subset in a Bayesian situation. Our results show that people’s erroneous strategies are highly dependent on the visualization. A central finding is that the visualization’s characteristic of making the nested-sets structure of a Bayesian situation transparent has a facilitating effect on people’s Bayesian reasoning. For example, compared to the unit square, a tree diagram does not explicitly visualize the set-subset relations that are relevant in a Bayesian situation. Accordingly, compared to a unit square, a tree diagram partly hinders people to find the correct denominator in a Bayesian situation, and, in particular, triggers to select a wrong numerator. By analyzing people’s erroneous strategies in Bayesian situations, we contribute to investigating approaches to facilitate Bayesian reasoning and to further develop the teaching of Bayesian reasoning. (shrink)

We present a neural dynamic model that perceptually grounds nested noun phrases, that is, noun phrases that contain further (possibly also nested) noun phrases as parts. The model receives input from the visual array and a representation of a noun phrase from language processing. It organizes a search for the denoted object in the visual scene. The model is a neural dynamic architecture of interacting neural populations which has clear interfaces with perceptual processes. It solves a set of (...) theoretical challenges, including the problem of keeping a nested structure in short-term memory in a way that solves the problem of 2 and massive binding problem emphasized by Jackendoff. The model organizes a search for the objects that are referenced in that structure. We motivate the model, demonstrate simulation results, and discuss how it differs from related models. (shrink)

Several authors proposed to devise logical structures for Natural Language (NL) semantics in which noun phrases yield referential terms rather than standard Generalized Quantifiers. In this view, two main problems arise: the need to refer to the maximal sets of entities involved in the predications and the need to cope with Independent Set (IS) readings, where two or more sets of entities are introduced in parallel. The article illustrates these problems and their consequences, then presents an extension of (...) the proposal made in Sher (J Philos Logic 26:1–43, 1997 ) in order to properly represent the meaning of IS readings involving NL quantifiers. The solution proposed here allows to uniformly deal with both standard linear and IS readings, regardless of their actual existence in NL or quantifiers’ monotonicity. Sentences featuring nested quantifications are particularly problematic. By avoiding parallel nested quantification in the formulae, the proper true values are achieved. (shrink)

The phenomenon of base-rate neglect has elicited much debate. One arena of debate concerns how people make judgments under conditions of uncertainty. Another more controversial arena concerns human rationality. In this target article, we attempt to unpack the perspectives in the literature on both kinds of issues and evaluate their ability to explain existing data and their conceptual coherence. From this evaluation we conclude that the best account of the data should be framed in terms of a dual-process model of (...) judgment, which attributes base-rate neglect to associative judgment strategies that fail to adequately represent the set structure of the problem. Base-rate neglect is reduced when problems are presented in a format that affords accurate representation in terms of nested sets of individuals. (shrink)

The terms nested sets, partitive frequencies, inside-outside view, and dual processes add little but confusion to our original analysis (Gigerenzer & Hoffrage 1995; 1999). The idea of nested set was introduced because of an oversight; it simply rephrases two of our equations. Representation in terms of chances, in contrast, is a novel contribution yet consistent with our computational analysis System 1.dual process theory” is: Unless the two processes are defined, this distinction can account post hoc for almost (...) everything. In contrast, an ecological view of cognition helps to explain how insight is elicited from the outside (the external representation of information) and, more generally, how cognitive strategies match with environmental structures. (shrink)

Philippe Huneman has recently questioned the widespread application of mechanistic models of scientific explanation based on the existence of structural explanations, i.e. explanations that account for the phenomenon to be explained in virtue of the mathematical properties of the system where the phenomenon obtains, rather than in terms of the mechanisms that causally produce the phenomenon. Structural explanations are very diverse, including cases like explanations in terms of bowtie structures, in terms of the topological properties of the system, or in (...) terms of equilibrium. The role of mathematics in bowtie structured systems and in topologically constrained systems has recently been examined in different papers. However, the specific role that mathematical properties play in equilibrium explanations requires further examination, as different authors defend different interpretations, some of them closer to the new-mechanistic approach than to the structural model advocated by Huneman. In this paper, we cover this gap by investigating the explanatory role that mathematics play in Blaser and Kirschner’s nested equilibrium model of the stability of persistent long-term human-microbe associations. We argue that their model is explanatory because: i) it provides a mathematical structure in the form of a set of differential equations that together satisfy an ESS; ii) that the nested nature of the ESSs makes the explanation of host-microbe persistent associations robust to any perturbation; iii) that this is so because the properties of the ESS directly mirror the properties of the biological system in a non-causal way. The combination of these three theses make equilibrium explanations look more similar to structural explanations than to causal-mechanistic explanation. (shrink)

Background Informed consent is considered to be the standard method for respecting the autonomy of individual participants in research and practices and is thought to be based on several conditions: (1) providing information on the purpose of the research or a specific treatment, what it will entail, (2) the participants being mentally competent to understand the information and weigh it in the balance, and (3) the participants to be free from coercion. While there are studies of informed consent in other (...) countries, especially Low and Middle Income Countries (LMICs), this study explored the experiences of clinicians regarding the process of obtaining informed consent to participate in a Randomised Controlled Trial (RCT) in particular and treatment in general in healthcare settings, both general and mental health, specifically focusing on the tension between individualistic concept of autonomy and collectivist values in cultures such as Pakistan. Methods Qualitative interviews with 20 clinicians from healthcare settings in Pakistan who also served as recruiters in a suicide prevention RCT in Pakistan. The interviews were guided by semi-structured topic guide. All interviews were audio-recorded and transcribed verbatim. Results The interviews revealed that shared decision making was more morally important than individual autonomy, the role of the family played a dominant part in the consent-taking procedure, the decision of the elder and/or family patriarch took prominence, and that clinician-researchers encountered significant challenges in consent process in Pakistan, while recruiting patients into the trial as well as during routine treatment processes in healthcare settings. Four distinct themes emerged which were (1) Family deciding for patients, (2) Benefits of involving family in consent process, (3) Gender disparity in consent process, (4) Challenges experienced by clinician-researchers during consent process in Pakistan. Conclusions The concept of consent is generally considered important in many cultures, however, there are two strands of understanding. There seems to be consensus that participant agreement is necessary to protect the participant but with regards to autonomy there are significant cultural differences whether it is the right for autonomy of the individual (individualistic concept) or family, community, or expert authority in other cultures. In Pakistan clinician-researchers sometimes preferred one approach and sometimes the other as they appreciated the interests of the patient to be. (shrink)

The complexity of the human mind and its interaction with the environment is one of the main epistemological debates throughout history. Recent ideas, framed as the 4E perspective to cognition, highlight that human experience depends causally on both cerebral and extracranial processes, but also is embedded in a particular sociomaterial context and is a product of historical accumulation of trajectory changes throughout life. Accordingly, the human microbiome is one of the most intriguing actors modulating brain function and physiology. Here, we (...) present the 4E approach to the Human Microbiome for understanding mental processes from a broader perspective, encompassing one's body physiology and environment throughout their lifespan, interconnected by microbiome community structure and dynamics. We review evidence supporting the approach theoretically and motivates the study of the global set of microbial ecosystem networks encountered by a person across their lifetime (from skin to gut to natural and built environments). We furthermore trace future empirical implementation of the approach. We finally discuss novel research opportunities and clinical interventions aimed toward developing low‐cost/high‐benefit integrative and personalized bio‐psycho‐socio‐environmental treatments for mental health and including the brain‐gut‐microbiome axis. (shrink)

Barbey & Sloman's (B&S's) base-rate respect model is anticipated by Reyna's denominator neglect model. There are parallels at three levels: (a) explanations are grounded in a general cognitive theory (rather than in domain-specific ideas); (b) problem structure is treated as a key source of reasoning errors; and most importantly, (c) nested set relations are seen as the cause of base-rate neglect.

Parental burnout is a unique and context-specific syndrome resulting from a chronic imbalance of risks over resources in the parenting domain. The current research aims to evaluate the psychometric properties of the Spanish version of the Parental Burnout Assessment across Spanish-speaking countries with two consecutive studies. In Study 1, we analyzed the data through a bifactor model within an Exploratory Structural Equation Modeling on the pooled sample of participants obtaining good fit indices. We then attained measurement invariance across both gender (...) and countries in a set of nested models with gradually increasing parameter constraints. Latent means comparisons across countries showed that among the participants’ countries, Chile had the highest parental burnout score, likewise, comparisons across gender evidenced that mothers displayed higher scores than fathers, as shown in previous studies. Reliability coefficients were high. In Study 2, we tested the relations between parental burnout and three specific consequences, i.e., escape and suicidal ideations, parental neglect, and parental violence toward one’s children. The medium to large associations found provided support for the PBA’s predictive validity. Overall, we concluded that the Spanish version of the PBA has good psychometric properties. The results support its relevance for the assessment of parental burnout among Spanish-speaking parents, offering new opportunities for cross-cultural research in the parenting domain. (shrink)

Barbey & Sloman (B&S) claim that frequency formats and other task manipulations induce people to substitute associative thinking for rule-based thinking about nested sets. My critique focuses on the substitution assumption. B&S demonstrate that nested sets are important to solve base-rate problems but they do not show that thinking about these nested sets relies on a different type of reasoning.

-/- This unique book develops an operational approach to preference and rationality as the author employs operators over binary relations to capture the concept of rationality. -/- A preference is a basis of individual behavior and social judgment and is mathematically regarded as a binary relation on the set of alternatives. Traditionally, an individual/social preference is assumed to satisfy completeness and transitivity. However, each of the two conditions is often considered to be too demanding; and then, weaker rationality conditions are (...) introduced by researchers. This book argues that the preference rationality conditions can be captured mathematically by “operators,” which are mappings from the set of operators to itself. This operational approach nests traditional concepts in individual/social decision theory and clarifies the underlying formal structure of preference rationality. -/- The author also applies his approach to welfare economics. The core problem of ‘new welfare economics,’ developed by Kaldor, Hicks, and Samuelson, is the rationality of social preference. In this book the author translates the social criteria proposed by those three economists into operational forms, which provide new insights into welfare economics extending beyond ‘new welfare economics.’ . (shrink)

Management scholars have paid close attention to the construct of organizational or corporate reputation, particularly in the applied business ethics and corporate social responsibility fields. Extant research demonstrates that CR is one of the key mediators between CSR and important organizational outcomes, which ultimately improve organizational performance. Yet, hitherto the research focused on CR construct has been plagued by multiple definitions, conflicting conceptualizations, and unclear operationalizations. The purpose of this article is to provide theoretical ground for positioning of CR as (...) an assessment construct that is modeled as a second-order factor affecting individual first-order dimensions, and to provide methodological and empirical support toward such conceptualization. We assert that intangible, socially complex, and causally ambiguous CR can be accurately estimated through its individual measurable dimensions. Using survey data from Peru, we empirically test the hypothesized second-order reflective model within a hierarchy of nested and non-nested models, and compare its model fit and predictive power with alternative conceptualizations. Modeling CR as a second-order reflective construct relies on a set of theoretical propositions and yields several methodological advantages, including strong conceptual interpretability and parsimony when tested within a nomological context. We explicitly demonstrate positive organizational outcomes of CR: customer trust, corporate identification, in-role behavior, and extra-role behavior. Then, we demonstrate that the shorter scales of CR can be used as a good proxy for the full construct measure. The paper concludes by highlighting theoretical insights, and methodological and managerial implications of the findings. (shrink)

We believe that when assessing the likelihood of uncertain events, statistically unsophisticated people utilize a coarse internal scale that only has a limited number of categories. The success of the nested sets hypothesis may lie in its ability to provide an appropriate set structure of the problem by reducing the computational demands.

The promise of scientific and technological innovation – particularly in fields such as nanotechnology – is increasingly set against what has been articulated as a deficit in public trust in both the new technologies and regulatory mechanisms. Whilst the development of new technology is cast as providing contributions to both quality of life and national competitiveness, what has been termed a ‘legitimacy crisis’ is seen as threatening the vitality of this process. However in contrast to the risk debates that dominated (...) the technological controversies of the late 1990s the vitality of technological innovation is now cast as vulnerable to lack of public confidence and trust in the regulatory and governance structures upon which such innovation depends. In order to address this deficit in public trust, science policy has increasingly turned to the social sciences, suggesting that public values might be incorporated into the development of nanotechnology at an early stage. Public ambivalence therefore constitutes the problem addressed by the increasingly central role that public engagement and participation play in contemporary science policy. Although the recent proliferation of public engagement activities is premised on the need to address this ambivalence through direct engagement, we re-interpret ambivalence as an engaged – rather than passive – mode of relating to technological determinism. Whilst the move toward forms of direct public engagement might be regarded as symptomatic of the emergence of affective mode of governance we interpret public ambivalence as a nested set of enthusiasms and anxieties. Accordingly we suggest that public engagement might be re-thought, utilising ambivalence as a creative resource, rather than as the problem. (shrink)

Consistent with Barbey & Sloman (B&S), it is proposed that performance on Bayesian inference tasks is well explained by nested sets theory (NST). However, contrary to those authors' view, it is proposed that NST does better by dispelling with dual-systems assumptions. This article examines why, and sketches out a series of NST's core principles, which were not previously defined.

This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic paradigms: labelled and nested sequent calculi. The formalism of labelled sequents has been successful in that cut-free calculi in possession of desirable proof-theoretic properties can be automatically generated for large classes of logics. Despite these qualities, labelled systems make use of a complicated syntax that explicitly incorporates (...) the semantics of the associated logic, and such systems typically violate the subformula property to a high degree. By contrast, nested sequent calculi employ a simpler syntax and adhere to a strict reading of the subformula property, making such systems useful in the design of automated reasoning algorithms. However, the downside of the nested sequent paradigm is that a general theory concerning the automated construction of such calculi (as in the labelled setting) is essentially absent, meaning that the construction of nested systems and the confirmation of their properties is usually done on a case-by-case basis. The refinement method connects both paradigms in a fruitful way, by transforming labelled systems into nested (or, refined labelled) systems with the properties of the former preserved throughout the transformation process. To demonstrate the method of refinement and some of its applications, we consider grammar logics, first-order intuitionistic logics, and deontic STIT logics. The introduced refined labelled calculi will be used to provide the first proof-search algorithms for deontic STIT logics. Furthermore, we employ our refined labelled calculi for grammar logics to show that every logic in the class possesses the effective Lyndon interpolation property. (shrink)

Neste artigo, pretendo examinar a tese cartesiana da livre criação das verdades eternas a partir da conjugação dos atributos divinos que, segundo Descartes, são conhecidos por nós e sua tese de que, entre as verdades eternas livremente criadas por Deus, estão incluídos os princípios lógicos. A partir desse exame, concluo que, até onde o intelecto finito do homem pode conceber, a tese cartesiana da livre criação das verdades eternas envolve ao menos as seguintes teses: a) Deus, por ser infinito e (...) puro pensamento em ato, estabelece necessariamente em si todas as essências e verdades, incluindo essências e verdades que para o intelecto finito parecem impossíveis, já que lhe aparecem como contraditórias; b) ao estabelecer as essências e verdades, Deus instancia algumas (e assim as cria) como conteúdos de ideias inatas nas mentes finitas, que são criadas com estrutura lógica; c) ao estabelecer as essências e verdades, Deus instancia no mundo atual ao menos algumas das essências e verdades não contraditórias instanciadas nas mentes finitas; e d) embora a mente humana finita não as possa conceber clara e distintamente, é certo que Deus instancia no mundo atual ao menos algumas das essências e verdades que aparecem como contraditórias, isto é, instancia no mundo atual ao menos algumas das essências e verdades que para a mente finita aparecem como impossíveis por serem por ela inconcebíveis, o que é confirmado por ao menos dois casos mencionados por Descartes. In this article I intend to examine the Cartesian view on the free creation of the eternal truths considering the conjunction of the divine attributes, which according to the Cartesian thesis, are known to us and his thesis that logical principles are among the eternal truths freely created by God. From this examination I conclude that, as far as the finite intellect of man can conceive, the Cartesian view of the free creation of the eternal truths involves at least the following theses: a) being pure and infinite thinking in action, God necessarily sets in himself all the form of essence and truth, including all essence and truth that for, the finite intellect, seem impossible since they may appear to him as contradictory; b) while establishing all essence and truth, God instantiates some of them (and thus creates some of them) as contents of innate ideas in finite minds, which are created with a logical structure; c) while establishing all essence and truth God instantiates in the actual world at least some of the non-contradictory essences which are instantiated in the finite mind; and d) although the finite human mind cannot conceive it clearly and distinctly, it is certain that God instantiates in the actual world at least some of essence and truth that seem to be contradictory for the human mind, that is, God instantiates at least some of the essences and truths which appear to the finite mind as impossible since inconceivable, which is confirmed by at least two cases mentioned by Descartes. (shrink)

Resumo Neste artigo, defender-se-á uma interpretação do filme A Time to Kill, como sendo uma narrativa cinematográfica falível, mesmo sem a presença de um narrador. Neste texto, assume-se, que uma narrativa falível resulta de um defeito estético e ético do filme. Deste modo, a estrutura estética do filme representa a intenção do realizador em contar a sua versão da história, influenciando assim o seu significado e efeito empático. Com o evoluir da narrativa cinematográfica, as regras de inferência tornam-se cada vez (...) mais complexas. Ainda assim, a convenção cinematográfica estabelece um contexto e define limites identificadores para a sua interpretação. Uma história mal contada inibe a reconstrução imaginativa do espectador, no que diz respeito às motivações das personagens e da causalidade narrativa. Portanto, a qualidade narrativa é essencial para o raciocínio narrativo e empatia estética. Se a narrativa oferece uma compreensão do mundo e de outras pessoas, que de outra forma seriam inacessíveis, e se a forma ou o estilo da narrativa determinam a sua eficácia, então, as formas assumidas pelas nossas histórias têm consequências epistemológicas. Palavras-chave : estética, ética, identificação, narrativa falível, narrativa, raçaIn this paper, I argue for an interpretation of A Time to Kill as an unreliable, yet narrator-less, cinematic narrative. In my view, unreliable narration is an aesthetic and ethical flaw of the film rather than of the narrator. Thus, the film’s aesthetic structure represents the director’s storytelling intentions, and influences its meaning and empathic affect. As cinematic narrative evolves, rules of inference become increasingly complex. Still, filmic convention establishes a context and sets identifiable boundaries for interpretation. A poorly told story inhibits the viewer’s imaginative reconstruction of narrative causation and characters’ motives. Thus, narrative quality is essential to narrative reasoning and aesthetic empathy. If narrative provides an understanding of the world and other people that is otherwise inaccessible, and if the form or style of narrative determines its effectiveness, then the forms our stories take have epistemological consequences. Keywords : aesthetics, ethics, identification, narrative, race, unreliable narrative. (shrink)

Evidence favors the nested sets hypothesis, introduced by fuzzy-trace theory (FTT) in the 1990s to explain effects and extended to many tasks, including conjunction fallacy, syllogistic reasoning, and base-rate effects (e.g., Brainerd & Reyna 1990; Reyna 1991; 2004; Reyna & Adam 2003; Reyna & Brainerd 1995). Crucial differences in mechanisms distinguish the FTT and Barbey & Sloman (B&S) accounts, but both contrast with frequency predictions (see Reyna & Brainerd, in press).

Barbieri introduced and developed the concept of organic codes. The most basic of them is the genetic code, a set of correspondence rules between otherwise unrelated sequences: strings of nucleotides on the one hand, polypeptidic chains on the other hand. Barbieri noticed that it implies ‘coding by convention’ as arbitrary as the semantic relations a language establishes between words and outer objects. Moreover, the major transitions in life evolution originated in new organic codes similarly involving conventional rules. Independently, dealing with (...) heredity as communication over time and relying on information theory, we asserted that the conservation of genomes over the ages demands that error-correcting codes make them resilient to casual errors. Moreover, the better conservation of very old parts of the genome demands that they result from combining successively established nested codes such that the older an information, the more numerous component codes protect it. Barbieri’s concept of organic code and that of genomic error-correcting code may seem unrelated. We show however that organic codes actually entail error-correcting properties. Error-correcting, in general, results from constraints being imposed on a set of sequences. Mathematical equalities are conveniently used in communication engineering for expressing constraints but error correction only needs that constraints exist. Biological sequences are similarly endowed with error-correcting ability by physical-chemical or linguistic constraints, thus defining ‘soft codes’. These constraints are moreover presumably efficient for correcting errors. Insofar as biological sequences are subjected to constraints, organic codes necessarily involve soft codes, and their successive onset results in the nested structure we hypothesized. Organic codes are generated and maintained by means of molecular ‘semantic feedback loops’. Each of these loops involves genes which code for proteins, the enzymatic action of which controls a function needed for the protein assembly. Taken together, thus, they control the assembly of their own structure as instructed by the genome and, once closed, these loops ensure their own conservation. However, the semantic feedback loops do not prevent the genome lengthening. It increases both the redundancy of the genome and the information quantity it bears, thus improving the genome reliability and the specificity of the enzymes, which enables further evolution. (shrink)

This textbook is a second edition of the successful, Mathematical Logic: On Numbers, Sets, Structures, and Symmetry. It retains the original two parts found in the first edition, while presenting new material in the form of an added third part to the textbook. The textbook offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Part I, Logic Sets, and Numbers, shows how mathematical logic is (...) used to develop the number structures of classical mathematics. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are used to study and classify mathematical structures. The added Part III to the book is closer to what one finds in standard introductory mathematical textbooks. Definitions, theorems, and proofs that are introduced are still preceded by remarks that motivate the material, but the exposition is more formal, and includes more advanced topics. The focus is on the notion of countable categoricity, which analyzed in detail using examples from the first two parts of the book. This textbook is suitable for graduate students in mathematical logic and set theory and will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background. (shrink)

The target article makes an impressive case that nested set operations (NS) facilitate probability computations by helping make clear the relevant natural frequency partitions; however, NS can also contribute to common errors. That NS constitute a general reasoning process is supported by their role in deductive, modal, causal, and other reasoning. That NS are solely a rule-based process is problematic.

In recent years, there has been a proliferation of neuroscientific theories of consciousness. These include theories which explicitly point to EM fields, notably Operational Architectonics and, more recently, the General Resonance Theory. In phenomenological terms, human consciousness is a unified composition of contents. These contents are specific and meaningful, and they exist from a subjective point of view. Human conscious experience is temporally continuous, limited in content, and coherent. Based upon those phenomenal observations, pre-existing theories of consciousness, and a large (...) body of experimental evidence, I derived the Temporally-Integrated Causality Landscape. In brief, the TICL proposes that the neural correlate of consciousness is a structure of temporally integrated causality occurring over a large portion of the thalamocortical system. This structure is composed of a large, integrated set of neuronal elements, which contains some subsystems, defined as having a higher level of temporally-integrated causality than the System as a whole. Each Subsystem exists from the point of view of the System, in the form of meaningful content. In this article, I review the TICL and consider the importance of EM forces as a mechanism of neural causality. I compare the fundamentals of TICL to those of several other neuroscientific theories. Using five major characteristics of phenomenal consciousness as a standard, I compare the basic tenets of Integrated Information Theory, Global Neuronal Workspace, General Resonance Theory, Operational Architectonics, and the Temporo-spatial Theory of Consciousness with the framework of the TICL. While the literature concerned with these theories tends to focus on different lines of evidence, there are fundamental areas of agreement. This means that, in time, it may be possible for many of them to converge upon the truth. In this analysis, I conclude that a primary distinction which divides these theories is the feature of spatial and temporal nesting. Interestingly, this distinction does not separate along the fault line between theories explicitly concerned with EM fields and those which are not. I believe that reconciliation is possible, at least in principle, among those theories that recognize the following: just as the contents of consciousness are distinctions within consciousness, the neural correlates of conscious content should be distinguishable from but fall within the spatial and temporal boundaries of the full neural correlates of consciousness. (shrink)

This book is the sixth volume in the series of Collected Papers on Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. Building upon the foundational contributions of previous volumes, this edition focuses on the exploration and development of Various New Uncertain Concepts, further enriching the study of uncertainty and complexity through innovative theoretical advancements and practical applications. The volume is meticulously organized into 15 chapters, each presenting unique perspectives and contributions to the field. From (...) theoretical explorations to real-world applications, these chapters provide a cohesive and comprehensive overview of the state of the art in uncertain combinatorics, emphasizing the versatility and power of the newly introduced concepts and methodologies. The first chapter (SuperHypertree-depth – Structural Analysis in SuperHyperGraphs) explores the concept of SuperHypertree-depth, an extension of the classical graph parameter Tree-depth and its hypergraph counterpart Hypertree-depth. By introducing hierarchical nesting within SuperHyperGraphs, where both vertices and edges can represent recursive subsets, this study investigates the mathematical properties and structural implications of these extended parameters. The findings highlight the relationships between SuperHypertree-depth and its traditional graph-theoretic equivalents, providing a deeper understanding of their applicability to hierarchical and complex systems. The second chapter (Obstructions for Hypertree-width and SuperHypertree-width) examines the role of ultrafilters as obstructions in determining Hypertree-width and extends the concept to SuperHypertree-width. Building on hypergraph theory, which abstracts traditional graph frameworks into more complex domains, the study investigates how recursive structures within SuperHyperGraphs redefine the computational and structural properties of these parameters. Ultrafilters, with their broad mathematical significance, serve as critical tools for understanding the limitations and potentials of these advanced graph metrics. The third chapter (SuperHypertree-Length and SuperHypertree-Breadth in SuperHyperGraphs) investigates the extension of the graph-theoretic parameters Tree-length and Tree-breadth to the realms of hypergraphs and SuperHyperGraphs. By leveraging the hierarchical nesting of SuperHyperGraphs, the study explores how these parameters adapt to increasingly complex and multi-level structures. Comparative analyses between these extended parameters and their classical counterparts reveal new insights into their relevance and utility in advanced graph and hypergraph theory. Plithogenic Sets, which generalize Fuzzy and Neutrosophic Sets, are extended in the fourth chapter (Extended HyperPlithogenic Sets and Generalized Plithogenic Graphs) to Extended Plithogenic Sets, HyperPlithogenic Sets, and SuperHyperPlithogenic Sets. This study further investigates their application to graph theory through the concepts of Extended Plithogenic Graphs and Generalized Extended Plithogenic Graphs. The chapter provides a concise exploration of these frameworks, offering insights into their potential for addressing uncertainty and complexity in graph structures. Soft Sets provide an effective framework for decision-making by mapping parameters to subsets of a universal set, addressing uncertainty and vagueness. The fifth chapter (Double-Framed Superhypersoft Set and Double-Framed Treesoft Set) introduces the Double-Framed SuperHypersoft Set and the Double-Framed Treesoft Set as extensions of traditional and advanced soft set frameworks, such as Hypersoft and SuperHypersoft Sets. The chapter explores their relationships with existing concepts, offering new tools to handle complex decision-making scenarios with enhanced structural flexibility. The sixth paper (HyperPlithogenic Cubic Set and SuperHyperPlithogenic Cubic Set) introduces the concepts of the HyperPlithogenic Cubic Set and SuperHyperPlithogenic Cubic Set, which extend the Plithogenic Cubic Set by integrating both interval-valued and single-valued fuzzy memberships. These sets leverage multi-attribute aggregation techniques inherent to plithogenic structures, allowing for nuanced representations of uncertainty. Additionally, related constructs such as the HyperPlithogenic Fuzzy Cubic Set, HyperPlithogenic Intuitionistic Fuzzy Cubic Set, and HyperPlithogenic Neutrosophic Cubic Set are explored, further enriching the theoretical and practical applications of this framework. The seventh chapter (L-Neutrosophic Sets and Nonstationary Neutrosophic Sets) extends the foundational concepts of fuzzy sets by integrating Neutrosophic and Plithogenic frameworks. By introducing L-Neutrosophic Sets and Nonstationary Neutrosophic Sets, the study enhances the representation of uncertainty through independent membership components: truth, indeterminacy, and falsity. These advanced constructs also incorporate multi-dimensional and contradictory attributes, providing a robust means of modeling complex decision-making and uncertain data. Plithogenic and Rough Sets, known for generalizing uncertainty modeling and classification, are extended in the eight chapter (Forest HyperPlithogenic and Forest HyperRough Sets) to Forest HyperPlithogenic Sets, Forest SuperHyperPlithogenic Sets, Forest HyperRough Sets, and Forest SuperHyperRough Sets. These frameworks incorporate hierarchical and recursive structures to advance existing set-theoretic paradigms. The chapter explores their applications in multi-level data analysis and uncertainty classification, demonstrating their adaptability to complex systems. Building on Fuzzy, Neutrosophic, and Plithogenic Sets, the tenth chapter (Symbolic HyperPlithogenic Sets) introduces Symbolic HyperPlithogenic Sets and Symbolic n-SuperHyperPlithogenic Sets. These sets incorporate symbolic components and algebraic coefficients, enabling flexible operations within a defined prevalence order. By extending symbolic representation into hyperplithogenic and superhyperplithogenic domains, the chapter opens new pathways for addressing uncertainty and hierarchical complexity in mathematical modeling. Soft Sets, designed to manage uncertainty and imprecision, have evolved through various extensions like Hypersoft Sets and SuperHypersoft Sets. The eleventh chapter (N-SuperHypersoft and Bijective SuperHypersoft Sets) introduces N-SuperHypersoft Sets, N-Treesoft Sets, Bijective SuperHypersoft Sets, and Bijective Treesoft Sets. These new constructs enhance decision-making frameworks by incorporating advanced hierarchical and bijective relationships, building on existing theories and expanding their applications. Plithogenic Sets, known for integrating multi-valued attributes and contradictions, and Rough Sets, which partition data into definable approximations, are combined in the twelfth chapter (Plithogenic Rough Sets) to form Plithogenic Rough Sets. This fusion provides a powerful framework for addressing uncertainty in dynamic and complex decision-making scenarios, offering a novel approach to uncertainty modeling. Expanding on Neutrosophic Sets, which represent truth, indeterminacy, and falsehood, this chapter introduces Plithogenic Duplets and Plithogenic Triplets. These constructs leverage the Plithogenic framework to incorporate attributes, values, and contradiction measures. The thirteenth chapter (Plithogenic Duplets and Triplets) examines their relationships with Neutrosophic Duplets and Triplets, offering new tools for multi-dimensional data representation and decision-making. Building on foundational concepts like Rough Sets and Vague Sets, the fourteenth chapter (SuperRough and SuperVague Sets) introduces SuperRough Sets and SuperVague Sets. These generalized frameworks extend uncertainty modeling by incorporating hierarchical structures. The study also demonstrates that SuperRough Sets can evolve into SuperHyperRough Sets, providing further generalizations for advanced data classification and analysis. The fifteenth chapter (Neutrosophic TreeSoft Expert and ForestSoft Sets) revisits the Neutrosophic TreeSoft Set, which combines the hierarchical structure of TreeSoft Sets with the Neutrosophic framework for uncertainty representation. Additionally, it introduces the Neutrosophic TreeSoft Expert Set, incorporating expert knowledge into the model. The chapter also explores the ForestSoft Set and its extension, the Neutrosophic ForestSoft Set, to provide multi-level, tree-structured approaches for complex data representation and analysis. (shrink)

Recent semantic approaches to scientific structuralism, aiming to make precise the concept of shared structure between models, formally frame a model as a type of set-structure. This framework is then used to provide a semantic account of (a) the structure of a scientific theory, (b) the applicability of a mathematical theory to a physical theory, and (c) the structural realist’s appeal to the structural continuity between successive physical theories. In this paper, I challenge the idea that, to (...) be so used, the concept of a model and so the concept of shared structure between models must be formally framed within a single unified framework, set-theoretic or other. I first investigate the Bourbaki-inspired assumption that structures are types of set-structured systems and next consider the extent to which this problematic assumption underpins both Suppes’ and recent semantic views of the structure of a scientific theory. I then use this investigation to show that, when it comes to using the concept of shared structure, there is no need to agree with French that “without a formal framework for explicating this concept of ‘structure-similarity’ it remains vague, just as Giere’s concept of similarity between models does ...” (French, 2000, Synthese, 125, pp. 103–120, p. 114). Neither concept is vague; either can be made precise by appealing to the concept of a morphism, but it is the context (and not any set-theoretic type) that determines the appropriate kind of morphism. I make use of French’s (1999, From physics to philosophy (pp. 187–207). Cambridge: Cambridge University Press) own example from the development of quantum theory to show that, for both Weyl and Wigner’s programmes, it was the context of considering the ‘relevant symmetries’ that determined that the appropriate kind of morphism was the one that preserved the shared Lie-group structure of both the theoretical and phenomenological models. (shrink)

Giovanni Pico della Mirandola had his 900 Conclusions printed late in 1486, just a few weeks before Pope Innocent VIII attacked thirteen of them. Did Pico intend to provoke the Vatican? If not, what was his aim, what were his means and what was the product? The Conclusions looks like a miscellany, just as Pico described it. But disorder was only on the surface, in line with a purpose explicitly stated: keeping the holiest truths hidden. Pico’s informants about esoteric wisdom (...) included more than two dozen authorities—some named as individuals, others unnamed, some ancient, others medieval—listed in the first of two parts of the Conclusions. Not named at all were contemporaries and near contemporaries who introduced the prince to these sages from the past. (shrink)

In setting up a formal system to specify a grammar formalism, the conventional (mathematical) wisdom is to start with primitives (basic primitive structures) as simple as possible, and then introduce various operations for constructing more complex structures. An alternate approach is to start with complex (more complicated) primitives, which directly capture some crucial linguistic properties and then introduce some general operations for composing these complex structures. These two approaches provide different domains of locality, i.e., domains over which various types of (...) linguistic dependencies can be specified. The latter approach, characterized as complicate locally, simplify globally (CLSG), pushes non‐local dependencies to become local, i.e., they arise in the basic primitive structures to start with.The CLSG approach has led to some new insights into syntactic description, semantic composition, language generation, statistical processing, and psycholinguistic phenomena, all these with possible relevance to the cognitive architecture of language. In this paper, we will describe these results in an introductory manner making use of the framework of lexicalized tree‐adjoining grammar (LTAG), a key example of the CLSG approach, thereby describing the interplay between formal analysis on the one hand and linguistic and processing issues on the other hand. (shrink)

A normative account of global political organization must address three fundamental questions. One concerns the way in which political jurisdictions are to be delimited and their territorial boundaries drawn; another concerns the allocation of powers of sovereignty to those jurisdictions; the third concerns the principles for the distribution of economic benefits and burdens worldwide. The aim of my dissertation is to defend an account of global justice that extends to each of these questions. In doing so, I reject the answers (...) embodied in the prevailing international states system. ;In Chapter One, I consider one of the most sophisticated attempts to defend the states system on grounds of political morality---John Rawls's "The Law of Peoples." I argue that Rawls's defense fails because it is not adequately responsive to its own animating moral ideal, namely the ideal of popular sovereignty. Properly understood, popular sovereignty imposes on global political institutions constraints that are inconsistent with the features of the states system that Rawls defends. These constraints are expressed in two conditions: a deliberativeness condition, which ensures the integrity of the communicative structures required for rational collective will formation; and a pre-commitment condition, which ensures the willing acceptance by individuals of membership in the same polity. Together, these conditions entail a set of political human rights for individuals, and a set of self-determination rights for groups. ;Thomas Pogge has proposed a federative model of global political organization that, suitably modified, is responsive to these rights. His account calls for a federative dispersion of sovereign powers among nested jurisdictions, and incorporates a voluntaristic principle for the demarcation of borders. However, Pogge's defense is incomplete. In Chapter Two, I argue that the ideal of popular sovereignty provides the necessary foundation for his model. The same ideal leads us to reject Pogge's assertion of a universal right to democratic governance. ;In Chapter Three I articulate and defend a conception of global distributive justice that mandates transfers of wealth from more- to less-affluent societies with the disjunctive target of either immigration-pressure equilibrium---roughly, the point at which all economically motivated applications for immigration are granted---or maximal human development rates for the worst-off societies worldwide. (shrink)

Standard microbial evolutionary ontology is organized according to a nested hierarchy of entities at various levels of biological organization. It typically detects and defines these entities in relation to the most stable aspects of evolutionary processes, by identifying lineages evolving by a process of vertical inheritance from an ancestral entity. However, recent advances in microbiology indicate that such an ontology has important limitations. The various dynamics detected within microbiological systems reveal that a focus on the most stable entities (or (...) features of entities) over time inevitably underestimates the extent and nature of microbial diversity. These dynamics are not the outcome of the process of vertical descent alone. Other processes, often involving causal interactions between entities from distinct levels of biological organisation, or operating at different time scales, are responsible not only for the destabilisation of pre-existing entities, but also for the emergence and stabilisation of novel entities in the microbial world. In this article we consider microbial entities as more or less stabilised functional wholes, and sketch a network-based ontology that can represent a diverse set of processes including, for example, as well as phylogenetic relations, interactions that stabilise or destabilise the interacting entities, spatial relations, ecological connections, and genetic exchanges. We use this pluralistic framework for evaluating (i) the existing ontological assumptions in evolution (e.g. whether currently recognized entities are adequate for understanding the causes of change and stabilisation in the microbial world), and (ii) for identifying hidden ontological kinds, essentially invisible from within a more limited perspective. We propose to recognize additional classes of entities that provide new insights into the structure of the microbial world, namely “processually equivalent” entities, “processually versatile” entities, and “stabilized” entities. (shrink)

This paper is an exploration of how we do things with music—that is, the way that we use music as an esthetic technology to enact micro-practices of emotion regulation, communicative expression, identity construction, and interpersonal coordination that drive core aspects of our emotional and social existence. The main thesis is: from birth, music is directly perceived as an affordance-laden structure. Music, I argue, affords a sonic world, an exploratory space or nested acoustic environment that further affords possibilities for, (...) among other things, (1) emotion regulation and (2) social coordination. When we do things with music, we are engaged in the work of creating and cultivating the self, as well as creating and cultivating a shared world that we inhabit with others. I develop this thesis by first introducing the notion of a musical affordance . Next, I look at how emotional affordances in music are exploited to construct and regulate emotions. I summon empirical research on neonate music therapy to argue that this is something we emerge from the womb knowing how to do. I then look at social affordances in music, arguing that joint attention to social affordances in music alters how music is both perceived and appropriated by joint attenders within social listening contexts. In support, I describe the experience of listening to and engaging with music in a live concert setting. Thinking of music as an affordance-laden structure thus reaffirms the crucial role that music plays in constructing and regulating emotional and social experiences in everyday life. (shrink)

We employ a recently developed methodology -- called "structural refinement" -- to extract nested sequent systems for a sizable class of intuitionistic modal logics from their respective labelled sequent systems. This method can be seen as a means by which labelled sequent systems can be transformed into nested sequent systems through the introduction of propagation rules and the elimination of structural rules, followed by a notational translation. The nested systems we obtain incorporate propagation rules that are parameterized (...) with formal grammars, and which encode certain frame conditions expressible as first-order Horn formulae that correspond to a subclass of the Scott-Lemmon axioms. We show that our nested systems are sound, cut-free complete, and admit hp-admissibility of typical structural rules. (shrink)

Este ensaio examina o relacionamento possível entre o pensamento de Martin Heidegger enquanto emerge no Zollikon Seminaire na sua troca de idéias com Medard Boss e a perspectiva da psicanálise como aparece através do prisma da releitura de Freud oferecido por Jacques Lacan. Heidegger entende Freud como vítima de uma compreensão positivista da ciência que procura explicar o comportamento humano patológico por um complexo de causas discerníveis conscientemente. Quando determinados fenômenos não podem ser explicados desta maneira, Freud postula um jogo (...) de causas psíquicas que não são conscientes, cuja soma ele chama o "inconsciente". Desde que todos os fenômenos humanos são, para Heidegger, discerníveis via uma profunda fenomenologia do ser humano como o ser-no-mundo, a construção hipotética de Freud é desnecessária e, a longo prazo, perniciosa. Mas Lacan propõe uma nova maneira de compreender o inconsciente descoberto por Freud, a saber, que não deve ser entendido como um sistema físico de forças hidráulicas, mas como um processo que seja estruturado como um idioma. A pergunta levantada neste ensaio é se Heidegger seria ou não igualmente hostil à hipótese de Freud, apresentada a ele dentro da forma de Lacan, como algo "estruturado como um idioma". O ensaio sugere que a resposta poderia ser "provavelmente não". Baseado num exemplo clínico altamente simplificado, este ensaio esforça-se para mostrar a compatibilidade entre determinados conceitos básicos de Heidegger e diversos, de Lacan, em especial as noções da verdade e da liberdade.This paper examines the possible relationship between the thought of Martin Heidegger as it emerges in the Zollikon Seminaire through his exchange with Medard Boss and the perspective of psychoanalysis as it appears through the prism of Jacques Lacan's rereading of Freud. Heidegger takes Freud to be victim of a positivist conception of science that seeks to explain pathological human behaviour by a complex of consciously discernible causes. When certain phenomena cannot be explained in this way, Freud postulates a set of psychic causes that are not conscious, the sum total of which he calls the "unconscious." Since all human phenomena are, for Heidegger, discernible through a thorough-going phenomenology of human being as being-in-the-world, Freud's hypothetical construct is unnecessary and, in the long run, pernicious. But Lacan proposes a new way to understand the unconscious that Freud discovered, namely, that it is not to be thought of as analogous to a physical system of hydraulic forces but rather to a process that is structured like a language. The question raised in the paper is whether or not Heidegger would have been equally hostile to Freud's hypothesis, if it had been presented to him in Lacanian fashion as something "structured like a language". The paper suggests that the answer could be "probably not". On the basis of a highly simplified clinical example, it endeavors to show the compatibility between certain basic Heideggerean concepts and several of those essential to Lacan, especially the notions of truth and freedom. (shrink)

The paper essentially shows that the paraconsistent logicDR satisfies the depth relevance condition. The systemDR is an extension of the systemDK of [7] and the non-triviality of a dialectical set theory based onDR has been shown in [3]. The depth relevance condition is a strengthened relevance condition, taking the form: If DR- AB thenA andB share a variable at the same depth, where the depth of an occurrence of a subformulaB in a formulaA is roughly the number of nested (...) ''s required to reach the occurrence ofB inA. The method of proof is to show that a model structureM consisting of {M 0 , M1, ..., M}, where theM i s are all characterized by Meyer''s 6-valued matrices (c. f, [2]), satisfies the depth relevance condition. Then, it is shown thatM is a model structure for the systemDR. (shrink)

Many efforts are focused on transformation to wellbeing economies as economies oriented towards equity, social justice, and human wellbeing in a flourishing natural environment (wellbeing economics). Drawing from analysis of innovations associated with these efforts, we emerge a framework of wellbeing-oriented ‘economic operating infrastructure’ (EOI). This is presented as a typology of six core types of economic transformation innovations nested from innovations with the broadest reach (narratives) to the most specific (products and services). Development of the typology was guided (...) by a set of wellbeing economies values that help in identifying which innovations to include. The innovations were identified by research on the internet, technical reports, and published articles. The typology elements are: innovations in economic narratives; governance; financing mechanisms; exchange mechanisms; business structures; and the products and services derived from them. Examples are presented in each category to illustrate how this infrastructure is emerging in alignment with establishing wellbeing economies. This exploratory and descriptive typology provides a preliminary framework for developing a strategic approach to economic transformation through wellbeing economic infrastructure development. Four EOI-based activities are identified to accelerate this transformation. (shrink)

We give an example of a dense o-minimal structure in which there is a definable quotient that cannot be eliminated, even after naming parameters. Equivalently, there is an interpretable set which cannot be put in parametrically definable bijection with any definable set. This gives a negative answer to a question of Eleftheriou, Peterzil, and Ramakrishnan. Additionally, we show that interpretable sets in dense o-minimal structures admit definable topologies which are “tame” in several ways: (a) they are Hausdorff, (b) (...) every point has a neighborhood which is definably homeomorphic to a definable set, (c) definable functions are piecewise continuous, (d) definable subsets have finitely many definably connected components, and (e) the frontier of a definable subset has lower dimension than the subset itself. (shrink)

We investigate some logics which use the concept of minimal models in their definition. Minimal objects are widely used in Logic and Computer Science. They are applied in the context of Inductive Definitions, Logic Programming and Artificial Intelligence. An example of logic which uses this concept is the MIN logic due to van Benthem [20]. He shows that MIN is equivalent to the Least Fixed Point logic in expressive power. In [6], we extended MIN to the MIN Logic and proved (...) it is equivalent to second-order logic in expressive power. Here, we exhibit a fragment of MIN, the MINΔ logic, which is more expressive than LFP, less expressive than MIN and closed under boolean connectives and first-order quantification. In order to do this, in the Section 2, we prove that the Downward Löwenheim-Skolem Theorem holds for arbitrary countable sets of LFP-formulas by showing that every infinite structure has a countable LFP-substructure. The method may be used to generalize this theorem to any set of LFP-formulas. We also analyse the expressive power of the Nested Abnormality Theories of Lifschitz, another formalism based on minimal models used in Artificial Intelligence, and we demonstrate that for each second-order theory Γ there is a NAT which is a conservative extension of Γ. We give a translation from second-order sentences into such NATs which is linear in the size of the sentence in prenex normal form. Finally, we establish a hierarchy of expressiveness of these logics that deal with the concept of minimal models. (shrink)

This paper presents new results from a detailed study of the structure of autocatalytic sets. We show how autocatalytic sets can be decomposed into smaller autocatalytic subsets, and how these subsets can be identified and classified. We then argue how this has important consequences for the evolvability, enablement, and emergence of autocatalytic sets. We end with some speculation on how all this might lead to a generalized theory of autocatalytic sets, which could possibly be applied (...) to entire ecologies or even economies. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:“An Equivocal Couple Overwhelmed by Life”A Phenomenological Analysis of PregnancySara HeinämaaTwo conceptions of human generativity prevail in contemporary feminist philosophy. First, several contributors argue that the experience of pregnancy, when analyzed by phenomenological tools, undermines several distinctions that are central to Western philosophy, most importantly the subject-object distinction and the self-other and own-alien distinctions. This line of argument was already outlined by Iris Marion Young in her influential essay (...) “Pregnant Embodiment: Subjectivity and Alienation” (1984). The other dominant argument is related to the first one, and it states that organic birth is the event that establishes the first experiential separation between the self and the other. On this understanding, the mother-fetus relation would not involve any relations between two corporeal selves; all such relations would be postnatal. This notion has been defended, for example, by Christine Schües (1997; 2000) and Johanna Oksala (2003).1On the other hand, classical phenomenology is dominated by the idea that the rigorous first-person methodology that is essential to phenomenology dictates that the sense of birth must be studied primarily by reflection on the structures of our own recollection or memory. Consequently, the primary sense of human birth would be that of an unattainable limit. This is argued on the basis of the existential fact that we all are born but cannot recall our own birth, or else on the basis of the transcendental fact that the structure [End Page 31] of retention ties each living present to an earlier one and implies that the transcendental ego cannot be subject to generation.2 From this perspective, all analyses and reflections of the experiences of labor, gestation, and pregnancy would be secondary since the sense of birth that these experiences involve is the nativity of another human being and not the nativity of the reflecting self.This paper challenges both the feminist and the classical phenomenological approach. I maintain that careful phenomenological analyses of the experience of pregnancy undermine both notions. Such analyses show, on the one hand, that pregnancy does not imply a nondistinction or self-other fusion but on the contrary involves a specific self-other divide. At the same time, they demonstrate that the sense of birth is more complex than the classical recollection-paradigm suggests and that it includes more components than the signification of an unattainable limit. A proper phenomenology of birth must take into account not only the universal fact that we all are born, but also the equally universal fact that each of us is born from another human being, that is, some other human subject.3 This other human being who “gave” us birth or “from whose flesh we were born” provides us with a unique perspective on our own past, beyond the limits of our own recollection. Her perspective is incomparable to any other external perspective; rather than simply giving us an additional third-person viewpoint on our own organic birth, this one person is able to open a second-person perspective on our pre- and postnatal life and the transition between them—all of which is beyond our own recollection.My argument proceeds by the following steps:First, I develop a fresh discourse on the experience of pregnancy, by studying a set of remarks to be found in Julia Kristeva’s postphenomenological discourse on maternity, on the one hand, and in Simone de Beauvoir’s existential-phenomenological discourse on feminine embodiment, on the other hand. I use these remarks as leading clues for a novel phenomenological study of the experience of pregnancy.4 Contra Young’s influential account mentioned above, I argue that gestation, as experienced by women who live it in the first person, includes a separation between two sensory-motor beings in a nesting relation: the pregnant self and the embryonic other. The alternative account that I provide hinges on my analysis of the experience of fetal movements and the role of touch-sensations and kinesthetic sensations in such experiences. Ultimately, I argue that pregnancy does not erode the self-other boundary or the own-alien boundary but reestablishes both divisions.Second, I compare my account of the experience of pregnancy to Merleau... (shrink)

Experience in thesis and peer reviewing revealed that most authors have much difficulty in presenting the structural supports of their study. This becomes evident in both their oral and written scientific reports in which little congruency or lack of it is frequently observed between title of the study, general objective (aim), and the hypothesis. Likewise, confusion is usually present when distinguishing purpose from objective when presenting the research problem. In order to aid in approaching the mentioned difficulties an exercise termed (...) Trivium is proposed and explained. This term that designated the main subjects in scholar formation during medieval times, is used to designate the effective coupling of the above three structural elements (title, objective, hypothesis) that, properly used, confer epistemological basis to their scientific reports. Likewise, in order to reinforce this exercise a Quadrivium is recommended in which a fourth structural element is added, i.e., a premise, as the theoretical basis that precisely indicates the purpose of the study and provides immediate support to the hypothesis. Examples to illustrate these exercises are provided. Abiding by this logic may significantly aid science students and some open-minded researchers in adequately constructing their scientific reports, while avoiding frustrating experiences due to uncomfortable observations by peers on their manuscripts. (shrink)

We start by studying the relationship between two invariants isolated by Shelah, the sets of good and approachable points. As part of our study of these invariants, we prove a form of “singular cardinal compactness” for Jensen's square principle. We then study the relationship between internally approachable and tight structures, which parallels to a certain extent the relationship between good and approachable points. In particular we characterise the tight structures in terms of PCF theory and use our characterisation to (...) prove some covering results for tight structures, along with some results on tightness and stationary reflection. Finally, we prove some absoluteness theorems in PCF theory, deduce a covering theorem, and apply that theorem to the study of precipitous ideals. (shrink)