Results for 'intuitionistic logic'

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  1. Intuitionistic Logic.Dirk van Dalen - 2002 - In D. M. Gabbay & F. Guenthner (eds.), ¸ Itegabbay2002. Kluwer Academic Publishers. pp. 1-115.
     
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  2. Truth-Maker Semantics for Intuitionistic Logic.Kit Fine - 2014 - Journal of Philosophical Logic 43 (2-3):549-577.
    I propose a new semantics for intuitionistic logic, which is a cross between the construction-oriented semantics of Brouwer-Heyting-Kolmogorov and the condition-oriented semantics of Kripke. The new semantics shows how there might be a common semantical underpinning for intuitionistic and classical logic and how intuitionistic logic might thereby be tied to a realist conception of the relationship between language and the world.
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  3.  72
    Dual Intuitionistic Logic and a Variety of Negations: The Logic of Scientific Research.Yaroslav Shramko - 2005 - Studia Logica 80 (2-3):347-367.
    We consider a logic which is semantically dual (in some precise sense of the term) to intuitionistic. This logic can be labeled as “falsification logic”: it embodies the Popperian methodology of scientific discovery. Whereas intuitionistic logic deals with constructive truth and non-constructive falsity, and Nelson's logic takes both truth and falsity as constructive notions, in the falsification logic truth is essentially non-constructive as opposed to falsity that is conceived constructively. We also briefly (...)
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  4.  30
    Semi-Intuitionistic Logic.Juan Manuel Cornejo - 2011 - Studia Logica 98 (1-2):9-25.
    The purpose of this paper is to define a new logic $${\mathcal {SI}}$$ called semi-intuitionistic logic such that the semi-Heyting algebras introduced in [ 4 ] by Sankappanavar are the semantics for $${\mathcal {SI}}$$ . Besides, the intuitionistic logic will be an axiomatic extension of $${\mathcal {SI}}$$.
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  5.  22
    Intuitionistic Logic, Model Theory and Forcing.Melvin Fitting - 1969 - Amsterdam: North-Holland Pub. Co..
  6.  22
    Intuitionistic Logic and Modality Via Topology.Leo Esakia - 2004 - Annals of Pure and Applied Logic 127 (1-3):155-170.
    In the pioneering article and two papers, written jointly with McKinsey, Tarski developed the so-called algebraic and topological frameworks for the Intuitionistic Logic and the Lewis modal system. In this paper, we present an outline of modern systems with a topological tinge. We consider topological interpretation of basic systems GL and G of the provability logic in terms of the Cantor derivative and the Hausdorff residue.
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  7.  68
    Natural Deduction for Dual-Intuitionistic Logic.Luca Tranchini - 2012 - Studia Logica 100 (3):631-648.
    We present a natural deduction system for dual-intuitionistic logic. Its distinctive feature is that it is a single-premise multiple-conclusions system. Its relationships with the natural deduction systems for intuitionistic and classical logic are discussed.
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  8.  37
    Intuitionistic Logic with Strong Negation.Yuri Gurevich - 1977 - Studia Logica 36 (1-2):49 - 59.
    This paper is a reaction to the following remark by grzegorczyk: "the compound sentences are not a product of experiment. they arise from reasoning. this concerns also negations; we see that the lemon is yellow, we do not see that it is not blue." generally, in science the truth is ascertained as indirectly as falsehood. an example: a litmus-paper is used to verify the sentence "the solution is acid." this approach gives rise to a (very intuitionistic indeed) conservative extension (...)
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  9.  21
    Semi-Intuitionistic Logic with Strong Negation.Juan Manuel Cornejo & Ignacio Viglizzo - 2018 - Studia Logica 106 (2):281-293.
    Motivated by the definition of semi-Nelson algebras, a propositional calculus called semi-intuitionistic logic with strong negation is introduced and proved to be complete with respect to that class of algebras. An axiomatic extension is proved to have as algebraic semantics the class of Nelson algebras.
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  10.  26
    Dual-Intuitionistic Logic.Igor Urbas - 1996 - Notre Dame Journal of Formal Logic 37 (3):440-451.
    The sequent system LDJ is formulated using the same connectives as Gentzen's intuitionistic sequent system LJ, but is dual in the following sense: (i) whereas LJ is singular in the consequent, LDJ is singular in the antecedent; (ii) whereas LJ has the same sentential counter-theorems as classical LK but not the same theorems, LDJ has the same sentential theorems as LK but not the same counter-theorems. In particular, LDJ does not reject all contradictions and is accordingly paraconsistent. To obtain (...)
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  11.  51
    Bi-Simulating in Bi-Intuitionistic Logic.Guillermo Badia - 2016 - Studia Logica 104 (5):1037-1050.
    Bi-intuitionistic logic is the result of adding the dual of intuitionistic implication to intuitionistic logic. In this note, we characterize the expressive power of this logic by showing that the first order formulas equivalent to translations of bi-intuitionistic propositional formulas are exactly those preserved under bi-intuitionistic directed bisimulations. The proof technique is originally due to Lindstrom and, in contrast to the most common proofs of this kind of result, it does not use (...)
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  12.  26
    Intuitionistic Logic According to Dijkstra's Calculus of Equational Deduction.Jaime Bohórquez V. - 2008 - Notre Dame Journal of Formal Logic 49 (4):361-384.
    Dijkstra and Scholten have proposed a formalization of classical predicate logic on a novel deductive system as an alternative to Hilbert's style of proof and Gentzen's deductive systems. In this context we call it CED (Calculus of Equational Deduction). This deductive method promotes logical equivalence over implication and shows that there are easy ways to prove predicate formulas without the introduction of hypotheses or metamathematical tools such as the deduction theorem. Moreover, syntactic considerations (in Dijkstra's words, "letting the symbols (...)
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  13.  4
    Intuitionistic Logic Model Theory and Forcing.F. R. Drake - 1971 - Journal of Symbolic Logic 36 (1):166-167.
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  14. On an Intuitionistic Logic for Pragmatics.Gianluigi Bellin, Massimiliano Carrara & Daniele Chiffi - 2018 - Journal of Logic and Computation 50 (28):935–966..
    We reconsider the pragmatic interpretation of intuitionistic logic [21] regarded as a logic of assertions and their justi cations and its relations with classical logic. We recall an extension of this approach to a logic dealing with assertions and obligations, related by a notion of causal implication [14, 45]. We focus on the extension to co-intuitionistic logic, seen as a logic of hypotheses [8, 9, 13] and on polarized bi-intuitionistic logic (...)
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  15. The Proper Explanation of Intuitionistic Logic: On Brouwer's Demonstration of the Bar Theorem.Mark Van Atten & Göran Sundholm - unknown
    Brouwer's demonstration of his Bar Theorem gives rise to provocative questions regarding the proper explanation of the logical connectives within intuitionistic and constructivist frameworks, respectively, and, more generally, regarding the role of logic within intuitionism. It is the purpose of the present note to discuss a number of these issues, both from an historical, as well as a systematic point of view.
     
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  16. From Intuitionistic Logic to Dynamic Operational Quantum Logic.Sonja Smets - 2006 - Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1):257-275.
    Research within the operational approach to the logical foundations of physics has recently pointed out a new perspective in which quantum logic can be viewed as an intuitionistic logic with an additional operator to capture its essential, i.e., non-distributive, properties. In this paper we will offer an introduction to this approach. We will focus further on why quantum logic has an inherent dynamic nature which is captured in the meaning of "orthomodularity" and on how it motivates (...)
     
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  17.  11
    Questions and Dependency in Intuitionistic Logic.Ivano Ciardelli, Rosalie Iemhoff & Fan Yang - 2020 - Notre Dame Journal of Formal Logic 61 (1):75-115.
    In recent years, the logic of questions and dependencies has been investigated in the closely related frameworks of inquisitive logic and dependence logic. These investigations have assumed classical logic as the background logic of statements, and added formulas expressing questions and dependencies to this classical core. In this paper, we broaden the scope of these investigations by studying questions and dependency in the context of intuitionistic logic. We propose an intuitionistic team semantics, (...)
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  18.  35
    A Semantic Hierarchy for Intuitionistic Logic.Guram Bezhanishvili & Wesley H. Holliday - 2019 - Indagationes Mathematicae 30 (3):403-469.
    Brouwer's views on the foundations of mathematics have inspired the study of intuitionistic logic, including the study of the intuitionistic propositional calculus and its extensions. The theory of these systems has become an independent branch of logic with connections to lattice theory, topology, modal logic and other areas. This paper aims to present a modern account of semantics for intuitionistic propositional systems. The guiding idea is that of a hierarchy of semantics, organized by increasing (...)
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  19. The Philosophical Basis of Intuitionistic Logic.Michael Dummett - 1975 - In Truth and Other Enigmas. Cambridge: Harvard UP. pp. 215--247.
  20.  9
    Intuitionistic Logic and Implicit Definability.Larisa Maksimova - 2000 - Annals of Pure and Applied Logic 105 (1-3):83-102.
    It is proved that there are exactly 16 superintuitionistic propositional logics with the projective Beth property. These logics are finitely axiomatizable and have the finite model property. Simultaneously, all varieties of Heyting algebras with strong epimorphisms surjectivity are found.
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  21. Intuitionistic Logic and Elementary Rules.Ian Humberstone & David Makinson - 2011 - Mind 120:1035-1051.
    The interplay of introduction and elimination rules for propositional connectives is often seen as suggesting a distinguished role for intuitionistic logic. We prove three formal results about intuitionistic propositional logic that bear on that perspective, and discuss their significance.
     
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  22. Intuitionistic Logic as Epistemic Logic.Jaakko Hintikka - 2001 - Synthese 127 (1-2):7 - 19.
    In the present day and age, it seems that every constructivist philosopher of mathematics and her brother wants to be known as an intuitionist. In this paper, It will be shown that such a self-identification is in most cases mistaken. For one thing, not any old (or new) constructivism is intuitionism because not any old relevant construction is carried out mentally in intuition, as Brouwer envisaged. (edited).
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  23. The Development of Intuitionistic Logic.Mark Van Atten - unknown
     
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  24.  11
    Intuitionistic Logic As Epistemic Logic.Jaakko Hintikka - 2001 - Synthese 127 (1):7-19.
  25.  59
    The Intended Interpretation of Intuitionistic Logic.Scott Weinstein - 1983 - Journal of Philosophical Logic 12 (2):261 - 270.
  26.  87
    Intuitionistic Logic and Elementary Rules.Lloyd Humberstone & David Makinson - 2011 - Mind 120 (480):1035-1051.
    The interplay of introduction and elimination rules for propositional connectives is often seen as suggesting a distinguished role for intuitionistic logic. We prove three formal results concerning intuitionistic propositional logic that bear on that perspective, and discuss their significance. First, for a range of connectives including both negation and the falsum, there are no classically or intuitionistically correct introduction rules. Second, irrespective of the choice of negation or the falsum as a primitive connective, classical and (...) consequence satisfy exactly the same structural, introduction, and elimination (briefly, elementary) rules. Third, for falsum as primitive only, intuitionistic consequence is the least consequence relation that satisfies all classically correct elementary rules. (shrink)
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  27. Semantical Analysis of Intuitionistic Logic I.Saul A. Kripke - 1963 - In Michael Dummett & J. N. Crossley (eds.), Formal Systems and Recursive Functions: Proceedings of the Eighth Logic Colloquium, Oxford July 1963. North Holland. pp. 92-130.
  28.  23
    A Note on Dual-Intuitionistic Logic.Norihiro Kamide - 2003 - Mathematical Logic Quarterly 49 (5):519.
    Dual-intuitionistic logics are logics proposed by Czermak , Goodman and Urbas . It is shown in this paper that there is a correspondence between Goodman's dual-intuitionistic logic and Nelson's constructive logic N−.
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  29.  90
    The Information in Intuitionistic Logic.Johan Benthem - 2009 - Synthese 167 (2):251-270.
    Issues about information spring up wherever one scratches the surface of logic. Here is a case that raises delicate issues of 'factual' versus 'procedural' information, or 'statics' versus 'dynamics'. What does intuitionistic logic, perhaps the earliest source of informational and procedural thinking in contemporary logic, really tell us about information? How does its view relate to its 'cousin' epistemic logic? We discuss connections between intuitionistic models and recent protocol models for dynamic-epistemic logic, as (...)
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  30.  4
    A Short Introduction to Intuitionistic Logic.G. E. Mint͡s - 2000 - Kluwer Academic / Plenum Publishers.
    Intuitionistic logic is presented here as part of familiar classical logic which allows mechanical extraction of programs from proofs. to make the material more accessible, basic techniques are presented first for propositional logic; Part II contains extensions to predicate logic. This material provides an introduction and a safe background for reading research literature in logic and computer science as well as advanced monographs. Readers are assumed to be familiar with basic notions of first order (...)
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  31.  23
    $\in_I$ : An Intuitionistic Logic Without Fregean Axiom and with Predicates for Truth and Falsity.Steffen Lewitzka - 2009 - Notre Dame Journal of Formal Logic 50 (3):275-301.
    We present $\in_I$-Logic (Epsilon-I-Logic), a non-Fregean intuitionistic logic with a truth predicate and a falsity predicate as intuitionistic negation. $\in_I$ is an extension and intuitionistic generalization of the classical logic $\in_T$ (without quantifiers) designed by Sträter as a theory of truth with propositional self-reference. The intensional semantics of $\in_T$ offers a new solution to semantic paradoxes. In the present paper we introduce an intuitionistic semantics and study some semantic notions in this broader (...)
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  32.  12
    Implicational Formulas in Intuitionistic Logic.Alasdair Urquhart - 1974 - Journal of Symbolic Logic 39 (4):661-664.
  33.  51
    Unification in Intuitionistic Logic.Silvio Ghilardi - 1999 - Journal of Symbolic Logic 64 (2):859-880.
    We show that the variety of Heyting algebras has finitary unification type. We also show that the subvariety obtained by adding it De Morgan law is the biggest variety of Heyting algebras having unitary unification type. Proofs make essential use of suitable characterizations (both from the semantic and the syntactic side) of finitely presented projective algebras.
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  34.  8
    Intuitionistic Logic According to Dijkstra's Calculus of Equational Deduction.Jaime Bohórquez - 2008 - Notre Dame Journal of Formal Logic 49 (4):361-384.
    Dijkstra and Scholten have proposed a formalization of classical predicate logic on a novel deductive system as an alternative to Hilbert's style of proof and Gentzen's deductive systems. In this context we call it CED . This deductive method promotes logical equivalence over implication and shows that there are easy ways to prove predicate formulas without the introduction of hypotheses or metamathematical tools such as the deduction theorem. Moreover, syntactic considerations have led to the "calculational style," an impressive array (...)
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  35.  14
    A Probabilistic Extension of Intuitionistic Logic.Z. Ognjanovic & Z. Markovic - 2003 - Mathematical Logic Quarterly 49 (4):415.
    We introduce a probabilistic extension of propositional intuitionistic logic. The logic allows making statements such as P≥sα, with the intended meaning “the probability of truthfulness of α is at least s”. We describe the corresponding class of models, which are Kripke models with a naturally arising notion of probability, and give a sound and complete infinitary axiomatic system. We prove that the logic is decidable.
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  36.  14
    Infinitary Intuitionistic Logic From a Classical Point of View.Mark E. Nadel - 1978 - Annals of Mathematical Logic 14 (2):159-191.
  37.  20
    A Lower Bound for Intuitionistic Logic.Pavel Hrubeš - 2007 - Annals of Pure and Applied Logic 146 (1):72-90.
    We give an exponential lower bound on the number of proof-lines in intuitionistic propositional logic, IL, axiomatised in the usual Frege-style fashion; i.e., we give an example of IL-tautologies A1,A2,… s.t. every IL-proof of Ai must have a number of proof-lines exponential in terms of the size of Ai. We show that the results do not apply to the system of classical logic and we obtain an exponential speed-up between classical and intuitionistic logic.
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  38.  9
    Complement-Topoi and Dual Intuitionistic Logic.Luis Estrada-González - 2010 - Australasian Journal of Logic 9:26-44.
    Mortensen studies dual intuitionistic logic by dualizing topos internal logic, but he did not study a sequent calculus. In this paper I present a sequent calculus for complement-topos logic, which throws some light on the problem of giving a dualization for LJ.
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  39.  9
    Semantical Analysis of Intuitionistic Logic I.Saul A. Kripke, J. N. Crossley & M. A. E. Dummett - 1970 - Journal of Symbolic Logic 35 (2):330-332.
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  40.  3
    Knowability and Intuitionistic Logic.David Vidi & Graham Solomon - 2001 - Philosophia 28 (1-4):319-334.
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  41.  73
    LK, LJ, Dual Intuitionistic Logic, and Quantum Logic.Hiroshi Aoyama - 2004 - Notre Dame Journal of Formal Logic 45 (4):193-213.
    In this paper, we study the relationship among classical logic, intuitionistic logic, and quantum logic . These logics are related in an interesting way and are not far apart from each other, as is widely believed. The results in this paper show how they are related with each other through a dual intuitionistic logic . Our study is completely syntactical.
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  42.  51
    Completeness and Incompleteness for Intuitionistic Logic.Charles McCarty - 2008 - Journal of Symbolic Logic 73 (4):1315-1327.
    We call a logic regular for a semantics when the satisfaction predicate for at least one of its nontheorems is closed under double negation. Such intuitionistic theories as second-order Heyting arithmetic HAS and the intuitionistic set theory IZF prove completeness for no regular logics, no matter how simple or complicated. Any extensions of those theories proving completeness for regular logics are classical, i.e., they derive the tertium non datur. When an intuitionistic metatheory features anticlassical principles or (...)
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  43.  14
    Stable Formulas in Intuitionistic Logic.Nick Bezhanishvili & Dick de Jongh - 2018 - Notre Dame Journal of Formal Logic 59 (3):307-324.
    In 1995 Visser, van Benthem, de Jongh, and Renardel de Lavalette introduced NNIL-formulas, showing that these are exactly the formulas preserved under taking submodels of Kripke models. In this article we show that NNIL-formulas are up to frame equivalence the formulas preserved under taking subframes of frames, that NNIL-formulas are subframe formulas, and that subframe logics can be axiomatized by NNIL-formulas. We also define a new syntactic class of ONNILLI-formulas. We show that these are the formulas preserved in monotonic images (...)
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  44.  17
    Foundations of Intuitionistic Logic.G. Kreisel - 1965 - Journal of Symbolic Logic 30 (2):243-244.
  45.  43
    Possibilities, Models, and Intuitionistic Logic: Ian Rumfitt’s The Boundary Stones of Thought.Stewart Shapiro - 2019 - Inquiry: An Interdisciplinary Journal of Philosophy 62 (7):812-825.
    ABSTRACTAIan Rumfitt's new book presents a distinctive and intriguing philosophy of logic, one that ultimately settles on classical logic as the uniquely correct one–or at least rebuts some prominent arguments against classical logic. The purpose of this note is to evaluate Rumfitt's perspective by focusing on some themes that have occupied me for some time: the role and importance of model theory and, in particular, the place of counter-arguments in establishing invalidity, higher-order logic, and the logical (...)
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  46.  45
    Arithmetical Necessity, Provability and Intuitionistic Logic.Rob Goldblatt - 1978 - Theoria 44 (1):38-46.
  47.  24
    Intuitionistic Logic and Local Mathematical Theories.Yvon Gauthier - 1977 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 23 (27-30):411-414.
  48.  69
    Realizability and Intuitionistic Logic.J. Diller & A. S. Troelstra - 1984 - Synthese 60 (2):253 - 282.
  49.  15
    Identity and Existence in Intuitionistic Logic.Dana Scott, M. P. Fourman, C. J. Mulvey & D. S. Scott - 1985 - Journal of Symbolic Logic 50 (2):548-549.
  50.  13
    A Refined Interpretation of Intuitionistic Logic by Means of Atomic Polymorphism.José Espírito Santo & Gilda Ferreira - 2020 - Studia Logica 108 (3):477-507.
    We study an alternative embedding of IPC into atomic system F whose translation of proofs is based, not on instantiation overflow, but instead on the admissibility of the elimination rules for disjunction and absurdity. As compared to the embedding based on instantiation overflow, the alternative embedding works equally well at the levels of provability and preservation of proof identity, but it produces shorter derivations and shorter simulations of reduction sequences. Lambda-terms are employed in the technical development so that the algorithmic (...)
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