Results for 'Non-Classical '

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  1.  16
    Party contributions from non-classical logics.Contributions From Non-Classical Logics - 2004 - In S. Rahman (ed.), Logic, Epistemology, and the Unity of Science. Dordrecht: Kluwer Academic Publishers. pp. 457.
  2.  35
    Labelled non-classical logics.Luca Viganò - 2000 - Boston: Kluwer Academic Publishers.
    The subject of Labelled Non-Classical Logics is the development and investigation of a framework for the modular and uniform presentation and implementation of non-classical logics, in particular modal and relevance logics. Logics are presented as labelled deduction systems, which are proved to be sound and complete with respect to the corresponding Kripke-style semantics. We investigate the proof theory of our systems, and show them to possess structural properties such as normalization and the subformula property, which we exploit not (...)
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  3.  30
    Non-classical Models of ZF.S. Jockwich Martinez & G. Venturi - 2020 - Studia Logica 109 (3):509-537.
    This paper contributes to the generalization of lattice-valued models of set theory to non-classical contexts. First, we show that there are infinitely many complete bounded distributive lattices, which are neither Boolean nor Heyting algebra, but are able to validate the negation-free fragment of \. Then, we build lattice-valued models of full \, whose internal logic is weaker than intuitionistic logic. We conclude by using these models to give an independence proof of the Foundation axiom from \.
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  4.  35
    Independence Proofs in Non-Classical Set Theories.Sourav Tarafder & Giorgio Venturi - 2023 - Review of Symbolic Logic 16 (4):979-1010.
    In this paper we extend to non-classical set theories the standard strategy of proving independence using Boolean-valued models. This extension is provided by means of a new technique that, combining algebras (by taking their product), is able to provide product-algebra-valued models of set theories. In this paper we also provide applications of this new technique by showing that: (1) we can import the classical independence results to non-classical set theory (as an example we prove the independence of (...)
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  5.  78
    Non-Classical Negation in the Works of Helena Rasiowa and Their Impact on the Theory of Negation.Dimiter Vakarelov - 2006 - Studia Logica 84 (1):105-127.
    The paper is devoted to the contributions of Helena Rasiowa to the theory of non-classical negation. The main results of Rasiowa in this area concerns–constructive logic with strong (Nelson) negation.
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  6.  11
    Truth diagrams for some non-classical and modal logics.Can Başkent - 2024 - Journal of Applied Non-Classical Logics 34 (4).
    This paper examines truth diagrams for some non-classical, modal and dynamic logics. Truth diagrams are diagrammatic and visual ways to represent logical truth akin to truth tables, developed by Peter C.-H. Cheng. Currently, it is only given for classical propositional logic. In this paper, we establish truth diagrams for Priest's Logic of Paradox, Belnap–Dunn's Four-Valued Logic, MacColl's Connexive Logic, Bochvar–Halldén's Logic of Non-Sense, Carnielli–Coniglio's logic of formal inconsistency as well as classical modal logic and its dynamic extension (...)
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  7. Non-classical Comparative Logic I: Standard Categorical Logic–from SLe to IFLe.Amer Amikhteh & Seyed Ahmad Mirsanei - 2021 - Logical Studies 12 (1):1-24.
    n this paper, a non-classical axiomatic system was introduced to classify all moods of Aristotelian syllogisms, in addition to the axiom "Every a is an a" and the bilateral rules of obversion of E and O propositions. This system consists of only 2 definitions, 2 axioms, 1 rule of a premise, and moods of Barbara and Datisi. By adding first-degree propositional negation to this system, we prove that the square of opposition holds without using many of the other rules (...)
     
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  8.  20
    Non-classical foundations of set theory.Sourav Tarafder - 2022 - Journal of Symbolic Logic 87 (1):347-376.
    In this paper, we use algebra-valued models to study cardinal numbers in a class of non-classical set theories. The algebra-valued models of these non-classical set theories validate the Axiom of Choice, if the ground model validates it. Though the models are non-classical, the foundations of cardinal numbers in these models are similar to those in classical set theory. For example, we show that mathematical induction, Cantor’s theorem, and the Schröder–Bernstein theorem hold in these models. We also (...)
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  9.  44
    Some non-classical logics seen from a variety of perspectives.Nuel Belnap - 2003 - Journal of Sun Yatsen University 43:167-179.
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  10.  65
    Non-classical probabilities invariant under symmetries.Alexander R. Pruss - 2021 - Synthese 199 (3-4):8507-8532.
    Classical real-valued probabilities come at a philosophical cost: in many infinite situations, they assign the same probability value—namely, zero—to cases that are impossible as well as to cases that are possible. There are three non-classical approaches to probability that can avoid this drawback: full conditional probabilities, qualitative probabilities and hyperreal probabilities. These approaches have been criticized for failing to preserve intuitive symmetries that can be preserved by the classical probability framework, but there has not been a systematic (...)
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  11.  83
    Proofs and Countermodels in Non-Classical Logics.Sara Negri - 2014 - Logica Universalis 8 (1):25-60.
    Proofs and countermodels are the two sides of completeness proofs, but, in general, failure to find one does not automatically give the other. The limitation is encountered also for decidable non-classical logics in traditional completeness proofs based on Henkin’s method of maximal consistent sets of formulas. A method is presented that makes it possible to establish completeness in a direct way: For any given sequent either a proof in the given logical system or a countermodel in the corresponding frame (...)
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  12.  88
    Interpolation in non-classical logics.Giovanna D’Agostino - 2008 - Synthese 164 (3):421 - 435.
    We discuss the interpolation property on some important families of non classical logics, such as intuitionistic, modal, fuzzy, and linear logics. A special paragraph is devoted to a generalization of the interpolation property, uniform interpolation.
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  13.  42
    Skolem Functions in Non-Classical Logics.Tore Fjetland Øgaard - 2017 - Australasian Journal of Logic 14 (1):181-225.
    This paper shows how to conservatively extend theories formulated in non-classical logics such as the Logic of Paradox, the Strong Kleene Logic and relevant logics with Skolem functions. Translations to and from the language extended by Skolem functions into the original one are presented and shown to preserve derivability. It is also shown that one may not always substitute s=f(t) and A(t, s) even though A determines the extension of a function and f is a Skolem function for A.
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  14.  4
    Truth diagrams for some non-classical and modal logics.Can Başkent - 2024 - Journal of Applied Non-Classical Logics 34 (4):527-560.
    This paper examines truth diagrams for some non-classical, modal and dynamic logics. Truth diagrams are diagrammatic and visual ways to represent logical truth akin to truth tables, developed by Peter C.-H. Cheng. Currently, it is only given for classical propositional logic. In this paper, we establish truth diagrams for Priest's Logic of Paradox, Belnap–Dunn's Four-Valued Logic, MacColl's Connexive Logic, Bochvar–Halldén's Logic of Non-Sense, Carnielli–Coniglio's logic of formal inconsistency as well as classical modal logic and its dynamic extension (...)
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  15. Non-classical Metatheory for Non-classical Logics.Andrew Bacon - 2013 - Journal of Philosophical Logic 42 (2):335-355.
    A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical metatheory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena of higher order vagueness and the revenge liar are just two such examples. The aim of (...)
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  16.  93
    Should the Non‐Classical Logician be Embarrassed?Lucas Rosenblatt - 2022 - Philosophy and Phenomenological Research 104 (2):388-407.
    Non‐classical logicians do not typically reject classically valid logical principles across the board. In fact, they sometimes suggest that their preferred logic recovers classical reasoning in most circumstances. This idea has come to be known in the literature as ‘classical recapture’. Recently, classical logicians have raised various doubts about it. The main problem is said to be that no rigorous explanation has been given of how is it exactly that classical logic can be recovered. The (...)
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  17.  49
    Non-Classical Circular Definitions.Shawn Standefer - 2017 - Australasian Journal of Logic 14 (1).
    Circular denitions have primarily been studied in revision theory in the classical scheme. I present systems of circular denitions in the Strong Kleene and supervaluation schemes and provide complete proof systems for them. One class of denitions, the intrinsic denitions, naturally arises in both schemes. I survey some of the features of this class of denitions.
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  18. Definability and Interpolation in Non-Classical Logics.Larisa Maksimova - 2006 - Studia Logica 82 (2):271-291.
    Algebraic approach to study of classical and non-classical logical calculi was developed and systematically presented by Helena Rasiowa in [48], [47]. It is very fruitful in investigation of non-classical logics because it makes possible to study large families of logics in an uniform way. In such research one can replace logics with suitable classes of algebras and apply powerful machinery of universal algebra. In this paper we present an overview of results on interpolation and definability in modal (...)
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  19.  50
    Non-classical operations hidden in classical logic.Vladimir Sotirov - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):309-324.
    Objects of consideration are various non-classical connectives “hidden” in the classical logic in the form of G˛s with ˛ —a classical connective, and s—a propositional variable. One of them is negation, which is defined as G ⇒ s; another is necessity, which is defined as G ∧ s. The new operations are axiomatized and it is shown that they belong to the 4-valued logic of Lukasiewicz. A 2-point Kripke semantics is built leading directly to the 4-valued logical (...)
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  20.  16
    Truth diagrams for some non-classical and modal logics.Can Başkent - 2024 - Journal of Applied Non-Classical Logics 34 (4):527-560.
    This paper examines truth diagrams for some non-classical, modal and dynamic logics. Truth diagrams are diagrammatic and visual ways to represent logical truth akin to truth tables, developed by Peter C.-H. Cheng. Currently, it is only given for classical propositional logic. In this paper, we establish truth diagrams for Priest's Logic of Paradox, Belnap–Dunn's Four-Valued Logic, MacColl's Connexive Logic, Bochvar–Halldén's Logic of Non-Sense, Carnielli–Coniglio's logic of formal inconsistency as well as classical modal logic and its dynamic extension (...)
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  21.  39
    Non-Classical Probabilities for Decision Making in Situations of Uncertainty.Dominik Klein, Ondrej Majer & Soroush Rafiee Rad - 2020 - Roczniki Filozoficzne 68 (4):315-343.
    Analyzing situations where information is partial, incomplete or contradictory has created a demand for quantitative belief measures that are weaker than classic probability theory. In this paper, we compare two frameworks that have been proposed for this task, Dempster-Shafer theory and non-standard probability theory based on Belnap-Dunn logic. We show the two frameworks to assume orthogonal perspectives on informational shortcomings, but also provide a partial correspondence result. Lastly, we also compare various dynamical rules of the two frameworks, all seen as (...)
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  22. Non-Classical Logics.Kazem Sadegh-Zadeh - 2011 - In Handbook of Analytic Philosophy of Medicine. Dordrecht, Heidelberg, New York, London: Springer.
     
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  23.  72
    Belief revision in non-classical logics.Dov Gabbay, Odinaldo Rodrigues & Alessandra Russo - 2008 - Review of Symbolic Logic 1 (3):267-304.
    In this article, we propose a belief revision approach for families of (non-classical) logics whose semantics are first-order axiomatisable. Given any such (non-classical) logic , the approach enables the definition of belief revision operators for , in terms of a belief revision operation satisfying the postulates for revision theory proposed by Alchourrrdenfors and Makinson (AGM revision, Alchourrukasiewicz's many-valued logic. In addition, we present a general methodology to translate algebraic logics into classical logic. For the examples provided, we (...)
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  24.  67
    An Alleged Tension between non-Classical Logics and Applied Classical Mathematics.Sebastian Horvat & Iulian D. Toader - 2024 - The Philosophical Quarterly 1:1-19.
    Timothy Williamson has maintained that the applicability of classical mathematics in science raises a problem for the endorsement, in non-mathematical domains, of a wide range of non-classical logics. We show that this is false.
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  25. A non-classical extension of classical implicative propositional logic.M. Spinks - 2000 - Bulletin of Symbolic Logic 6:255.
  26.  64
    Non-Classical Correlations in Bistable Perception?Thomas Filk - 2011 - Axiomathes 21 (2):221-232.
    A violation of Bell’s inequalities is generally considered to be the Holy Grail of experimental proof that a specific natural phenomenon cannot be explained in a classical framework and is based on a non-boolean structure of predications. Generalized quantum theory allows for such non-boolean predications. We formulate temporal Bell’s inequalities for cognitive two-state systems and indicate how these inequalities can be tested. This will introduce the notion of temporally non-local measurements. The Necker-Zeno model for bistable perception predicts a violation (...)
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  27. Introduction - Non-classical logic.R. Routley - 1983 - Logique Et Analyse 26 (2):121.
     
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  28.  15
    Post-non-classical philosophy: postmodern “deconstruction” and rational reconstruction of the history of science.L. B. Sultanova - 2020 - Liberal Arts in Russia 9 (1):16.
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  29.  6
    Non-Classical Set Theories and Logics Associated With Them.Sourav Tarafder - 2019 - Bulletin of Symbolic Logic 25 (4):451-451.
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  30. Introduction to Non-Classical Logic.Graham Priest - 2001 - Cambridge and New York: Cambridge University Press.
    This is the first introductory textbook on non-classical propositional logics.
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  31.  76
    Towards a Non-classical Meta-theory for Substructural Approaches to Paradox.Lucas Rosenblatt - 2021 - Journal of Philosophical Logic 50 (5):1007-1055.
    In the literature on self-referential paradoxes one of the hardest and most challenging problems is that of revenge. This problem can take many shapes, but, typically, it besets non-classical accounts of some semantic notion, such as truth, that depend on a set of classically defined meta-theoretic concepts, like validity, consistency, and so on. A particularly troubling form of revenge that has received a lot of attention lately involves the concept of validity. The difficulty lies in that the non-classical (...)
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  32.  27
    Correction: Non-classical probabilities invariant under symmetries.Alexander R. Pruss - 2022 - Synthese 200 (5):1-4.
    A serious error in the proof of a recent characterization of the existence of full conditional probabilities invariant under symmetries is corrected.
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  33.  70
    Meaning-Preserving Translations of Non-classical Logics into Classical Logic: Between Pluralism and Monism.Gerhard Schurz - 2021 - Journal of Philosophical Logic 51 (1):27-55.
    In order to prove the validity of logical rules, one has to assume these rules in the metalogic. However, rule-circular ‘justifications’ are demonstrably without epistemic value. Is a non-circular justification of a logical system possible? This question attains particular importance in view of lasting controversies about classical versus non-classical logics. In this paper the question is answered positively, based on meaning-preserving translations between logical systems. It is demonstrated that major systems of non-classical logic, including multi-valued, paraconsistent, intuitionistic (...)
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  34.  34
    Structural Analysis of Non-Classical Logics: The Proceedings of the Second Taiwan Philosophical Logic Colloquium.Syraya Chin-Mu Yang, Duen-Min Deng & Hanti Lin (eds.) - 2015 - Heidelberg, Germany: Springer.
    This volume brings together a group of logic-minded philosophers and philosophically oriented logicians to address a diversity of topics on the structural analysis of non-classical logics. It mainly focuses on the construction of different types of models for various non-classical logics of current interest, including modal logics, epistemic logics, dynamic logics, and observational predicate logic. The book presents a wide range of applications of two well-known approaches in current research: structural modeling of certain philosophical issues in the framework (...)
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  35.  19
    Vygotsky's non-classical dialectical metapsychology.Dorothy Robbins - 2003 - Journal for the Theory of Social Behaviour 33 (3):303–312.
    The approach taken here is to begin to understand the focus from abstract to concrete in learning to master the principles of methodology, which are different from Western methods and procedures. This methodology is opposed to the empiricist approach of establishing rules and procedures from the concrete to the abstract. The initial discussion revolves around an explanation of the use of metaphor, metatheory, and psychology understood as a non-classical science. There is then a discussion on dialectics, dialectical synthesis, and (...)
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  36.  86
    Natural deduction for non-classical logics.David Basin, Seán Matthews & Luca Viganò - 1998 - Studia Logica 60 (1):119-160.
    We present a framework for machine implementation of families of non-classical logics with Kripke-style semantics. We decompose a logic into two interacting parts, each a natural deduction system: a base logic of labelled formulae, and a theory of labels characterizing the properties of the Kripke models. By appropriate combinations we capture both partial and complete fragments of large families of non-classical logics such as modal, relevance, and intuitionistic logics. Our approach is modular and supports uniform proofs of soundness, (...)
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  37. Dynamic Non-Classicality.Matthew Mandelkern - 2020 - Australasian Journal of Philosophy 98 (2):382-392.
    I show that standard dynamic approaches to the semantics of epistemic modals invalidate the classical laws of excluded middle and non-contradiction, as well as the law of epistemic non-contradiction. I argue that these facts pose a serious challenge.
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  38.  48
    Non-classical Elegance for Sequent Calculus Enthusiasts.Andreas Fjellstad - 2017 - Studia Logica 105 (1):93-119.
    In this paper we develop what we can describe as a “dual two-sided” cut-free sequent calculus system for the non-classical logics of truth lp, k3, stt and a non-reflexive logic ts which is, arguably, more elegant than the three-sided sequent calculus developed by Ripley for the same logics. Its elegance stems from how it employs more or less the standard sequent calculus rules for the various connectives and truth, and the fact that it offers a rather neat connection between (...)
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  39.  74
    Non-Classical Behavior of Atoms in an Interferometer.Lepša Vušković, Dušan Arsenović & Mirjana Božić - 2002 - Foundations of Physics 32 (9):1329-1346.
    Using the time-dependent wave function we have studied the properties of the atomic transverse motion in an interferometer, and the cause of the non-classical behavior of atoms reported by Kurtsiefer, Pfau, and Mlynek [Nature 386, 150 (1997)]. The transverse wave function is derived from the solution of the two-dimensional Schrödinger's equation, written in the form of the Fresnel–Kirchhoff diffraction integral. It is assumed that the longitudinal motion is classical. Comparing data of the space distribution and of the transverse (...)
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  40.  74
    A Double‐Slit Experiment for Non‐Classical Interference Effects in Decision Making.Pierfrancesco La Mura - 2014 - Topics in Cognitive Science 6 (1):58-62.
    We discuss the possible nature and role of non-physical entanglement, and the classical vs. non-classical interface, in models of human decision-making. We also introduce an experimental setting designed after the double-slit experiment in physics, and discuss how it could be used to discriminate between classical and non-classical interference effects in human decisions.
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  41.  34
    Common cause completability of non-classical probability spaces.Zalán Gyenis & Miklós Rédei - 2016 - Belgrade Philosophical Annual 29 (29).
    We prove that under some technical assumptions on a general, non-classical probability space, the probability space is extendible into a larger probability space that is common cause closed in the sense of containing a common cause of every correlation between elements in the space. It is argued that the philosophical significance of this common cause completability result is that it allows the defence of the Common Cause Principle against certain attempts of falsification. Some open problems concerning possible strengthening of (...)
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  42.  48
    Non-classical logics, model theory, and computability: proceedings of the Third Latin-American Symposium on Mathematical Logic, Campinas, Brazil, July 11-17, 1976.Ayda I. Arruda, Newton C. A. Costa & R. Chuaqui (eds.) - 1977 - New York: sale distributors for the U.S.A. and Canada, Elsevier/North-Holland.
  43. Non‐Classical Knowledge.Ethan Jerzak - 2017 - Philosophy and Phenomenological Research 98 (1):190-220.
    The Knower paradox purports to place surprising a priori limitations on what we can know. According to orthodoxy, it shows that we need to abandon one of three plausible and widely-held ideas: that knowledge is factive, that we can know that knowledge is factive, and that we can use logical/mathematical reasoning to extend our knowledge via very weak single-premise closure principles. I argue that classical logic, not any of these epistemic principles, is the culprit. I develop a consistent theory (...)
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  44. Expected utility theory under non-classical uncertainty.V. I. Danilov & A. Lambert-Mogiliansky - 2010 - Theory and Decision 68 (1-2):25-47.
    In this article, Savage’s theory of decision-making under uncertainty is extended from a classical environment into a non-classical one. The Boolean lattice of events is replaced by an arbitrary ortho-complemented poset. We formulate the corresponding axioms and provide representation theorems for qualitative measures and expected utility. Then, we discuss the issue of beliefs updating and investigate a transition probability model. An application to a simple game context is proposed.
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  45.  43
    A Non-Classical Theory of Truth, with an Application to Intuitionism.Storrs McCall - 1970 - American Philosophical Quarterly 7 (1):83 - 88.
    Any "classical" theory of truth will satisfy tarski's criterion ("p" is true if and only if p), And the principle of bivalence (every proposition is either true or false). A non-Classical theory may be obtained by rejecting these principles: - in fact it is shown that rejection of the second entails rejection of the first. If the resulting non-Classical theory is formalized, A system structurally isomorphic to either s4 or s5 is obtained. An attempt is made to (...)
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  46.  63
    On AGM for Non-Classical Logics.Renata Wassermann - 2011 - Journal of Philosophical Logic 40 (2):271 - 294.
    The AGM theory of belief revision provides a formal framework to represent the dynamics of epistemic states. In this framework, the beliefs of the agent are usually represented as logical formulas while the change operations are constrained by rationality postulates. In the original proposal, the logic underlying the reasoning was supposed to be supraclassical, among other properties. In this paper, we present some of the existing work in adapting the AGM theory for non-classical logics and discuss their interconnections and (...)
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  47. Assertion, denial and non-classical theories.Greg Restall - 2012 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 81--99.
    In this paper I urge friends of truth-value gaps and truth-value gluts – proponents of paracomplete and paraconsistent logics – to consider theories not merely as sets of sentences, but as pairs of sets of sentences, or what I call ‘bitheories,’ which keep track not only of what holds according to the theory, but also what fails to hold according to the theory. I explain the connection between bitheories, sequents, and the speech acts of assertion and denial. I illustrate the (...)
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  48.  4
    Common cause completability of non classical probability spaces.Zalán Gyenis & Miklós Rédei - 2016 - Belgrade Philosophical Annual 29:15-32.
    We prove that under some technical assumptions on a general, non-classical probability space, the probability space is extendible into a larger probability space that is common cause closed in the sense of containing a common cause of every correlation between elements in the space. It is argued that the philosophical significance of this common cause completability result is that it allows the defence of the Common Cause principle against certain attempts of falsification. Some open problems concerning possible strengthening of (...)
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  49.  15
    Classical and Non-Classical Versions of the Ontological Argument.K. V. Sorvin - 2018 - Russian Journal of Philosophical Sciences 11:143-159.
    The article is devoted to the interpretation of the ontological argument as a theoretical construction that is connected with understanding of the reflexive relationship of thinking and existence. The author concludes that the consistent implementation of this approach requires an appeal to the historically transitory forms of the ontological argument which reconstructs the logic of the evolution of reflexive systems. The ontological argument is considered as a developing theoretical construct. Therefore, theoretical constructs conceptualized as non-classical versions of the ontological (...)
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  50. A fundamental non-classical logic.Wesley Holliday - 2023 - Logics 1 (1):36-79.
    We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present a Fitch-style natural deduction system for the logic that contains only the introduction and elimination rules for the logical constants. From this starting point, if one adds the rule that Fitch called Reiteration, one obtains a proof system for intuitionistic logic in the given signature; (...)
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