Results for 'axiom of extensionality'

983 found
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  1. A Theory of Names and True Intensionality.Reinhard Muskens - 2012 - In Maria Aloni, V. Kimmelman, Floris Roelofsen, G. Weidman Sassoon, Katrin Schulz & M. Westera (eds.), Logic, Language and Meaning: 18th Amsterdam Colloquium. Springer. pp. 441-449.
    Standard approaches to proper names, based on Kripke's views, hold that the semantic values of expressions are (set-theoretic) functions from possible worlds to extensions and that names are rigid designators, i.e.\ that their values are \emph{constant} functions from worlds to entities. The difficulties with these approaches are well-known and in this paper we develop an alternative. Based on earlier work on a higher order logic that is \emph{truly intensional} in the sense that it does not validate the axiom scheme (...)
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  2. Intensional Models for the Theory of Types.Reinhard Muskens - 2007 - Journal of Symbolic Logic 72 (1):98-118.
    In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention to applications. (...)
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  3.  58
    The Logic of Systems of Granular Partitions.Thomas Bittner, Barry Smith & Maureen Donnelly - 2005 - IFOMIS Reports.
    The theory of granular partitions is designed to capture in a formal framework important aspects of the selective character of common-sense views of reality. It comprehends not merely the ways in which we can view reality by conceiving its objects as gathered together not merely into sets, but also into wholes of various kinds, partitioned into parts at various levels of granularity. We here represent granular partitions as triples consisting of a rooted tree structure as first component, a domain satisfying (...)
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  4. Prospects for a Naive Theory of Classes.Hartry Field, Harvey Lederman & Tore Fjetland Øgaard - 2017 - Notre Dame Journal of Formal Logic 58 (4):461-506.
    The naive theory of properties states that for every condition there is a property instantiated by exactly the things which satisfy that condition. The naive theory of properties is inconsistent in classical logic, but there are many ways to obtain consistent naive theories of properties in nonclassical logics. The naive theory of classes adds to the naive theory of properties an extensionality rule or axiom, which states roughly that if two classes have exactly the same members, they are (...)
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  5. In Defence of Extensional Evidence.Matheus Silva - manuscript
    Intensional evidence is any reason to accept a proposition that is not the truth values of the proposition accepted or, if it is a complex proposition, is not the truth values of its propositional contents. Extensional evidence is non-intensional evidence. Someone can accept a complex proposition, but deny its logical consequences when her acceptance is based on intensional evidence, while the logical consequences of the proposition presuppose the acceptance of extensional evidence, e.g., she can refuse the logical consequence of a (...)
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  6. The Axiom of Choice in Quine's New Foundations for Mathematical Logic.Ernst P. Specker - 1954 - Journal of Symbolic Logic 19 (2):127-128.
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  7. High-Order Metaphysics as High-Order Abstractions and Choice in Set Theory.Vasil Penchev - 2020 - Epistemology eJournal (Elsevier: SSRN) 13 (21):1-3.
    The link between the high-order metaphysics and abstractions, on the one hand, and choice in the foundation of set theory, on the other hand, can distinguish unambiguously the “good” principles of abstraction from the “bad” ones and thus resolve the “bad company problem” as to set theory. Thus it implies correspondingly a more precise definition of the relation between the axiom of choice and “all company” of axioms in set theory concerning directly or indirectly abstraction: the principle of abstraction, (...)
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  8. The Axiom of Infinity.Bertrand Russell - 1903 - Hibbert Journal 2:809-812.
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  9. Prototypes, Poles, and Topological Tessellations of Conceptual Spaces.Thomas Mormann - 2021 - Synthese 199:3675 - 3710.
    Abstract. The aim of this paper is to present a topological method for constructing discretizations (tessellations) of conceptual spaces. The method works for a class of topological spaces that the Russian mathematician Pavel Alexandroff defined more than 80 years ago. Alexandroff spaces, as they are called today, have many interesting properties that distinguish them from other topological spaces. In particular, they exhibit a 1-1 correspondence between their specialization orders and their topological structures. Recently, a special type of Alexandroff spaces was (...)
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  10.  76
    The Axiom of Infinity.Cassius Jackson Keyser - 1904 - Hibbert Journal 3:380-383.
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  11.  65
    The Axiom of Infinity: A New Presupposition of Thought.Cassius Jackson Keyser - 1903 - Hibbert Journal 2:532-552.
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  12. Two notions of fusion and the landscape of extensionality.Roberto Loss - 2021 - Philosophical Studies 178 (10):3443-3463.
    There are two main ways in which the notion of mereological fusion is usually defined in the current literature in mereology which have been labelled ‘Leśniewski fusion’ and ‘Goodman fusion’. It is well-known that, with Minimal Mereology as the background theory, every Leśniewski fusion also qualifies as a Goodman fusion. However, the converse does not hold unless stronger mereological principles are assumed. In this paper I will discuss how the gap between the two notions can be filled, focussing in particular (...)
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  13. On Language Adequacy.Urszula Wybraniec-Skardowska - 2015 - Studies in Logic, Grammar and Rhetoric 40 (1):257-292.
    The paper concentrates on the problem of adequate reflection of fragments of reality via expressions of language and inter-subjective knowledge about these fragments, called here, in brief, language adequacy. This problem is formulated in several aspects, the most being: the compatibility of language syntax with its bi-level semantics: intensional and extensional. In this paper, various aspects of language adequacy find their logical explication on the ground of the formal-logical theory T of any categorial language L generated by the so-called classical (...)
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  14. Two Kinds of Definition in Spinoza's Ethics.Kristina Meshelski - 2011 - British Journal for the History of Philosophy 19 (2):201-218.
    Spinoza scholars have claimed that we are faced with a dilemma: either Spinoza's definitions in his Ethics are real, in spite of indications to the contrary, or the definitions are nominal and the propositions derived from them are false. I argue that Spinoza did not recognize the distinction between real and nominal definitions. Rather, Spinoza classified definitions according to whether they require a priori or a posteriori justification, which is a classification distinct from either the real/nominal or the intensional/extensional classification. (...)
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  15.  47
    A State-of-Affairs-Semantic Solution to the Problem of Extensionality in Free Logic.Hans-Peter Leeb - 2020 - Journal of Philosophical Logic 49 (6):1091-1109.
    If one takes seriously the idea that a scientific language must be extensional, and accepts Quine’s notion of truth-value-related extensionality, and also recognizes that a scientific language must allow for singular terms that do not refer to existing objects, then there is a problem, since this combination of assumptions must be inconsistent. I will argue for a particular solution to the problem, namely, changing what is meant by the word ‘extensionality’, so that it would not be the truth-value (...)
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  16. Mathematical Forms and Forms of Mathematics: Leaving the Shores of Extensional Mathematics.Jean-Pierre Marquis - 2013 - Synthese 190 (12):2141-2164.
    In this paper, I introduce the idea that some important parts of contemporary pure mathematics are moving away from what I call the extensional point of view. More specifically, these fields are based on criteria of identity that are not extensional. After presenting a few cases, I concentrate on homotopy theory where the situation is particularly clear. Moreover, homotopy types are arguably fundamental entities of geometry, thus of a large portion of mathematics, and potentially to all mathematics, at least according (...)
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  17. Russell’s Method of Analysis and the Axioms of Mathematics.Lydia Patton - 2017 - In Sandra Lapointe Christopher Pincock (ed.), Innovations in the History of Analytical Philosophy. London: Palgrave-Macmillan. pp. 105-126.
    In the early 1900s, Russell began to recognize that he, and many other mathematicians, had been using assertions like the Axiom of Choice implicitly, and without explicitly proving them. In working with the Axioms of Choice, Infinity, and Reducibility, and his and Whitehead’s Multiplicative Axiom, Russell came to take the position that some axioms are necessary to recovering certain results of mathematics, but may not be proven to be true absolutely. The essay traces historical roots of, and motivations (...)
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  18. The Extensionality of Parthood and Composition.Achille C. Varzi - 2008 - Philosophical Quarterly 58 (230):108-133.
    I focus on three mereological principles: the Extensionality of Parthood (EP), the Uniqueness of Composition (UC), and the Extensionality of Composition (EC). These principles are not equivalent. Nonetheless, they are closely related (and often equated) as they all reflect the basic nominalistic dictum, No difference without a difference maker. And each one of them—individually or collectively—has been challenged on philosophical grounds. In the first part I argue that such challenges do not quite threaten EP insofar as they are (...)
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  19.  61
    Asymmetric Hybrids: Dialogues for Computational Concept Combination.Guendalina Righetti, Daniele Porello, Nicolas Troquard, Oliver Kutz, Maria Hedblom & Pietro Galliani - 2022 - In Fabian Neuhaus & Boyan Brodaric (eds.), Formal Ontology in Information Systems - Proceedings of the Twelfth International Conference, {FOIS} 2021, Bozen-Bolzano, Italy, September 11-18, 2021. Frontiers in Artificial Intelligence and Applications. IOS Press. pp. 81-96.
    When people combine concepts these are often characterised as “hybrid”, “impossible”, or “humorous”. However, when simply considering them in terms of extensional logic, the novel concepts understood as a conjunctive concept will often lack meaning having an empty extension (consider “a tooth that is a chair”, “a pet flower”, etc.). Still, people use different strategies to produce new non-empty concepts: additive or integrative combination of features, alignment of features, instantiation, etc. All these strategies involve the ability to deal with conflicting (...)
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  20.  60
    Can Redescriptions of Outcomes Salvage the Axioms of Decision Theory?Jean Baccelli & Philippe Mongin - 2021 - Philosophical Studies 179 (5):1621-1648.
    The basic axioms or formal conditions of decision theory, especially the ordering condition put on preferences and the axioms underlying the expected utility formula, are subject to a number of counter-examples, some of which can be endowed with normative value and thus fall within the ambit of a philosophical reflection on practical rationality. Against such counter-examples, a defensive strategy has been developed which consists in redescribing the outcomes of the available options in such a way that the threatened axioms or (...)
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  21. The Gödel Incompleteness Theorems (1931) by the Axiom of Choice.Vasil Penchev - 2020 - Econometrics: Mathematical Methods and Programming eJournal (Elsevier: SSRN) 13 (39):1-4.
    Those incompleteness theorems mean the relation of (Peano) arithmetic and (ZFC) set theory, or philosophically, the relation of arithmetical finiteness and actual infinity. The same is managed in the framework of set theory by the axiom of choice (respectively, by the equivalent well-ordering "theorem'). One may discuss that incompleteness form the viewpoint of set theory by the axiom of choice rather than the usual viewpoint meant in the proof of theorems. The logical corollaries from that "nonstandard" viewpoint the (...)
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  22. Between Atomism and Superatomism.T. Scott Dixon - 2020 - Journal of Philosophical Logic 49 (6):1215-1241.
    There are at least three vaguely atomistic principles that have come up in the literature, two explicitly and one implicitly. First, standard atomism is the claim that everything is composed of atoms, and is very often how atomism is characterized in the literature. Second, superatomism is the claim that parthood is well-founded, which implies that every proper parthood chain terminates, and has been discussed as a stronger alternative to standard atomism. Third, there is a principle that lies between these two (...)
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  23. Foundation of All Axioms the Axioms of Consciousness (Consciousness and Special Relativity?).Frank de Silva - 1996 - Engineering in Medicine and Biology 15 (3):21-26.
    A description of consciousness leads to a contradiction with the postulation from special relativity that there can be no connections between simultaneous event. This contradiction points to consciousness involving quantum level mechanisms. The Quantum level description of the universe is re- evaluated in the light of what is observed in consciousness namely 4 Dimensional objects. A new improved interpretation of Quantum level observations is introduced. From this vantage point the following axioms of consciousness is presented. Consciousness consists of two distinct (...)
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  24. Extensional Scientific Realism Vs. Intensional Scientific Realism.Seungbae Park - 2016 - Studies in History and Philosophy of Science Part A 59:46-52.
    Extensional scientific realism is the view that each believable scientific theory is supported by the unique first-order evidence for it and that if we want to believe that it is true, we should rely on its unique first-order evidence. In contrast, intensional scientific realism is the view that all believable scientific theories have a common feature and that we should rely on it to determine whether a theory is believable or not. Fitzpatrick argues that extensional realism is immune, while intensional (...)
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  25. A System of Axioms for Minkowski Spacetime.Lorenzo Cocco & Joshua Babic - 2020 - Journal of Philosophical Logic:1-37.
    We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in [Maudlin 2012] and [Malament, unpublished]. It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of [Tarski 1959]: a predicate of betwenness and a (...)
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  26. The Use of Sets (and Other Extensional Entities) in the Analysis of Hylomorphically Complex Objects.Simon Evnine - 2018 - Metaphysics 1 (1):97-109.
    Hylomorphically complex objects are things that change their parts or matter or that might have, or have had, different parts or matter. Often ontologists analyze such objects in terms of sets (or functions, understood set-theoretically) or other extensional entities such as mereological fusions or quantities of matter. I urge two reasons for being wary of any such analyses. First, being extensional, such things as sets are ill-suited to capture the characteristic modal and temporal flexibility of hylomorphically complex objects. Secondly, sets (...)
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  27. An Elementary System of Axioms for Euclidean Geometry Based on Symmetry Principles.Boris Čulina - 2018 - Axiomathes 28 (2):155-180.
    In this article I develop an elementary system of axioms for Euclidean geometry. On one hand, the system is based on the symmetry principles which express our a priori ignorant approach to space: all places are the same to us, all directions are the same to us and all units of length we use to create geometric figures are the same to us. On the other hand, through the process of algebraic simplification, this system of axioms directly provides the Weyl’s (...)
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  28. Extensionalizing Intensional Second-Order Logic.Jonathan Payne - 2015 - Notre Dame Journal of Formal Logic 56 (1):243-261.
    Neo-Fregean approaches to set theory, following Frege, have it that sets are the extensions of concepts, where concepts are the values of second-order variables. The idea is that, given a second-order entity $X$, there may be an object $\varepsilon X$, which is the extension of X. Other writers have also claimed a similar relationship between second-order logic and set theory, where sets arise from pluralities. This paper considers two interpretations of second-order logic—as being either extensional or intensional—and whether either is (...)
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  29. Defending the Axioms-On the Philosophical Foundations of Set Theory, Penelope Maddy. [REVIEW]Eduardo Castro - 2012 - Teorema: International Journal of Philosophy 31 (1):147-150.
    Review of Maddy, Penelope "Defending the Axioms".
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  30. Reason‐Statements As Non‐Extensional Contexts.Jussi Suikkanen - 2012 - Philosophical Quarterly 62 (248):592-613.
    Many believe that, if true, reason-statements of the form ‘that X is F is a reason to φ’ describe a ‘favouring-relation’ between the fact that X is F and the act of φing. This favouring-relation has been assumed to share many features of other, more concrete relations. This combination of views leads to immediate problems. Firstly, unlike statements about many other relations, reason-statements can be true even when the relata do not exist, i.e., when the relevant facts do not obtain (...)
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  31. Extensional and Non-Truth-Functional Contexts.Adam Morton - 1969 - Journal of Philosophy 66 (6):159-164.
    I discuss Frege's argument - later called the slingshot - that if a construction is extensional and preserves logical equivalence then it is truth-functional. I consider some simple apparent counterexamples and conclude that they are not sentence-embedding in the required way.
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  32. The Many Faces of Spinoza's Causal Axiom.Martin Lin - 2019 - In Dominik Perler & Sebastian Bender (eds.), Causation and Cognition: Perspectives on Early Modern Philosophy. New York: Routledge.
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  33. Axioms for Actuality.Harold T. Hodes - 1984 - Journal of Philosophical Logic 13 (1):27 - 34.
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  34. Restricting Spinoza's Causal Axiom.John Morrison - 2015 - Philosophical Quarterly 65 (258):40-63.
    Spinoza's causal axiom is at the foundation of the Ethics. I motivate, develop and defend a new interpretation that I call the ‘causally restricted interpretation’. This interpretation solves several longstanding puzzles and helps us better understand Spinoza's arguments for some of his most famous doctrines, including his parallelism doctrine and his theory of sense perception. It also undermines a widespread view about the relationship between the three fundamental, undefined notions in Spinoza's metaphysics: causation, conception and inherence.
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  35. The Search for New Axioms in the Hyperuniverse Programme.Claudio Ternullo & Sy-David Friedman - 2016 - In Andrea Sereni & Francesca Boccuni (eds.), Objectivity, Realism, and Proof. FilMat Studies in the Philosophy of Mathematics. Berlin: Springer. pp. 165-188.
    The Hyperuniverse Programme, introduced in Arrigoni and Friedman (2013), fosters the search for new set-theoretic axioms. In this paper, we present the procedure envisaged by the programme to find new axioms and the conceptual framework behind it. The procedure comes in several steps. Intrinsically motivated axioms are those statements which are suggested by the standard concept of set, i.e. the `maximal iterative concept', and the programme identi fies higher-order statements motivated by the maximal iterative concept. The satisfaction of these statements (...)
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  36. Are Large Cardinal Axioms Restrictive?Neil Barton - manuscript
    The independence phenomenon in set theory, while pervasive, can be partially addressed through the use of large cardinal axioms. A commonly assumed idea is that large cardinal axioms are species of maximality principles. In this paper, I argue that whether or not large cardinal axioms count as maximality principles depends on prior commitments concerning the richness of the subset forming operation. In particular I argue that there is a conception of maximality through absoluteness, on which large cardinal axioms are restrictive. (...)
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  37.  92
    Maximality and Ontology: How Axiom Content Varies Across Philosophical Frameworks.Sy-David Friedman & Neil Barton - 2017 - Synthese 197 (2):623-649.
    Discussion of new axioms for set theory has often focused on conceptions of maximality, and how these might relate to the iterative conception of set. This paper provides critical appraisal of how certain maximality axioms behave on different conceptions of ontology concerning the iterative conception. In particular, we argue that forms of multiversism and actualism face complementary problems. The latter view is unable to use maximality axioms that make use of extensions, where the former has to contend with the existence (...)
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  38.  16
    Towards Even More Irresistible Axiom Weakening.Roberto Confalonieri, Pietro Galliani, Oliver Kutz, Daniele Porello, Guendalina Righetti & Nicolas Toquard - 2020 - In Proceedings of the 33rd International Workshop on Description Logics {(DL} 2020) co-located with the 17th International Conference on Principles of Knowledge Representation and Reasoning {(KR} 2020), Online Event, Rhodes, Greece.
    Axiom weakening is a technique that allows for a fine-grained repair of inconsistent ontologies. Its main advantage is that it repairs on- tologies by making axioms less restrictive rather than by deleting them, employing the use of refinement operators. In this paper, we build on pre- viously introduced axiom weakening for ALC, and make it much more irresistible by extending its definitions to deal with SROIQ, the expressive and decidable description logic underlying OWL 2 DL. We extend the (...)
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  39. Formalizing Euclid’s First Axiom.John Corcoran - 2014 - Bulletin of Symbolic Logic 20 (3):404-405.
    Formalizing Euclid’s first axiom. Bulletin of Symbolic Logic. 20 (2014) 404–5. (Coauthor: Daniel Novotný) -/- Euclid [fl. 300 BCE] divides his basic principles into what came to be called ‘postulates’ and ‘axioms’—two words that are synonyms today but which are commonly used to translate Greek words meant by Euclid as contrasting terms. -/- Euclid’s postulates are specifically geometric: they concern geometric magnitudes, shapes, figures, etc.—nothing else. The first: “to draw a line from any point to any point”; the last: (...)
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  40. Future Logic: Categorical and Conditional Deduction and Induction of the Natural, Temporal, Extensional, and Logical Modalities.Avi Sion - 1996 - Geneva, Switzerland: CreateSpace & Kindle; Lulu..
    Future Logic is an original, and wide-ranging treatise of formal logic. It deals with deduction and induction, of categorical and conditional propositions, involving the natural, temporal, extensional, and logical modalities. Traditional and Modern logic have covered in detail only formal deduction from actual categoricals, or from logical conditionals (conjunctives, hypotheticals, and disjunctives). Deduction from modal categoricals has also been considered, though very vaguely and roughly; whereas deduction from natural, temporal and extensional forms of conditioning has been all but totally ignored. (...)
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  41. On Quine's Ontology: Quantification, Extensionality and Naturalism (or From Commitment to Indifference).Daniel Durante Pereira Alves - 2019 - Proceedings of Ther 3rd Filomena Workshop.
    Much of the ontology made in the analytic tradition of philosophy nowadays is founded on some of Quine’s proposals. His naturalism and the binding between existence and quantification are respectively two of his very influential metaphilosophical and methodological theses. Nevertheless, many of his specific claims are quite controversial and contemporaneously have few followers. Some of them are: (a) his rejection of higher-order logic; (b) his resistance in accepting the intensionality of ontological commitments; (c) his rejection of first-order modal logic; and (...)
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  42. Semantics for Opaque Contexts.Kirk Ludwig & Greg Ray - 1998 - Philosophical Perspectives 12:141-66.
    In this paper, we outline an approach to giving extensional truth-theoretic semantics for what have traditionally been seen as opaque sentential contexts. We outline an approach to providing a compositional truth-theoretic semantics for opaque contexts which does not require quantifying over intensional entities of any kind, and meets standard objections to such accounts. The account we present aims to meet the following desiderata on a semantic theory T for opaque contexts: (D1) T can be formulated in a first-order extensional language; (...)
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  43. Operational Axioms for Diagonalizing States.Giulio Chiribella & Carlo Maria Scandolo - 2015 - EPTCS 195:96-115.
    In quantum theory every state can be diagonalized, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This elementary structure plays an ubiquitous role in quantum mechanics, quantum information theory, and quantum statistical mechanics, where it provides the foundation for the notions of majorization and entropy. A natural question then arises: can we reconstruct these notions from purely operational axioms? We address this question in the framework of general probabilistic theories, presenting a set of axioms that guarantee that (...)
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  44. On the Measurement of Need-Based Justice.Stefan Traub, Alexander Max Bauer, Mark Siebel, Nils Springhorn & Arne Robert Weiß - manuscript
    Need considerations play an important role in empirically informed theories of distributive justice. We propose a concept of need-based justice that is related to social participation and provide an ethical measurement of need-based justice. The β-ε-index satisfies the need-principle, monotonicity, sensitivity, transfer and several »technical« axioms. A numerical example is given.
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  45. Apperceptive Patterning: Artefaction, Extensional Beliefs and Cognitive Scaffolding.Ekin Erkan - 2020 - Cosmos and History 16 (1):125-178.
    In “Psychopower and Ordinary Madness” my ambition, as it relates to Bernard Stiegler’s recent literature, was twofold: 1) critiquing Stiegler’s work on exosomatization and artefactual posthumanism—or, more specifically, nonhumanism—to problematize approaches to media archaeology that rely upon technical exteriorization; 2) challenging how Stiegler engages with Giuseppe Longo and Francis Bailly’s conception of negative entropy. These efforts were directed by a prevalent techno-cultural qualifier: the rise of Synthetic Intelligence (including neural nets, deep learning, predictive processing and Bayesian models of cognition). This (...)
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  46. Repairing Ontologies Via Axiom Weakening.Daniele Porello & Oliver Kutz Nicolas Troquard, Roberto Confalonieri, Pietro Galliani, Rafael Peñaloza, Daniele Porello - 2018 - In Proceedings of the Thirty-Second {AAAI} Conference on Artificial Intelligence, (AAAI-18), the 30th innovative Applications of Artificial Intelligence (IAAI-18), and the 8th {AAAI} Symposium on Educational Advances in Artificial Intelligence (EAAI-18). pp. 1981--1988.
    Ontology engineering is a hard and error-prone task, in which small changes may lead to errors, or even produce an inconsistent ontology. As ontologies grow in size, the need for automated methods for repairing inconsistencies while preserving as much of the original knowledge as possible increases. Most previous approaches to this task are based on removing a few axioms from the ontology to regain consistency. We propose a new method based on weakening these axioms to make them less restrictive, employing (...)
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  47. Existence Assumptions and Logical Principles: Choice Operators in Intuitionistic Logic.Corey Edward Mulvihill - 2015 - Dissertation, University of Waterloo
    Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in (...)
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  48. If It's Clear, Then It's Clear That It's Clear, or is It? Higher-Order Vagueness and the S4 Axiom.Susanne Bobzien - 2012 - In B. Morison K. Ierodiakonou (ed.), Episteme, etc.: Essays in honour of Jonathan Barnes. OUP UK.
    The purpose of this paper is to challenge some widespread assumptions about the role of the modal axiom 4 in a theory of vagueness. In the context of vagueness, axiom 4 usually appears as the principle ‘If it is clear (determinate, definite) that A, then it is clear (determinate, definite) that it is clear (determinate, definite) that A’, or, more formally, CA → CCA. We show how in the debate over axiom 4 two different notions of clarity (...)
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  49.  26
    Naive Cubical Type Theory.Bruno Bentzen - 2022 - Mathematical Structures in Computer Science:1-27.
    This article proposes a way of doing type theory informally, assuming a cubical style of reasoning. It can thus be viewed as a first step toward a cubical alternative to the program of informalization of type theory carried out in the homotopy type theory book for dependent type theory augmented with axioms for univalence and higher inductive types. We adopt a cartesian cubical type theory proposed by Angiuli, Brunerie, Coquand, Favonia, Harper, and Licata as the implicit foundation, confining our presentation (...)
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  50. Two Approaches to Ontology Aggregation Based on Axiom Weakening.Daniele Porello, Nicolaas Troquard, Oliver Kutz, Rafael Penaloza, Roberto Confalonieri & Pietro Galliani - 2018 - In Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, {IJCAI} 2018, July 13-19, 2018, Stockholm, Sweden. pp. 1942--1948.
    Axiom weakening is a novel technique that allows for fine-grained repair of inconsistent ontologies. In a multi-agent setting, integrating ontologies corresponding to multiple agents may lead to inconsistencies. Such inconsistencies can be resolved after the integrated ontology has been built, or their generation can be prevented during ontology generation. We implement and compare these two approaches. First, we study how to repair an inconsistent ontology resulting from a voting-based aggregation of views of heterogeneous agents. Second, we prevent the generation (...)
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