An overview of contemporary part-whole theories, with reference to both their axiomatic developments and their philosophical underpinnings.

Given the fundamental role that concepts play in theories of cognition, philosophers and cognitive scientists have a common interest in concepts. Nonetheless, there is a great deal of controversy regarding what kinds of things concepts are, how they are structured, and how they are acquired. This chapter offers a detailed high-level overview and critical evaluation of the main theories of concepts and their motivations. Taking into account the various challenges that each theory faces, the chapter also presents a novel approach (...) to concepts that is organized around two ideas. The first is a pluralistic view of differing types of conceptual structure. The second is a model that treats concepts as atomic representations that are linked to various types of conceptual structures. (shrink)

Peter Ludlow shows how word meanings are much more dynamic than we might have supposed, and explores how they are modulated even during everyday conversation. The resulting view is radical, and has far-reaching consequences for our political and legal discourse, and for enduring puzzles in the foundations of semantics, epistemology, and logic.

The idea that qualities can be had partly or to an intermediate degree is controversial among contemporary metaphysicians, but also has a considerable pedigree among philosophers and scientists. In this paper, we first aim to show that metaphysical sense can be made of this idea by proposing a partial taxonomy of metaphysical accounts of graded qualities, focusing on three particular approaches: one which explicates having a quality to a degree in terms of having a property with an in-built degree, another (...) based on the idea that instantiation admits of degrees, and a third which derives the degree to which a quality is had from the aspects of multi-dimensional properties. Our second aim is to demonstrate that the choice between these accounts can make a substantial metaphysical difference. To make this point, we rely on two case studies (involving quantum observables and values) in which we apply the accounts in order to model apparent cases of metaphysical gradedness. (shrink)

The term fuzzy logic is used in this paper to describe an imprecise logical system, FL, in which the truth-values are fuzzy subsets of the unit interval with linguistic labels such as true, false, not true, very true, quite true, not very true and not very false, etc. The truth-value set, , of FL is assumed to be generated by a context-free grammar, with a semantic rule providing a means of computing the meaning of each linguistic truth-value in as a (...) fuzzy subset of [0, 1].Since is not closed under the operations of negation, conjunction, disjunction and implication, the result of an operation on truth-values in requires, in general, a linguistic approximation by a truth-value in . As a consequence, the truth tables and the rules of inference in fuzzy logic are (i) inexact and (ii) dependent on the meaning associated with the primary truth-value true as well as the modifiers very, quite, more or less, etc. (shrink)

We argue that artificial networks are explainable and offer a novel theory of interpretability. Two sets of conceptual questions are prominent in theoretical engagements with artificial neural networks, especially in the context of medical artificial intelligence: Are networks explainable, and if so, what does it mean to explain the output of a network? And what does it mean for a network to be interpretable? We argue that accounts of “explanation” tailored specifically to neural networks have ineffectively reinvented the wheel. In (...) response to, we show how four familiar accounts of explanation apply to neural networks as they would to any scientific phenomenon. We diagnose the confusion about explaining neural networks within the machine learning literature as an equivocation on “explainability,” “understandability” and “interpretability.” To remedy this, we distinguish between these notions, and answer by offering a theory and typology of interpretation in machine learning. Interpretation is something one does to an explanation with the aim of producing another, more understandable, explanation. As with explanation, there are various concepts and methods involved in interpretation: Total or Partial, Global or Local, and Approximative or Isomorphic. Our account of “interpretability” is consistent with uses in the machine learning literature, in keeping with the philosophy of explanation and understanding, and pays special attention to medical artificial intelligence systems. (shrink)

The current study represents an integrated model of explicit and implicit offensive language taxonomy. First, it focuses on a definitional revision and enrichment of the explicit offensive language taxonomy by reviewing the collection of available corpora and comparing tagging schemas applied there. The study relies mainly on the categories originally proposed by Zampieri et al. (2019) in terms of offensive language categorization schemata. After the explanation of semantic differences between particular concepts used in the tagging systems and the analysis of (...) theoretical frameworks, a finite set of classes is presented, which cover aspects of offensive language representation along with linguistically sound explanations (Lewandowska-Tomaszczyk et al. 2021). In the analytic procedure, offensive from non-offensive discourse is first distinguished, with the question of offence Target and the following categorization levels and sublevels. Based on the relevant data generated from Sketch Engine (https://www.sketchengine.eu/ententen-english-corpus/), we propose the concept of offensive language as a superordinate category in our system with a number of hierarchically arranged 17 subcategories. The categories are taxonomically structured into 4 levels and verified with the use of neural-based (lexical) embeddings. Together with a taxonomy of implicit offensive language and its subcategorization levels which has received little scholarly attention until now, the categorization is exemplified in samples of offensive discourses in selected English social media materials, i.e., publicly available 25 web-based hate speech datasets (consult Appendix 1 for a complete list). The offensive category levels (types of offence, targets, etc.) and aspects (offensive language property clusters) as well as the categories of explicitness and implicitness are discussed in the study and the computationally verified integrated explicit and implicit offensive language taxonomy proposed in the study. (shrink)

The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, (...) a trilattice of truth values – a specific algebraic structure with information ordering and two distinct logical orderings, one for truth and another for falsity. Each logical order not only induces its own logical vocabulary, but determines also its own entailment relation. We consider both semantic and syntactic ways of formalizing these relations and construct various logical calculi. (shrink)

In this paper we recall, improve, and extend several definitions, properties and applications of our previous 2019 research referred to NeutroAlgebras and AntiAlgebras (also called NeutroAlgebraic Structures and respectively AntiAlgebraic Structures). Let <A> be an item (concept, attribute, idea, proposition, theory, etc.). Through the process of neutrosphication, we split the nonempty space we work on into three regions {two opposite ones corresponding to <A> and <antiA>, and one corresponding to neutral (indeterminate) <neutA> (also denoted <neutroA>) between the opposites}, which may (...) or may not be disjoint – depending on the application, but they are exhaustive (their union equals the whole space). A NeutroAlgebra is an algebra which has at least one NeutroOperation or one NeutroAxiom (axiom that is true for some elements, indeterminate for other elements, and false for the other elements). A Partial Algebra is an algebra that has at least one Partial Operation, and all its Axioms are classical (i.e. axioms true for all elements). Through a theorem we prove that NeutroAlgebra is a generalization of Partial Algebra, and we give examples of NeutroAlgebras that are not Partial Algebras. We also introduce the NeutroFunction (and NeutroOperation). (shrink)

It has seemed natural to model phenomena related to vagueness in terms of graded membership. However, so far no satisfactory answer has been given to the question of what graded membership is nor has any attempt been made to describe in detail a procedure for determining degrees of membership. We seek to remedy these lacunae by building on recent work on typicality and graded membership in cognitive science and combining some of the results obtained there with a version of the (...) conceptual spaces framework. (shrink)

This paper is an introduction to a virtual special issue of AI and Law exploring the legacy of the influential HYPO system of Rissland and Ashley. The papers included are: Arguments and cases: An inevitable intertwining, BankXX: Supporting legal arguments through heuristic retrieval, Modelling reasoning with precedents in a formal dialogue Game, A note on dimensions and factors, An empirical investigation of reasoning with legal cases through theory construction and application, Automatically classifying case texts and predicting outcomes, A factor-based definition (...) of precedential constraint and An improved factor based approach to precedential constraint. After describing HYPO, in this introduction to the special issue I look at various aspects of its influence on AI and Law: the developments led by Rissland at Amherst; the developments led by Ashley in Pittsburgh; the expression of these ideas in terms of rule based systems, and their subsequent formalisation; value based theories, which were inspired by a critique of HYPO; and contemporary approaches which revive the idea of dimensions. (shrink)

We defend a set of acceptance rules that avoids the lottery paradox, that is closed under classical entailment, and that accepts uncertain propositions without ad hoc restrictions. We show that the rules we recommend provide a semantics that validates exactly Adams’ conditional logic and are exactly the rules that preserve a natural, logical structure over probabilistic credal states that we call probalogic. To motivate probalogic, we first expand classical logic to geo-logic, which fills the entire unit cube, and then we (...) project the upper surfaces of the geo-logical cube onto the plane of probabilistic credal states by means of standard, linear perspective, which may be interpreted as an extension of the classical principle of indifference. Finally, we apply the geometrical/logical methods developed in the paper to prove a series of trivialization theorems against question-invariance as a constraint on acceptance rules and against rational monotonicity as an axiom of conditional logic in situations of uncertainty. (shrink)

This paper addresses theoretical problems arising from the vagueness of language terms, and intuitions of the vagueness of the concepts to which they refer. It is argued that the central intuitions of prototype theory are sufficient to account for both typicality phenomena and psychological intuitions about degrees of membership in vaguely defined classes. The first section explains the importance of the relation between degrees of membership and typicality (or goodness of example) in conceptual categorization. The second and third section address (...) arguments advanced by Osherson and Smith (1997), and Kamp and Partee (1995), that the two notions of degree of membership and typicality must relate to fundamentally different aspects of conceptual representations. A version of prototype theory—the Threshold Model—is proposed to counter these arguments and three possible solutions to the problems of logical selfcontradiction and tautology for vague categorizations are outlined. In the final section graded membership is related to the social construction of conceptual boundaries maintained through language use. (shrink)

This paper considers Kamp and Partee's account of graded membership within a conceptual spaces framework and puts the account to the test in the domain of colors. Three experiments are reported that are meant to determine, on the one hand, the regions in color space where the typical instances of blue and green are located and, on the other hand, the degrees of blueness/greenness of various shades in the blue–green region as judged by human observers. From the locations of the (...) typical blue and typical green regions in conjunction with Kamp and Partee's account follow degrees of blueness/greenness for the color shades we are interested in. These predicted degrees are compared with the judged degrees, as obtained in the experiments. The results of the comparison support the account of graded membership at issue. (shrink)

We outline the rationale and preliminary results of using the State Context Property (SCOP) formalism, originally developed as a generalization of quantum mechanics, to describe the contextual manner in which concepts are evoked, used, and combined to generate meaning. The quantum formalism was developed to cope with problems arising in the description of (1) the measurement process, and (2) the generation of new states with new properties when particles become entangled. Similar problems arising with concepts motivated the formal treatment introduced (...) here. Concepts are viewed not as fixed representations, but entities existing in states of potentiality that require interaction with a context---a stimulus or another concept---to `collapse' to observable form as an exemplar, prototype, or other (possibly imaginary) instance. The stimulus situation plays the role of the measurement in physics, acting as context that induces a change of the cognitive state from superposition state to collapsed state. The collapsed state is more likely to consist of a conjunction of concepts for associative than analytic thought because more stimulus or concept properties take part in the collapse. We provide two contextual measures of conceptual distance---one using collapse probabilities and the other weighted properties---and show how they can be applied to conjunctions using the pet fish problem. (shrink)

This paper is concerned with a version of Kamp and Partee's account of graded membership that relies on the conceptual spaces framework. Three studies are reported, one to construct a particular shape space, one to detect which shapes representable in that space are typical for certain sorts of objects, and one to elicit degrees of category membership for the various shapes from which the shape space was constructed. Taking Kamp and Partee's proposal as given, the first two studies allowed us (...) to predict the degrees to which people would judge shapes representable in the space to be members of certain categories. These predictions were compared with the degrees that were measured in the third study. The comparison yielded a test of the account of graded membership at issue. The outcome of this test was found to support the conceptual spaces version of Kamp and Partee's account of graded membership. (shrink)

Edgington has proposed a solution to the sorites paradox in terms of ‘verities’, which she defines as degrees of closeness to clear truth. Central to her solution is the assumption that verities are formally probabilities. She is silent on what verities might derive from and on why they should be probabilities. This paper places Edgington’s solution in the framework of a spatial approach to conceptualization, arguing that verities may be conceived of as deriving from how our concepts relate to each (...) other. Building on work by Kamp and Partee, this paper further shows how verities, thus conceived of, may plausibly be assumed to have probabilistic structure. The new interpretation of verities is argued to also help answer the question of what the verities of indicative conditionals are, a question which Edgington leaves open. Finally, the question of how to accommodate higher-order vagueness, given this interpretation, is addressed. (shrink)

The canonical version of possible worlds semantics for story prefixes is due to David Lewis. This paper reassesses Lewis's theory and draws attention to some novel problems for his account.

A critical survey of the fundamental philosophical issues in the logic and formal ontology of space, with special emphasis on the interplay between mereology (the theory of parthood relations), topology (broadly understood as a theory of qualitative spatial relations such as continuity and contiguity), and the theory of spatial location proper.

The paper first introduces a cube of opposition that associates the traditional square of opposition with the dual square obtained by Piaget’s reciprocation. It is then pointed out that Blanché’s extension of the square-of-opposition structure into an conceptual hexagonal structure always relies on an abstract tripartition. Considering quadripartitions leads to organize the 16 binary connectives into a regular tetrahedron. Lastly, the cube of opposition, once interpreted in modal terms, is shown to account for a recent generalization of formal concept analysis, (...) where noticeable hexagons are also laid bare. This generalization of formal concept analysis is motivated by a parallel with bipolar possibility theory. The latter, albeit graded, is indeed based on four graded set functions that can be organized in a similar structure. (shrink)

In order to explore the quantifiability and formalizability of uncertainty a wide range of uncertainties are investigated. They are summarized under eight main categories: factual, possibilistic, metadoxastic, agential, interactive, value, structural, and linguistic uncertainty. This includes both classical uncertainty and the uncertainties commonly called great, deep, or radical. For five of the eight types of uncertainty, both quantitative and non-quantitative formalizations are meaningful and available. For one of them (interactive uncertainty), only non-quantitative formalizations seem to be meaningful, and for two (...) (agential and structural uncertainty) neither quantitative nor non-quantitative formalization seems to be a useful approach. (shrink)

Understanding novel phrases (e.g. upside‐down daisy) and classifying objects in categories named by phrases ought to have common properties, but you'd never know it from current theories. The best candidate for both jobs is the Theory Theory, but it faces difficulties when theories are impoverished. A potential solution is a dual approach that couples theories (representations‐about categories) with fixed mentalese expressions (representations‐of categories). Both representations combine information in parallel when understanding phrases. Although there are objections to the notion that theories (...) can combine, some of them lose their force when applied to a suitable dual model. (shrink)

A novel account of semantic information is proposed. The gist is that structural correspondence, analysed in terms of similarity, underlies an important kind of semantic information. In contrast to extant accounts of semantic information, it does not rely on correlation, covariation, causation, natural laws, or logical inference. Instead, it relies on structural similarity, defined in terms of correspondence between classifications of tokens into types. This account elucidates many existing uses of the notion of information, for example, in the context of (...) scientific models and structural representations in cognitive science. It is poised to open a new research program concerned with various kinds of semantic information, its functions, and its measurement. (shrink)

This paper is a contribution to Mathematical fuzzy logic, in particular to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and Δ-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate on five kinds of distinguished semantics for these logics–namely the class of algebras defined over the real unit (...) interval, the rational unit interval, the hyperreals , the strict hyperreals and finite chains, respectively–and we survey the known completeness methods and results for prominent logics. We also obtain new interesting relations between the real, rational and hyperreal semantics, and good characterizations for the completeness with respect to the semantics of finite chains. Finally, all completeness properties and distinguished semantics are also considered for the first-order versions of the logics where a number of new results are proved. (shrink)

The term “vagueness” describes a property of natural concepts, which normally have fuzzy boundaries, admit borderline cases, and are susceptible to Zeno's sorites paradox. We will discuss the psychology of vagueness, especially experiments investigating the judgment of borderline cases and contradictions. In the theoretical part, we will propose a probabilistic model that describes the quantitative characteristics of the experimental finding and extends Alxatib's and Pelletier's () theoretical analysis. The model is based on a Hopfield network for predicting truth values. Powerful (...) as this classical perspective is, we show that it falls short of providing an adequate coverage of the relevant empirical results. In the final part, we will argue that a substantial modification of the analysis put forward by Alxatib and Pelletier and its probabilistic pendant is needed. The proposed modification replaces the standard notion of probabilities by quantum probabilities. The crucial phenomenon of borderline contradictions can be explained then as a quantum interference phenomenon. (shrink)

On two standard views of vagueness, vagueness as to whether Harry is bald entails that nobody knows whether Harry is bald—either because vagueness is a type of missing truth, and so there is nothing to know, or because vagueness is a type of ignorance, and so even though there is a truth of the matter, nobody can know what that truth is. Vagueness as to whether Harry is bald does entail that nobody clearly knows that Harry is bald and that (...) nobody clearly knows that Harry is not bald. But it does not entail that nobody knows that Harry is bald or that nobody knows that Harry is not bald. Hence, the two standard views of vagueness are mistaken. (shrink)

Bottom of the Pyramid organizations are the ones that develop a set of capabilities that contribute to create short- and long-term sustainability values inside and outside the boundaries of BoP ecosystems. Capabilities have an important role in BoP organizations’ strategies that aim to solve BoP issues. Notwithstanding its developments, BoP research still lacks theoretical contributions for the analysis of organizations. We suggest special attention to the need of advancing knowledge on capabilities of BoP organizations because this field is scattered and (...) fragmented, misinterpreted, and still underdeveloped in the literature. We oriented our research formulating and seeking answers to our main question on what are the capabilities needed to enable organizations to create sustainability values in BoP ecosystems? We conducted an integrative review of BoP research for the period from 1998 to 2019, and we found 22 key capabilities of BoP organizations. We organized the capabilities into four major categories including BoP Responsible Consumption, BoP Responsible Business Model, BoP Responsible Management, and BoP Responsible Innovation. We advanced propositions and discussions regarding the capabilities and major categories’ popularity, interdependence and combination, short- and long-term temporal functions, sustainability roles, and effectiveness to address BoP issues. Our article organizes the field of capabilities of BoP organizations; advances contributions and implications for management, organizations, and policymaking; and opens fruitful avenues for future research. (shrink)

The purpose of this study is to propose new similarity measures namely rough variational coefficient similarity measure under the rough neutrosophic environment. The weighted rough variational coefficient similarity measure has been also defined. The weighted rough variational coefficient similarity measures between the rough ideal alternative and each alternative are xxxxx calculated to find the best alternative. The ranking order of all the alternatives can be determined by using the numerical values of similarity measures. Finally, an illustrative example has been provided (...) to show the effectiveness and validity of the proposed approach. Comparisons of decision results of existing rough similarity measures have been provided. (shrink)

Fuzzy logics are many-valued logics that are well suited to reasoning in the context of vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse areas such as fuzzy control, fuzzy databases, and fuzzy mathematics. This book provides an accessible and up-to-date introduction to this fast-growing and increasingly popular area. It focuses in particular on the development and applications of "proof-theoretic" presentations of fuzzy logics; the result of more than ten years of intensive work by researchers (...) in the area, including the authors. In addition to providing alternative elegant presentations of fuzzy logics, proof-theoretic methods are useful for addressing theoretical problems and developing efficient deduction and decision algorithms. Proof-theoretic presentations also place fuzzy logics in the broader landscape of non-classical logics, revealing deep relations with other logics studied in Computer Science, Mathematics, and Philosophy. The book builds methodically from the semantic origins of fuzzy logics to proof-theoretic presentations such as Hilbert and Gentzen systems, introducing both theoretical and practical applications of these presentations. (shrink)

We propose a theory for modeling concepts that uses the state-context-property theory (SCOP), a generalization of the quantum formalism, whose basic notions are states, contexts and properties. This theory enables us to incorporate context into the mathematical structure used to describe a concept, and thereby model how context influences the typicality of a single exemplar and the applicability of a single property of a concept. We introduce the notion `state of a concept' to account for this contextual influence, and show (...) that the structure of the set of contexts and of the set of properties of a concept is a complete orthocomplemented lattice. The structural study in this article is a preparation for a numerical mathematical theory of concepts in the Hilbert space of quantum mechanics that allows the description of the combination of concepts. (shrink)

In this thesis, I will defend a new kind of compatibilist account of free action, indirect conscious control compatibilism (or indirect compatibilism for short), and argue that some of our actions are free according to it. My argument has three components, and involves the development of a brand new tool for experimental philosophy, and the use of cognitive neuroscience. The first component of the argument shows that compatibilism (of some kind) is a conceptual truth. Contrary to the current orthodoxy in (...) the free will literature, which is that our concept of free will is an incompatibilist concept - a concept according to which we have free will only if determinism is false - I will show that our concept of free will is in fact a compatibilist concept - a concept according to which we can have free will even if determinism is true - and I do so using a new experimental philosophy methodology inspired by two-dimensional semantics. -/- Of course, even if our concept of free will is a compatibilist concept, this does not mean that there are any free actions in the world: the current empirical evidence from the brain sciences appears to show that there might be no, or very few, free actions in the world, even on many compatibilist understandings of what it would take for there to be free will. The second component of the argument addresses this concern by extending our understanding of compatibilism. Agents act freely either when their actions are caused by compatibilistically acceptable psychological processes, or are indirectly caused by those same processes. Hence the name of my account: indirect compatibilism. -/- The final component of the argument defends my new account against some interesting objections and provides evidence from cognitive neuroscience that some of our actions count as free by the lights of indirect compatibilism. (shrink)

This paper is devoted to present Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method for multi-attribute group decision making under rough neutrosophic environment. The concept of rough neutrosophic set is a powerful mathematical tool to deal with uncertainty, indeterminacy and inconsistency. In this paper, a new approach for multi-attribute group decision making problems is proposed by extending the TOPSIS method under rough neutrosophic environment. Rough neutrosophic set is characterized by the upper and lower approximation operators and the (...) pair of neutrosophic sets that are characterized by truth-membership degree, indeterminacy membership degree, and falsity membership degree. In the decision situation, ratings of alternatives with respect to each attribute are characterized by rough neutrosophic sets that reflect the decision makers’ opinion. Rough neutrosophic weighted averaging operator has been used to aggregate the individual decision maker’s opinion into group opinion for rating the importance of attributes and alternatives. Finally, a numerical example has been provided to demonstrate the applicability and effectiveness of the proposed approach. (shrink)

Two experiments are reported which demonstrated intransitivity in category judgments, thus challenging a widely held assumption that the relation between categorized sets is one of class inclusion. Subjects consistently accepted the truth of certain category statements, in spite of being aware of the existence of counterexamples. Implications for semantic memory theory are discussed.

Many results have been obtained on isolated graphs and complete graphs. In this paper, a necessary and sufficient condition will be proved for a single valued neutrosophic graph to be an isolated single valued neutrosophic graph.

The main purpose of this study is to probe into the human capacity of understanding systems and defects in human knowledge of the world. The study addresses the greyness levels and systems levels and explains why the world cannot be perceived as a purely white or black structure. It also clarifies why human knowledge of systems always remains grey. The investigation relies on logical and deductive reasoning and uses the theoretical foundations of systems thinking and Boulding’s systems hierarchy. The most (...) important argument that this study advances is that human knowledge, in any form or under any circumstances, is grey and incomplete and will remain grey. Because the notion of “perfect knowledge” is ambiguous given human epistemic limits, any proportion of knowledge is incomplete and prone to change. Less complexity could lead to more accurate predications, but even in the simplest forms of systems, reaching perfect knowledge seems to be an unwarranted claim. Furthermore, because our perception of past events is incomplete, we cannot predict the future with certainty, as a result of which both the past and the future appear grey to us. The world, as an integrated system, is neither black nor white, but it remains grey, and the systems partially recognized by humans are part of the grey world. Gaining knowledge and increasing discoveries only contribute to the grey systems that are already known. (shrink)