Results for 'non-classical logic'

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  1.  19
    Labelled Non-Classical Logics.Luca Viganò - 2000 - Boston, MA, USA: 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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  2.  8
    Party Contributions From Non-Classical Logics.Contributions From Non-Classical Logics - 2004 - In S. Rahman J. Symons (ed.), Logic, Epistemology, and the Unity of Science. Kluwer Academic Publisher. pp. 457.
  3. An Introduction to Non-Classical Logic: From If to Is.Graham Priest - 2008 - Cambridge University Press.
    This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, (...)
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  4.  57
    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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  5.  77
    An Algebraic Approach to Non-Classical Logics.Helena Rasiowa - 1974 - Amsterdam, Netherlands: Warszawa, Pwn - Polish Scientific Publishers.
  6.  53
    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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  7.  71
    A Non-Classical Logic for Physics.Robin Giles - 1974 - Studia Logica 33 (4):397 - 415.
  8. 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 (...)
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  9. An Introduction to Non-Classical Logic: From If to Is.Graham Priest - 2008 - Bulletin of Symbolic Logic 14 (4):544-545.
     
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  10.  24
    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 (...)
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  11. An Introduction to Non-Classical Logic.Graham Priest - 2001 - Bulletin of Symbolic Logic 12 (2):294-295.
     
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  12.  35
    Non-Classical Logics, Model Theory, and Computability: Proceedings of the Third Latin-American Symposium on Mathematical Logic, Campinas, Brazil, July 11-17, 1976. [REVIEW]Ayda I. Arruda, Newton C. A. Costa & R. Chuaqui (eds.) - 1977 - Sale Distributors for the U.S.A. And Canada, Elsevier/North-Holland.
  13.  33
    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 (...)
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  14.  20
    Meaning-Preserving Translations of Non-classical Logics into Classical Logic: Between Pluralism and Monism.Gerhard Schurz - 2022 - 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, (...)
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  15.  16
    Translating Non-Classical Logics Into Classical Logic by Using Hidden Variables.Juan C. Agudelo-Agudelo - 2017 - Logica Universalis 11 (2):205-224.
    Dyadic semantics is a sort of non-truth-functional bivalued semantics introduced in Caleiro et al. Logica Universalis, Birkhäuser, Basel, pp 169–189, 2005). Here we introduce an algorithmic procedure for constructing conservative translations of logics characterised by dyadic semantics into classical propositional logic. The procedure uses fresh propositional variables, which we call hidden variables, to represent the indeterminism of dyadic semantics. An alternative algorithmic procedure for constructing conservative translations of any finite-valued logic into classical logic is also (...)
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  16.  35
    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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  17. A Non-Classical Logical Foundation for Naturalised Realism.Emma Ruttkamp-Bloem, Giovanni Casini & Thomas Meyer - 2015 - In P. & M. Danćak Arazim (ed.), Logica Yearbook 2014. College Publications. pp. 249-266.
    In this paper, by suggesting a formal representation of science based on recent advances in logic-based Artificial Intelligence (AI), we show how three serious concerns around the realisation of traditional scientific realism (the theory/observation distinction, over-determination of theories by data, and theory revision) can be overcome such that traditional realism is given a new guise as ‘naturalised’. We contend that such issues can be dealt with (in the context of scientific realism) by developing a formal representation of science based (...)
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  18.  58
    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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  19. 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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  20.  60
    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 (...)
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  21.  53
    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 (...)
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  22. Non-Classical Logic, Structural Modelling and Meaning: The Proceedings of the Second Taiwan Philosophical Logic Colloquium TPLC-2014.D. M. Deng, Hanti Lin & Syraya C. M. Yang (eds.) - forthcoming - Springer Verlag.
     
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  23.  3
    Automated Theorem-Proving in Non-Classical Logics.Paul B. Thistlewaite, Michael A. McRobbie & Robert K. Meyer - 1988 - Pitman Publishing.
  24. Introduction - Non-classical logic.R. Routley - 1983 - Logique Et Analyse 26 (2):121.
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  25. Non-Classical Logics.Kazem Sadegh-Zadeh - 2nd ed. 2015 - In Handbook of Analytic Philosophy of Medicine. Springer Verlag.
     
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  26.  89
    Judgement Aggregation in Non-Classical Logics.Daniele Porello - 2017 - Journal of Applied Non-Classical Logics 27 (1-2):106-139.
    This work contributes to the theory of judgement aggregation by discussing a number of significant non-classical logics. After adapting the standard framework of judgement aggregation to cope with non-classical logics, we discuss in particular results for the case of Intuitionistic Logic, the Lambek calculus, Linear Logic and Relevant Logics. The motivation for studying judgement aggregation in non-classical logics is that they offer a number of modelling choices to represent agents’ reasoning in aggregation problems. By studying (...)
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  27.  43
    Non-Classical Logics and the Independence Results of Set Theory.Melvin Fitting - 1972 - Theoria 38 (3):133-142.
  28.  9
    Constructive Canonicity in Non-Classical Logics.Silvio Ghilardi & Giancarlo Meloni - 1997 - Annals of Pure and Applied Logic 86 (1):1-32.
    Sufficient syntactic conditions for canonicity in intermediate and intuitionistic modal logics are given. We present a new technique which does not require semantic first-order reduction and which is constructive in the sense that it works in an intuitionistic metatheory through a model without points which is classically isomorphic to the usual canonical model.
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  29. Non-Classical Logics, Model Theory, and Computability Proceedings of the Third Latin-American Symposium on Mathematical Logic, Campinas, Brazil, July 11-17, 1976. [REVIEW]Ayda I. Arruda, R. Chuaqui & Newton C. A. da Costa - 1977
  30. Non-Classical Logics, Model Theory and Computability.[author unknown] - 1980 - Critica 12 (34):154-158.
     
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  31.  9
    Decidability Results in Non-Classical Logics. Part I.Dov M. Gabbay - 1975 - Annals of Mathematical Logic 8 (3):237.
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  32.  1
    Ω-Bibliography of Mathematical Logic: Non-Classical Logics.Wolfgang Rautenberg (ed.) - 1987 - Berlin and Heidelberg: Springer.
    Gert H. Muller The growth of the number of publications in almost all scientific areas, as in the area of logic, is taken as a sign of our scientifically minded culture, but it also has a terrifying aspect. In addition, given the rapidly growing sophistica tion, specialization and hence subdivision of logic, researchers, students and teachers may have a hard time getting an overview of the existing literature, partic ularly if they do not have an extensive library available (...)
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  33.  19
    Automatic Checking Properties of Non-Classical Logics.Pavel Schreiner - 2006 - Journal of Applied Non-Classical Logics 16 (3-4):507-516.
    The paper gives a survey of results related to a problem of automatic recognizing important properties of non-classical logics.
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  34.  73
    The Probabilistic Argument for a Non-Classical Logic of Quantum Mechanics.Patrick Suppes - 1966 - Philosophy of Science 33 (1/2):14-21.
    The aim of this paper is to state the single most powerful argument for use of a non-classical logic in quantum mechanics. In outline the argument is the following. The working logic of a science is the logic of the events and propositions to which probabilities are assigned. A probability should be assigned to every element of the algebra of events. In the case of quantum mechanics probabilities may be assigned to events but not, without restriction, (...)
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  35.  25
    Equational Reasoning in Non-Classical Logics.Marcelo Frias & Ewa Orlowska - 1998 - Journal of Applied Non-Classical Logics 8 (1-2):27-66.
    ABSTRACT In this paper it is shown that a broad class of propositional logics can be interpreted in an equational logic based on fork algebras. This interpetability enables us to develop a fork-algebraic formalization of these logics and, as a consequence, to simulate non-classical means of reasoning with equational theories algebras.
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  36.  2
    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 (...)
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  37. The Method of Hypersequents in the Proof Theory of Propositional Non-Classical Logics.Arnon Avron - 1996 - In Wilfrid Hodges (ed.), Logic: Foundations to Applications. Oxford: pp. 1-32.
    Until not too many years ago, all logics except classical logic (and, perhaps, intuitionistic logic too) were considered to be things esoteric. Today this state of a airs seems to have completely been changed. There is a growing interest in many types of nonclassical logics: modal and temporal logics, substructural logics, paraconsistent logics, non-monotonic logics { the list is long. The diversity of systems that have been proposed and studied is so great that a need is felt (...)
     
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  38.  34
    An Introduction to Non-Classical Logic: From If to Is.Sam Butchart - 2010 - Australasian Journal of Philosophy 88 (4):745-748.
  39.  47
    An Introduction to Non-Classical Logic.Aladdin M. Yaqub - 2010 - Teaching Philosophy 33 (4):432-436.
  40.  7
    Tree Trimming: Four Non-Branching Rules for Priest’s Introduction to Non-Classical Logic.Marilynn Johnson - 2015 - Australasian Journal of Logic 12 (2):97-120.
    In An Introduction to Non-Classical Logic: From If to Is Graham Priest presents branching rules in Free Logic, Variable Domain Modal Logic, and Intuitionist Logic. I propose a simpler, non-branching rule to replace Priest's rule for universal instantiation in Free Logic, a second, slightly modified version of this rule to replace Priest's rule for universal instantiation in Variable Domain Modal Logic, and third and fourth rules, further modifying the second rule, to replace Priest's (...)
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  41. Classical Vs Non-Classical Logics: The Universality of Classical Logic.Dov M. Gabbay - 1993 - Max-Planck-Institut für Informatik.
  42.  17
    Investigating Finite Models of Non-Classical Logics with Relation Algebra and RELVIEW.Rudolf Berghammer & Renate A. Schmidt - 2006 - In Harrie de Swart, Ewa Orlowska, Gunther Smith & Marc Roubens (eds.), Theory and Applications of Relational Structures as Knowledge Instruments Ii. Springer. pp. 31--49.
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  43.  33
    Duality and Canonical Extensions of Bounded Distributive Lattices with Operators, and Applications to the Semantics of Non-Classical Logics II.Viorica Sofronie-Stokkermans - 2000 - Studia Logica 64 (2):151-172.
    The main goal of this paper is to explain the link between the algebraic models and the Kripke-style models for certain classes of propositional non-classical logics. We consider logics that are sound and complete with respect to varieties of distributive lattices with certain classes of well-behaved operators for which a Priestley-style duality holds, and present a way of constructing topological and non-topological Kripke-style models for these types of logics. Moreover, we show that, under certain additional assumptions on the variety (...)
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  44.  21
    Substitution Frege and Extended Frege Proof Systems in Non-Classical Logics.Emil Jeřábek - 2009 - Annals of Pure and Applied Logic 159 (1-2):1-48.
    We investigate the substitution Frege () proof system and its relationship to extended Frege () in the context of modal and superintuitionistic propositional logics. We show that is p-equivalent to tree-like , and we develop a “normal form” for -proofs. We establish connections between for a logic L, and for certain bimodal expansions of L.We then turn attention to specific families of modal and si logics. We prove p-equivalence of and for all extensions of , all tabular logics, all (...)
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  45. Natural Derivations for Priest, Introduction to Non-Classical Logic.Tony Roy - 2006 - Australasian Journal of Logic 4:47-192.
    This document collects natural derivation systems for logics described in Priest, An Introduction to Non-Classical Logic. It provides an alternative or supplement to the semantic tableaux of his text. Except that some chapters are collapsed, there are sections for each chapter in Priest, with an additional, final section on quantified modal logic. In each case, the language is briefly described and key semantic definitions stated, the derivation system is presented with a few examples given, and soundness and (...)
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  46.  73
    Duality and Canonical Extensions of Bounded Distributive Lattices with Operators, and Applications to the Semantics of Non-Classical Logics I.Viorica Sofronie-Stokkermans - 2000 - Studia Logica 64 (1):93-132.
    The main goal of this paper is to explain the link between the algebraic and the Kripke-style models for certain classes of propositional logics. We start by presenting a Priestley-type duality for distributive lattices endowed with a general class of well-behaved operators. We then show that finitely-generated varieties of distributive lattices with operators are closed under canonical embedding algebras. The results are used in the second part of the paper to construct topological and non-topological Kripke-style models for logics that are (...)
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  47.  4
    Luca Vigano. Labelled Non-Classical Logics, With a Foreword by Gabbay Dov, Kluwer Academic Publishers, 2000, 291 Pp. [REVIEW]Petr Hájek - 2004 - Bulletin of Symbolic Logic 10 (1):107-108.
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  48.  55
    Labelled Resolution for Classical and Non-Classical Logics.D. M. Gabbay & U. Reyle - 1997 - Studia Logica 59 (2):179-216.
    Resolution is an effective deduction procedure for classical logic. There is no similar "resolution" system for non-classical logics (though there are various automated deduction systems). The paper presents resolution systems for intuistionistic predicate logic as well as for modal and temporal logics within the framework of labelled deductive systems. Whereas in classical predicate logic resolution is applied to literals, in our system resolution is applied to L(abelled) R(epresentation) S(tructures). Proofs are discovered by a refutation (...)
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  49.  38
    Game Theoretical Semantics for Some Non-Classical Logics.Can Başkent - 2016 - Journal of Applied Non-Classical Logics 26 (3):208-239.
    Paraconsistent logics are the formal systems in which absurdities do not trivialise the logic. In this paper, we give Hintikka-style game theoretical semantics for a variety of paraconsistent and non-classical logics. For this purpose, we consider Priest’s Logic of Paradox, Dunn’s First-Degree Entailment, Routleys’ Relevant Logics, McCall’s Connexive Logic and Belnap’s four-valued logic. We also present a game theoretical characterisation of a translation between Logic of Paradox/Kleene’s K3 and S5. We underline how non-classical (...)
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  50.  2
    An Introduction to Non-Classical Logic[REVIEW]Stewart Shapiro - 2003 - Review of Metaphysics 56 (3):670-671.
    This book is just what its title says: an introduction to nonclassical logic. And it is a very good one. Given the extensive interest in nonclassical logics, in various parts of the philosophical scene, it is a welcome addition to the corpus. Typical courses in logic, at all levels and in both philosophy departments and mathematics departments, focus exclusively on classical logic. Most instructors, and some textbooks, give some mention to some nonclassical systems, but usually few (...)
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