Results for ' Classical Logic'

977 found
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  1.  16
    Party contributions from non-classical logics.Contributions From Non-Classical Logics - 2004 - In S. Rahman, Logic, Epistemology, and the Unity of Science. Dordrecht: Kluwer Academic Publishers. pp. 457.
  2.  10
    Olivier Gasquet and Andreas Herzig.From Classical to Normal Modal Logics - 1996 - In Heinrich Wansing, Proof theory of modal logic. Boston: Kluwer Academic Publishers.
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  3. Storage Operators and Second Order Lambda-Calculs.J. -L. Krivine Classical Logic - 1994 - Annals of Pure and Applied Logic 68:53-78.
  4.  66
    Classical Logic is not Uniquely Characterizable.Isabella McAllister - 2022 - Journal of Philosophical Logic 51 (6):1345-1365.
    I show that it is not possible to uniquely characterize classical logic when working within classical set theory. By building on recent work by Eduardo Barrio, Federico Pailos, and Damian Szmuc, I show that for every inferential level (finite and transfinite), either classical logic is not unique at that level or there exist intuitively valid inferences of that level that are not definable in modern classical set theory. The classical logician is thereby faced (...)
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  5.  96
    Classical Logic and the Strict Tolerant Hierarchy.Chris Scambler - 2020 - Journal of Philosophical Logic 49 (2):351-370.
    In their recent article “A Hierarchy of Classical and Paraconsistent Logics”, Eduardo Barrio, Federico Pailos and Damien Szmuc present novel and striking results about meta-inferential validity in various three valued logics. In the process, they have thrown open the door to a hitherto unrecognized domain of non-classical logics with surprising intrinsic properties, as well as subtle and interesting relations to various familiar logics, including classical logic. One such result is that, for each natural number n, there (...)
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  6.  42
    Conceptualizing Classical Logic.Oswaldo Chateaubriand - 2017 - Revista Portuguesa de Filosofia 73 (3-4):989-1000.
    Classical logic is often characterized through certain laws such as bi-valence and sharpness of concepts, among others. My view is that its most fundamental feature is a commitment to an objective conception of truth, which goes together with a realistic metaphysical view. Truth is objective in that it derives from the nature of reality, and is not dependent on beliefs, theories, practices, and the like. Classical logic is a theory of logical properties, logical truths, and logical (...)
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  7.  41
    Why classical logic is privileged: justification of logics based on translatability.Gerhard Schurz - 2021 - Synthese 199 (5-6):13067-13094.
    In Sect. 1 it is argued that systems of logic are exceptional, but not a priori necessary. Logics are exceptional because they can neither be demonstrated as valid nor be confirmed by observation without entering a circle, and their motivation based on intuition is unreliable. On the other hand, logics do not express a priori necessities of thinking because alternative non-classical logics have been developed. Section 2 reflects the controversies about four major kinds of non-classical logics—multi-valued, intuitionistic, (...)
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  8. Classical Logic Is Connexive.Camillo Fiore - 2024 - Australasian Journal of Logic (2):91-99.
    Connexive logics are based on two ideas: that no statement entails or is entailed by its own negation (this is Aristotle’s thesis) and that no statement entails both something and the negation of this very thing (this is Boethius' thesis). Usually, connexive logics are contra-classical. In this note, I introduce a reading of the connexive theses that makes them compatible with classical logic. According to this reading, the theses in question do not talk about validity alone; rather, (...)
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  9. Recapture Results and Classical Logic.Camillo Fiore & Lucas Rosenblatt - 2023 - Mind 132 (527):762–788.
    An old and well-known objection to non-classical logics is that they are too weak; in particular, they cannot prove a number of important mathematical results. A promising strategy to deal with this objection consists in proving so-called recapture results. Roughly, these results show that classical logic can be used in mathematics and other unproblematic contexts. However, the strategy faces some potential problems. First, typical recapture results are formulated in a purely logical language, and do not generalize nicely (...)
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  10. An Introduction to Non-Classical Logic: From If to Is.Graham Priest - 2008 - New York: 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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  11. Vague Objects within Classical Logic and Standard Mereology, and without Indeterminate Identity.Elisa Paganini - 2017 - Journal of Philosophical Logic 46 (4):457-465.
    Weatherson argues that whoever accepts classical logic, standard mereology and the difference between vague objects and any others, should conclude that there are no vague objects. Barnes and Williams claim that a supporter of vague objects who accepts classical logic and standard mereology should recognize that the existence of vague objects implies indeterminate identity. Even though it is not clearly stated, they all seem to be committed to the assumption that reality is ultimately constituted by mereological (...)
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  12.  4
    Inside Classical Logic: Truth, Contradictions, Fractionality.Mario Piazza & Matteo Tesi - forthcoming - Studia Logica:1-30.
    Fractional semantics provides a multi-valued interpretation of a variety of logics, governed by purely proof-theoretic principles. This approach employs a method of systematic decomposition of formulas through a well-disciplined sequent calculus, assigning a fractional value that measures the “quantity of identity” (intuitively, “quantity of truth”) within a sequent. A key consequence of this framework is the breakdown of the traditional symmetry between truth and contradiction. In this paper, we explore the ramifications of this novel perspective on classical logic. (...)
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  13.  83
    Classical logic and truth-value gaps.Philip Hugly & Charles Sayward - 1992 - Philosophical Papers 21 (2):141-150.
    An account of the logic of bivalent languages with truth-value gaps is given. This account is keyed to the use of tables introduced by S. C. Kleene. The account has two guiding ideas. First, that the bivalence property insures that the language satisfies classical logic. Second, that the general concepts of a valid sentence and an inconsistent sentence are, respectively, as sentences which are not false in any model and sentences which are not true in any model. (...)
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  14. Meta-Classical Non-Classical Logics.Eduardo Barrio, Camillo Fiore & Federico Pailos - 2024 - Review of Symbolic Logic 17 (4):1146-1171.
    Recently, it has been proposed to understand a logic as containing not only a validity canon for inferences but also a validity canon for metainferences of any finite level. Then, it has been shown that it is possible to construct infinite hierarchies of ‘increasingly classical’ logics—that is, logics that are classical at the level of inferences and of increasingly higher metainferences—all of which admit a transparent truth predicate. In this paper, we extend this line of investigation by (...)
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  15.  21
    Classical Logic with n Truth Values as a Symmetric Many-Valued Logic.A. Salibra, A. Bucciarelli, A. Ledda & F. Paoli - 2020 - Foundations of Science 28 (1):115-142.
    We introduce Boolean-like algebras of dimension n ($$n{\mathrm {BA}}$$ n BA s) having n constants $${{{\mathsf {e}}}}_1,\ldots,{{{\mathsf {e}}}}_n$$ e 1, …, e n, and an $$(n+1)$$ ( n + 1 ) -ary operation q (a “generalised if-then-else”) that induces a decomposition of the algebra into n factors through the so-called n-central elements. Varieties of $$n{\mathrm {BA}}$$ n BA s share many remarkable properties with the variety of Boolean algebras and with primal varieties. The $$n{\mathrm {BA}}$$ n BA s provide the (...)
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  16. 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 (...)
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  17.  68
    Noncontractive Classical Logic.Lucas Rosenblatt - 2019 - Notre Dame Journal of Formal Logic 60 (4):559-585.
    One of the most fruitful applications of substructural logics stems from their capacity to deal with self-referential paradoxes, especially truth-theoretic paradoxes. Both the structural rules of contraction and the rule of cut play a crucial role in typical paradoxical arguments. In this paper I address a number of difficulties affecting noncontractive approaches to paradox that have been discussed in the recent literature. The situation was roughly this: if you decide to go substructural, the nontransitive approach to truth offers a lot (...)
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  18. Classical Logic through Refutation and Rejection.Achille C. Varzi & Gabriele Pulcini - forthcoming - In Achille C. Varzi & Gabriele Pulcini, Landscapes in Logic (Volume on Philosophical Logics). College Publications.
    We offer a critical overview of two sorts of proof systems that may be said to characterize classical propositional logic indirectly (and non-standardly): refutation systems, which prove sound and complete with respect to classical contradictions, and rejection systems, which prove sound and complete with respect to the larger set of all classical non-tautologies. Systems of the latter sort are especially interesting, as they show that classical propositional logic can be given a paraconsistent characterization. In (...)
     
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  19.  24
    Classical logic, argument and dialectic.M. D'Agostino & S. Modgil - 2018 - Artificial Intelligence 262 (C):15-51.
  20.  94
    On an inferential semantics for classical logic.David C. Makinson - 2014 - Logic Journal of the IGPL 22 (1):147-154.
    We seek a better understanding of why an inferential semantics devised by Tor Sandqvist yields full classical logic, by providing and analysing a direct proof via a suitable maximality construction.
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  21. Classical Logic or Non-Reflexive Logic?: A Case of Semantic Underdetermination.Jonas Becker Arenhart & Décio Krause - 2012 - Revista Portuguesa de Filosofia 68 (1-2):73-86.
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  22.  44
    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. Classical Logic and Neutrosophic Logic. Answers to K. Georgiev.Florentin Smarandache - 2016 - Neutrosophic Sets and Systems 13:79-83.
    In this paper, we make distinctions between Classical Logic (where the propositions are 100% true, or 100 false) and the Neutrosophic Logic (where one deals with partially true, partially indeterminate and partially false propositions) in order to respond to K. Georgiev’s criticism [1]. We recall that if an axiom is true in a classical logic system, it is not necessarily that the axiom be valid in a modern (fuzzy, intuitionistic fuzzy, neutrosophic etc.) logic system.
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  24. A Classical Logic of Existence and Essence.Sergio Galvan & Alessandro Giordani - 2020 - Logic and Logical Philosophy 29 (4):541-570.
    The purpose of this paper is to provide a new system of logic for existence and essence, in which the traditional distinctions between essential and accidental properties, abstract and concrete objects, and actually existent and possibly existent objects are described and related in a suitable way. In order to accomplish this task, a primitive relation of essential identity between different objects is introduced and connected to a first order existence property and a first order abstractness property. The basic idea (...)
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  25.  50
    On All Strong Kleene Generalizations of Classical Logic.Stefan Wintein - 2016 - Studia Logica 104 (3):503-545.
    By using the notions of exact truth and exact falsity, one can give 16 distinct definitions of classical consequence. This paper studies the class of relations that results from these definitions in settings that are paracomplete, paraconsistent or both and that are governed by the Strong Kleene schema. Besides familiar logics such as Strong Kleene logic, the Logic of Paradox and First Degree Entailment, the resulting class of all Strong Kleene generalizations of classical logic also (...)
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  26.  56
    Classical Logic and the Liar.Yannis Stephanou - 2020 - Logic and Logical Philosophy 29 (1):35-56.
    The liar and kindred paradoxes show that we can derive contradictions when we reason in accordance with classical logic from the schema (T) about truth: S is true iff p, where ‘p’ is to be replaced with a sentence and ‘S’ with a name of that sentence. The paper presents two arguments to the effect that the blame lies not with (T) but with classical logic. The arguments derive contradictions using classical logic, but instead (...)
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  27.  6
    The Event Calculus in Classical Logic - Alternative Axiomatisations.Rob Miller & Murray Shanahan - 1999 - Linköping Electronic Articles in Computer and Information Science 4.
    We present several alternative classical logic axiomatisations of the Event Calculus, a narrative based formalism for reasoning about actions and change. We indicate the range of applicability and key characteristics of each alternative formulation.
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  28.  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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  29. Normalisation for Bilateral Classical Logic with some Philosophical Remarks.Nils Kürbis - 2021 - Journal of Applied Logics 2 (8):531-556.
    Bilateralists hold that the meanings of the connectives are determined by rules of inference for their use in deductive reasoning with asserted and denied formulas. This paper presents two bilateral connectives comparable to Prior's tonk, for which, unlike for tonk, there are reduction steps for the removal of maximal formulas arising from introducing and eliminating formulas with those connectives as main operators. Adding either of them to bilateral classical logic results in an incoherent system. One way around this (...)
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  30. The (Greatest) Fragment of Classical Logic that Respects the Variable-Sharing Principle (in the FMLA-FMLA Framework).Damian E. Szmuc - 2021 - Bulletin of the Section of Logic 50 (4):421-453.
    We examine the set of formula-to-formula valid inferences of Classical Logic, where the premise and the conclusion share at least a propositional variable in common. We review the fact, already proved in the literature, that such a system is identical to the first-degree entailment fragment of R. Epstein's Relatedness Logic, and that it is a non-transitive logic of the sort investigated by S. Frankowski and others. Furthermore, we provide a semantics and a calculus for this (...). The semantics is defined in terms of a \-matrix built on top of a 5-valued extension of the 3-element weak Kleene algebra, whereas the calculus is defined in terms of a Gentzen-style sequent system where the left and right negation rules are subject to linguistic constraints. (shrink)
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  31.  72
    A Proof System for Classical Logic.Witold A. Pogorzelski & Piotr Wojtylak - 2005 - Studia Logica 80 (1):95-104.
  32. Classical logic and inexact predicates.David H. Sanford - 1974 - Mind 83 (329):112-113.
  33.  16
    Paraconsistent classical logic.Richard Sylvan & Igor Urbas - 1993 - Logique Et Analyse 141 (142):3-24.
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  34. Classical logic without bivalence.Tor Sandqvist - 2009 - Analysis 69 (2):211-218.
    Semantic justifications of the classical rules of logical inference typically make use of a notion of bivalent truth, understood as a property guaranteed to attach to a sentence or its negation regardless of the prospects for speakers to determine it as so doing. For want of a convincing alternative account of classical logic, some philosophers suspicious of such recognition-transcending bivalence have seen no choice but to declare classical deduction unwarranted and settle for a weaker system; intuitionistic (...)
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  35. 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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  36. Non-Classical Logics, Model Theory and Computability.[author unknown] - 1980 - Critica 12 (34):154-158.
     
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  37. Classical Logic.Kazem Sadegh-Zadeh - 2011 - In Handbook of Analytic Philosophy of Medicine. Dordrecht, Heidelberg, New York, London: Springer.
    Western (deductive) logic originated in Greek antiquity. It found its first expression in those works of the great philosopher Aristotle (384–322 BC) which have come to be known as the Organon, i.e., ‘instrument’. Aristotle’s logic, also known as syllogistics, was unsystematically concerned with patterns of reasoning and argumentation. It remained in this rudimentary state relatively unchanged and unchallenged until the second half of the nineteenth century. At that time, logic underwent a period of unprecedented reform and modernization, (...)
     
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  38.  50
    On the Costs of Classical Logic.Luca Castaldo - 2021 - Erkenntnis 88 (3):1157-1188.
    This article compares classical (or -like) and nonclassical (or -like) axiomatisations of the fixed-point semantics developed by Kripke (J Philos 72(19): 690–716, 1975). Following the line of investigation of Halbach and Nicolai (J Philos Logic 47(2): 227–257, 2018), we do not compare and qua theories of truth simpliciter, but rather qua axiomatisations of the Kripkean conception of truth. We strengthen the central results of Halbach and Nicolai (2018) and Nicolai (Stud Log 106(1): 101–130, 2018), showing that, on the (...)
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  39. Schönfinkel-type Operators for Classical Logic.Katalin Bimbó - 2010 - Studia Logica 95 (3):355-378.
    We briefly overview some of the historical landmarks on the path leading to the reduction of the number of logical connectives in classical logic. Relying on the duality inherent in Boolean algebras, we introduce a new operator ( Nallor ) that is the dual of Schönfinkel’s operator. We outline the proof that this operator by itself is sufficient to define all the connectives and operators of classical first-order logic ( Fol ). Having scrutinized the proof, we (...)
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  40.  19
    The Logic of Intentional Objects: A Meinongian Version of Classical Logic.Jacek Pasniczek - 1997 - Dordrecht, Netherland: Springer.
    Intentionality is one of the most frequently discussed topics in contemporary phenomenology and analytic philosophy. This book investigates intentionality from the point of view of intentional objects. According to the classical approach to this concept, whatever can be consciously experienced is regarded as an intentional object. Thus, not only ordinary existing individuals but also various kinds of non-existents and non-individuals are considered as intentional. Alexius Meinong, an Austrian philosopher, is particularly well-known as the `inventor' of an abundant ontology of (...)
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  41.  31
    Complementary Proof Nets for Classical Logic.Gabriele Pulcini & Achille C. Varzi - 2023 - Logica Universalis 17 (4):411-432.
    A complementary system for a given logic is a proof system whose theorems are exactly the formulas that are not valid according to the logic in question. This article is a contribution to the complementary proof theory of classical propositional logic. In particular, we present a complementary proof-net system, $$\textsf{CPN}$$ CPN, that is sound and complete with respect to the set of all classically invalid (one-side) sequents. We also show that cut elimination in $$\textsf{CPN}$$ CPN enjoys (...)
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  42. Classical logic with non-referring names.Richard L. Epstein - 2005 - Logique Et Analyse 48 (192):189-207.
     
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  43.  86
    Modal Extensions of Sub-classical Logics for Recovering Classical Logic.Marcelo E. Coniglio & Newton M. Peron - 2013 - Logica Universalis 7 (1):71-86.
    In this paper we introduce non-normal modal extensions of the sub-classical logics CLoN, CluN and CLaN, in the same way that S0.5 0 extends classical logic. The first modal system is both paraconsistent and paracomplete, while the second one is paraconsistent and the third is paracomplete. Despite being non-normal, these systems are sound and complete for a suitable Kripke semantics. We also show that these systems are appropriate for interpreting □ as “is provable in classical (...)”. This allows us to recover the theorems of propositional classical logic within three sub-classical modal systems. (shrink)
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  44.  49
    Classical logic, storage operators and second-order lambda-calculus.Jean-Louis Krivine - 1994 - Annals of Pure and Applied Logic 68 (1):53-78.
    We describe here a simple method in order to obtain programs from proofs in second-order classical logic. Then we extend to classical logic the results about storage operators proved by Krivine for intuitionistic logic. This work generalizes previous results of Parigot.
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  45.  49
    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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  46.  66
    Paraconsistency in classical logic.Gabriele Pulcini & Achille C. Varzi - 2018 - Synthese 195 (12):5485-5496.
    Classical propositional logic can be characterized, indirectly, by means of a complementary formal system whose theorems are exactly those formulas that are not classical tautologies, i.e., contradictions and truth-functional contingencies. Since a formula is contingent if and only if its negation is also contingent, the system in question is paraconsistent. Hence classical propositional logic itself admits of a paraconsistent characterization, albeit “in the negative”. More generally, any decidable logic with a syntactically incomplete proof theory (...)
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  47.  12
    Embedding classical logic into basic orthologic with a primitive modality.G. Battilotti - 1998 - Logic Journal of the IGPL 6 (3):383-402.
    In the present paper we give the first proof-theoretical example of an embedding of classical logic into a quantum-like logic. This is performed in the framework of basic logic, where a proof-theoretical approach to quantum logic is convenient. We consider basic orthologic, that corresponds to a sequential formulation of paraconsistent quantum logic, and which is given by basic orthologic added with weakening and contraction, in a language with Girard's negation. In the paper we first (...)
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  48.  24
    Combining classical logic, paraconsistency and relevance.Arnon Avron - 2005 - Journal of Applied Logic 3 (1):133-160.
  49. A non-classical logical foundation for naturalised realism.Emma Ruttkamp-Bloem, Giovanni Casini & Thomas Meyer - 2015 - In Pavel Arazim & Michal Dancak, The 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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  50.  67
    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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