Results for 'non-classical logic'

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  1.  9
    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.
  2.  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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  3.  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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  4.  36
    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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  5.  38
    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.
  6. Non-Classical Logics, Model Theory and Computability.[author unknown] - 1980 - Critica 12 (34):154-158.
     
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  7. 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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  8.  66
    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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  9. 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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  10. 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.
  11.  18
    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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  12. 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
  13. Introduction - Non-classical logic.R. Routley - 1983 - Logique Et Analyse 26 (2):121.
     
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  14. Non-Classical Logics.Kazem Sadegh-Zadeh - 2nd ed. 2015 - In Handbook of Analytic Philosophy of Medicine. Springer Verlag.
     
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  15. 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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  16. An Introduction to Non-Classical Logic.Graham Priest - 2001 - Bulletin of Symbolic Logic 12 (2):294-295.
     
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  17.  22
    A fundamental non-classical logic.Wesley Holliday - forthcoming - Logics.
    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 (...)
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  18. 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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  19.  54
    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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  20.  73
    A non-classical logic for physics.Robin Giles - 1974 - Studia Logica 33 (4):397 - 415.
  21.  5
    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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  22.  25
    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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  23.  61
    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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  24. 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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  25.  38
    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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  26.  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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  27.  93
    An Algebraic Approach to Non-Classical Logics.Helena Rasiowa - 1974 - Amsterdam, Netherlands: Warszawa, Pwn - Polish Scientific Publishers.
  28.  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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  29. Classical Vs Non-Classical Logics: The Universality of Classical Logic.Dov M. Gabbay - 1993 - Max-Planck-Institut für Informatik.
  30.  44
    Non-classical logics and the independence results of set theory.Melvin Fitting - 1972 - Theoria 38 (3):133-142.
  31.  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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  32. 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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  33.  61
    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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  34.  54
    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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  35. 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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  36.  6
    Syraya Chin-Mu Yang, Duen-Min Deng, Hanti Lin (eds.), Structural Analysis of Non-Classical Logics: The Proceedings of the Second Taiwan Philosophical Logic Colloquium (Berlin/Heidelberg: Springer Verlag, 2016), 278 pp. [REVIEW]Kristina Šekrst - 2016 - Prolegomena 15 (2):220-223.
    Review of Syraya Chin-Mu Yang, Duen-Min Deng, Hanti Lin, Structural Analysis of Non-Classical Logics: The Proceedings of the Second Taiwan Philosophical Logic Colloquium, 278 pp.
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  37.  6
    Automated Theorem-proving in Non-classical Logics.Paul B. Thistlewaite, Michael A. McRobbie & Robert K. Meyer - 1988 - Pitman Publishing.
  38.  12
    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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  39.  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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  40.  10
    Decidability results in non-classical logics. Part I.Dov M. Gabbay - 1975 - Annals of Mathematical Logic 8 (3):237.
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  41.  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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  42.  24
    Normal Natural Deduction Proof (In Non-Classical Logics).Wilfried Sieg & Saverio Cittadini - unknown
    Wilfred Sieg and Saverio Cittadini. Normal Natural Deduction Proof (In Non-Classical Logics.
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  43. 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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  44.  16
    Combining and Automating Classical and Non-Classical Logics in Classical Higher-Order Logic.Christoph Benzmüller - 2011 - Annals of Mathematics and Artificial Intelligence) 62 (1-2):103-128.
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  45.  9
    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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  46.  17
    The impossibility of certain higher-order non-classical logics with extensionality.J. Michael Dunn - 1988 - In D. F. Austin (ed.), Philosophical Analysis. Kluwer Academic Publishers. pp. 261--279.
  47.  55
    G. Priest's An Introduction to Non-Classical Logic (2001). [REVIEW]Hans-Peter Leeb - 2003 - History and Philosophy of Logic 24:65-66.
    The review gives a short description of the content of the book and discusses the treatment of conditionals in it.
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  48.  34
    An Introduction to Non-Classical Logic: From If to Is.Sam Butchart - 2010 - Australasian Journal of Philosophy 88 (4):745-748.
  49.  48
    An Introduction to Non-Classical Logic.Aladdin M. Yaqub - 2010 - Teaching Philosophy 33 (4):432-436.
  50. A non-classical extension of classical implicative propositional logic.M. Spinks - 2000 - Bulletin of Symbolic Logic 6:255.
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