Results for 'Intuitionistic conditional'

977 found
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  1.  59
    Basic Intuitionistic Conditional Logic.Yale Weiss - 2019 - Journal of Philosophical Logic 48 (3):447-469.
    Conditional logics have traditionally been intended to formalize various intuitively correct modes of reasoning involving conditional expressions in natural language. Although conditional logics have by now been thoroughly studied in a classical context, they have yet to be systematically examined in an intuitionistic context, despite compelling philosophical and technical reasons to do so. This paper addresses this gap by thoroughly examining the basic intuitionistic conditional logic ICK, the intuitionistic counterpart of Chellas’ important classical (...)
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  2.  62
    Intuitionistic Conditional Logics.Ivano Ciardelli & Xinghan Liu - 2020 - Journal of Philosophical Logic 49 (4):807-832.
    Building on recent work by Yale Weiss, we study conditional logics in the intuitionistic setting. We consider a number of semantic conditions which give rise, among others, to intuitionistic counterparts of Lewis’s logic VC and Stalnaker’s C2. We show how to obtain a sound and complete axiomatization of each logic arising from a combination of these conditions. On the way, we remark how, in the intuitionistic setting, certain classically equivalent principles of conditional logic come apart, (...)
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  3.  27
    An Intuitionistically Complete System of Basic Intuitionistic Conditional Logic.Grigory Olkhovikov - 2024 - Journal of Philosophical Logic 53 (5).
    We introduce a basic intuitionistic conditional logic IntCK\textsf{IntCK} that we show to be complete both relative to a special type of Kripke models and relative to a standard translation into first-order intuitionistic logic. We show that IntCK\textsf{IntCK} stands in a very natural relation to other similar logics, like the basic classical conditional logic CK\textsf{CK} and the basic intuitionistic modal logic IK\textsf{IK}. As for the basic intuitionistic conditional logic ICK\textsf{ICK} proposed in Weiss (_Journal of (...)
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  4.  82
    Sufficient conditions for the undecidability of intuitionistic theories with applications.Dov M. Gabbay - 1972 - Journal of Symbolic Logic 37 (2):375-384.
  5. 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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  6. Brouwerian intuitionism.Michael Detlefsen - 1990 - Mind 99 (396):501-534.
    The aims of this paper are twofold: firstly, to say something about that philosophy of mathematics known as 'intuitionism' and, secondly, to fit these remarks into a more general message for the philosophy of mathematics as a whole. What I have to say on the first score can, without too much inaccuracy, be compressed into two theses. The first is that the intuitionistic critique of classical mathematics can be seen as based primarily on epistemological rather than on meaning-theoretic considerations. (...)
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  7. Knowability and bivalence: intuitionistic solutions to the Paradox of Knowability.Julien Murzi - 2010 - Philosophical Studies 149 (2):269-281.
    In this paper, I focus on some intuitionistic solutions to the Paradox of Knowability. I first consider the relatively little discussed idea that, on an intuitionistic interpretation of the conditional, there is no paradox to start with. I show that this proposal only works if proofs are thought of as tokens, and suggest that anti-realists themselves have good reasons for thinking of proofs as types. In then turn to more standard intuitionistic treatments, as proposed by Timothy (...)
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  8.  96
    Intuitionistic Epistemic Logic, Kripke Models and Fitch’s Paradox.Carlo Proietti - 2012 - Journal of Philosophical Logic 41 (5):877-900.
    The present work is motivated by two questions. (1) What should an intuitionistic epistemic logic look like? (2) How should one interpret the knowledge operator in a Kripke-model for it? In what follows we outline an answer to (2) and give a model-theoretic definition of the operator K. This will shed some light also on (1), since it turns out that K, defined as we do, fulfills the properties of a necessity operator for a normal modal logic. The interest (...)
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  9.  53
    Intuitionistic Logic is a Connexive Logic.Davide Fazio, Antonio Ledda & Francesco Paoli - 2023 - Studia Logica 112 (1):95-139.
    We show that intuitionistic logic is deductively equivalent to Connexive Heyting Logic (CHL\textrm{CHL} CHL ), hereby introduced as an example of a strongly connexive logic with an intuitive semantics. We use the reverse algebraisation paradigm: CHL\textrm{CHL} CHL is presented as the assertional logic of a point regular variety (whose structure theory is examined in detail) that turns out to be term equivalent to the variety of Heyting algebras. We provide Hilbert-style and Gentzen-style proof systems for CHL\textrm{CHL} CHL ; moreover, (...)
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  10.  58
    Intuitionistic hybrid logic.Torben Braüner & Valeria de Paiva - 2006 - Journal of Applied Logic 4 (3):231-255.
    Hybrid logics are a principled generalization of both modal logics and description logics, a standard formalism for knowledge representation. In this paper we give the first constructive version of hybrid logic, thereby showing that it is possible to hybridize constructive modal logics. Alternative systems are discussed, but we fix on a reasonable and well-motivated version of intuitionistic hybrid logic and prove essential proof-theoretical results for a natural deduction formulation of it. Our natural deduction system is also extended with additional (...)
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  11.  23
    Intuitionistic notions of boundedness in ℕ.Fred Richman - 2009 - Mathematical Logic Quarterly 55 (1):31-36.
    We consider notions of boundedness of subsets of the natural numbers ℕ that occur when doing mathematics in the context of intuitionistic logic. We obtain a new characterization of the notion of a pseudobounded subset and we formulate the closely related notion of a detachably finite subset. We establish metric equivalents for a subset of ℕ to be detachably finite and to satisfy the ascending chain condition. Following Ishihara, we spell out the relationship between detachable finiteness and sequential continuity. (...)
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  12.  13
    Intuitionism.R. M. Hare - 1997 - In Sorting Out Ethics. Oxford, GB: Clarendon Press.
    Intuitionism, the second type of descriptivism, is the theory that the truth conditions of moral statements depend on irreducible moral properties, which must be defined in moral terms. The intuitionist claims that we have knowledge of moral truths derived from moral intuition. However, because it is a subjective experience, one person's intuition may differ from another's, and the theory offers no way to decide between them. Intuitionism, Hare argues, is really a kind of Subjectivist Naturalism, or Subjectivism; and, as with (...)
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  13.  84
    Intuitionism and the poverty of the inference argument.Alexander George - 1994 - Topoi 13 (2):79-82.
    Intuitionism is occasionally advanced on the grounds that a classical understanding of mathematical discourse could not be acquired, given limitations of the experience available to the language learner. In this note, focusing on the acquisition of the universal quantifier, I argue that this route of attack against a classical construal results, at best, in a Pyrrhic victory. The conditions under which it is successful are such as to redound upon the tenability of intuitionism itself. Adjudication will not follow merely from (...)
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  14. From Classical to Intuitionistic Probability.Brian Weatherson - 2003 - Notre Dame Journal of Formal Logic 44 (2):111-123.
    We generalize the Kolmogorov axioms for probability calculus to obtain conditions defining, for any given logic, a class of probability functions relative to that logic, coinciding with the standard probability functions in the special case of classical logic but allowing consideration of other classes of "essentially Kolmogorovian" probability functions relative to other logics. We take a broad view of the Bayesian approach as dictating inter alia that from the perspective of a given logic, rational degrees of belief are those representable (...)
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  15.  29
    Investigations into intuitionistic and other negations.Satoru Niki - 2022 - Bulletin of Symbolic Logic 28 (4):532-532.
    Intuitionistic logic formalises the foundational ideas of L.E.J. Brouwer’s mathematical programme of intuitionism. It is one of the earliest non-classical logics, and the difference between classical and intuitionistic logic may be interpreted to lie in the law of the excluded middle, which asserts that either a proposition is true or its negation is true. This principle is deemed unacceptable from the constructive point of view, in whose understanding the law means that there is an effective procedure to determine (...)
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  16. Lifschitz realizability for intuitionistic Zermelo–Fraenkel set theory.Ray-Ming Chen & Michael Rathjen - 2012 - Archive for Mathematical Logic 51 (7-8):789-818.
    A variant of realizability for Heyting arithmetic which validates Church’s thesis with uniqueness condition, but not the general form of Church’s thesis, was introduced by Lifschitz (Proc Am Math Soc 73:101–106, 1979). A Lifschitz counterpart to Kleene’s realizability for functions (in Baire space) was developed by van Oosten (J Symb Log 55:805–821, 1990). In that paper he also extended Lifschitz’ realizability to second order arithmetic. The objective here is to extend it to full intuitionistic Zermelo–Fraenkel set theory, IZF. The (...)
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  17. Frontiers of Conditional Logic.Yale Weiss - 2019 - Dissertation, The Graduate Center, City University of New York
    Conditional logics were originally developed for the purpose of modeling intuitively correct modes of reasoning involving conditional—especially counterfactual—expressions in natural language. While the debate over the logic of conditionals is as old as propositional logic, it was the development of worlds semantics for modal logic in the past century that catalyzed the rapid maturation of the field. Moreover, like modal logic, conditional logic has subsequently found a wide array of uses, from the traditional (e.g. counterfactuals) to the (...)
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  18.  65
    On intuitionistic modal and tense logics and their classical companion logics: Topological semantics and bisimulations.Jennifer M. Davoren - 2010 - Annals of Pure and Applied Logic 161 (3):349-367.
    We take the well-known intuitionistic modal logic of Fischer Servi with semantics in bi-relational Kripke frames, and give the natural extension to topological Kripke frames. Fischer Servi’s two interaction conditions relating the intuitionistic pre-order with the modal accessibility relation generalize to the requirement that the relation and its inverse be lower semi-continuous with respect to the topology. We then investigate the notion of topological bisimulation relations between topological Kripke frames, as introduced by Aiello and van Benthem, and show (...)
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  19. Nested Sequents for Intuitionistic Modal Logics via Structural Refinement.Tim Lyon - 2021 - In Anupam Das & Sara Negri, Automated Reasoning with Analytic Tableaux and Related Methods: TABLEAUX 2021. pp. 409-427.
    We employ a recently developed methodology -- called "structural refinement" -- to extract nested sequent systems for a sizable class of intuitionistic modal logics from their respective labelled sequent systems. This method can be seen as a means by which labelled sequent systems can be transformed into nested sequent systems through the introduction of propagation rules and the elimination of structural rules, followed by a notational translation. The nested systems we obtain incorporate propagation rules that are parameterized with formal (...)
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  20. De-Psychologizing Intuitionism: The Anti-Realist Rejection of Classical Logic.Sanford Shieh - 1993 - Dissertation, Harvard University
    The most puzzling and intriguing aspect of intuitionism as a philosophy of mathematics is its claim that classical deductive reasoning in mathematics is illegitimate. The two most well-known proponents of this position are L. E. J. Brouwer and Michael Dummett. Both of their criticisms of the use of classical logic in mathematics have, by and large, been taken to depend on the thesis that the principle of bivalence does not apply to mathematical statements; and the difference between these criticisms is (...)
     
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  21. Syntactic Interpolation for Tense Logics and Bi-Intuitionistic Logic via Nested Sequents.Tim Lyon, Alwen Tiu, Rajeev Gore & Ranald Clouston - 2020 - In Maribel Fernandez & Anca Muscholl, 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). pp. 1-16.
    We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path axioms, and for bi-intuitionistic logic. These logics do not have straightforward formalisations in the traditional Gentzen-style sequent calculus, but have all been shown to have cut-free nested sequent calculi. The proof of the interpolation theorem uses these calculi and is purely syntactic, without resorting (...)
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  22.  50
    Incompleteness of Intuitionistic Propositional Logic with Respect to Proof-Theoretic Semantics.Thomas Piecha & Peter Schroeder-Heister - 2019 - Studia Logica 107 (1):233-246.
    Prawitz proposed certain notions of proof-theoretic validity and conjectured that intuitionistic logic is complete for them [11, 12]. Considering propositional logic, we present a general framework of five abstract conditions which any proof-theoretic semantics should obey. Then we formulate several more specific conditions under which the intuitionistic propositional calculus turns out to be semantically incomplete. Here a crucial role is played by the generalized disjunction principle. Turning to concrete semantics, we show that prominent proposals, including Prawitz’s, satisfy at (...)
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  23.  67
    Completeness results for intuitionistic and modal logic in a categorical setting.M. Makkai & G. E. Reyes - 1995 - Annals of Pure and Applied Logic 72 (1):25-101.
    Versions and extensions of intuitionistic and modal logic involving biHeyting and bimodal operators, the axiom of constant domains and Barcan's formula, are formulated as structured categories. Representation theorems for the resulting concepts are proved. Essentially stronger versions, requiring new methods of proof, of known completeness theorems are consequences. A new type of completeness result, with a topos theoretic character, is given for theories satisfying a condition considered by Lawvere . The completeness theorems are used to conclude results asserting that (...)
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  24.  66
    Intuitionistic sets and ordinals.Paul Taylor - 1996 - Journal of Symbolic Logic 61 (3):705-744.
    Transitive extensional well founded relations provide an intuitionistic notion of ordinals which admits transfinite induction. However these ordinals are not directed and their successor operation is poorly behaved, leading to problems of functoriality. We show how to make the successor monotone by introducing plumpness, which strengthens transitivity. This clarifies the traditional development of successors and unions, making it intuitionistic; even the (classical) proof of trichotomy is made simpler. The definition is, however, recursive, and, as their name suggests, the (...)
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  25.  65
    Undecidability and intuitionistic incompleteness.D. C. McCarty - 1996 - Journal of Philosophical Logic 25 (5):559 - 565.
    Let S be a deductive system such that S-derivability (⊦s) is arithmetic and sound with respect to structures of class K. From simple conditions on K and ⊦s, it follows constructively that the K-completeness of ⊦s implies MP(S), a form of Markov's Principle. If ⊦s is undecidable then MP(S) is independent of first-order Heyting arithmetic. Also, if ⊦s is undecidable and the S proof relation is decidable, then MP(S) is independent of second-order Heyting arithmetic, HAS. Lastly, when ⊦s is many-one (...)
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  26.  71
    An Intuitionistic Model of Single Electron Interference.J. V. Corbett & T. Durt - 2010 - Studia Logica 95 (1-2):81-100.
    The double slit experiment for a massive scalar particle is described using intuitionistic logic with quantum real numbers as the numerical values of the particle's position and momentum. The model assigns physical reality to single quantum particles. Its truth values are given open subsets of state space interpreted as the ontological conditions of a particle. Each condition determines quantum real number values for all the particle's attributes. Questions, unanswerable in the standard theories, concerning the behaviour of single particles in (...)
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  27. An algebraic approach to intuitionistic connectives.Xavier Caicedo & Roberto Cignoli - 2001 - Journal of Symbolic Logic 66 (4):1620-1636.
    It is shown that axiomatic extensions of intuitionistic propositional calculus defining univocally new connectives, including those proposed by Gabbay, are strongly complete with respect to valuations in Heyting algebras with additional operations. In all cases, the double negation of such a connective is equivalent to a formula of intuitionistic calculus. Thus, under the excluded third law it collapses to a classical formula, showing that this condition in Gabbay's definition is redundant. Moreover, such connectives can not be interpreted in (...)
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  28.  98
    Axioms for classical, intuitionistic, and paraconsistent hybrid logic.Torben Braüner - 2006 - Journal of Logic, Language and Information 15 (3):179-194.
    In this paper we give axiom systems for classical and intuitionistic hybrid logic. Our axiom systems can be extended with additional rules corresponding to conditions on the accessibility relation expressed by so-called geometric theories. In the classical case other axiomatisations than ours can be found in the literature but in the intuitionistic case no axiomatisations have been published. We consider plain intuitionistic hybrid logic as well as a hybridized version of the constructive and paraconsistent logic N4.
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  29.  79
    Models for stronger normal intuitionistic modal logics.Kosta Došen - 1985 - Studia Logica 44 (1):39 - 70.
    This paper, a sequel to Models for normal intuitionistic modal logics by M. Boi and the author, which dealt with intuitionistic analogues of the modal system K, deals similarly with intuitionistic analogues of systems stronger than K, and, in particular, analogues of S4 and S5. For these prepositional logics Kripke-style models with two accessibility relations, one intuitionistic and the other modal, are given, and soundness and completeness are proved with respect to these models. It is shown (...)
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  30.  57
    Sufficient conditions for cut elimination with complexity analysis.João Rasga - 2007 - Annals of Pure and Applied Logic 149 (1-3):81-99.
    Sufficient conditions for first-order-based sequent calculi to admit cut elimination by a Schütte–Tait style cut elimination proof are established. The worst case complexity of the cut elimination is analysed. The obtained upper bound is parameterized by a quantity related to the calculus. The conditions are general enough to be satisfied by a wide class of sequent calculi encompassing, among others, some sequent calculi presentations for the first order and the propositional versions of classical and intuitionistic logic, classical and (...) modal logic S4, and classical and intuitionistic linear logic and some of its fragments. Moreover the conditions are such that there is an algorithm for checking if they are satisfied by a sequent calculus. (shrink)
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  31.  35
    The Logic ILP for Intuitionistic Reasoning About Probability.Angelina Ilić-Stepić, Zoran Ognjanović & Aleksandar Perović - 2024 - Studia Logica 112 (5):987-1017.
    We offer an alternative approach to the existing methods for intuitionistic formalization of reasoning about probability. In terms of Kripke models, each possible world is equipped with a structure of the form H,μ\langle H, \mu \rangle that needs not be a probability space. More precisely, though _H_ needs not be a Boolean algebra, the corresponding monotone function (we call it measure) μ:H[0,1]Q\mu : H \longrightarrow [0,1]_{\mathbb {Q}} satisfies the following condition: if α\alpha , β\beta , \(\alpha \wedge \beta (...)
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  32. One-Step Modal Logics, Intuitionistic and Classical, Part 2.Harold T. Hodes - 2021 - Journal of Philosophical Logic 50 (5):873-910.
    Part 1 [Hodes, 2021] “looked under the hood” of the familiar versions of the classical propositional modal logic K and its intuitionistic counterpart. This paper continues that project, addressing some familiar classical strengthenings of K and GL), and their intuitionistic counterparts. Section 9 associates two intuitionistic one-step proof-theoretic systems to each of the just mentioned intuitionistic logics, this by adding for each a new rule to those which generated IK in Part 1. For the systems associated (...)
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  33.  9
    Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic.Alexander V. Gheorghiu, Tao Gu & David J. Pym - forthcoming - Studia Logica:1-61.
    Proof-theoretic semantics (P-tS) is an innovative approach to grounding logical meaning in terms of proofs rather than traditional truth-conditional semantics. The point is not that one provides a proof system, but rather that one articulates meaning in terms of proofs and provability. To elucidate this paradigm shift, we commence with an introduction that contrasts the fundamental tenets of P-tS with the more prevalent model-theoretic approach to semantics. The contribution of this paper is a P-tS for a substructural logic, (...) multiplicative linear logic (IMLL). Specifically, we meticulously examine and refine the established P-tS for intuitionistic propositional logic. Subsequently, we present two novel and comprehensive forms of P-tS for IMLL. Notably, the semantics for IMLL in this paper embodies its resource interpretation through its number-of-uses reading (restricted to atoms). This stands in contrast to the conventional model-theoretic semantics of the logic, underscoring the value that P-tS brings to substructural logics. (shrink)
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  34. Socially conscious moral intuitionism.John Bengson, Terence Cuneo & Russ Shafer-Landau - 2023 - Noûs 57 (4):986-994.
    In “Trusting Moral Intuitions” we argued that moral intuitions are trustworthy due to their being the outputs of a cognitive practice, with social elements, in good working order. Backes, Eklund, and Michelson present several criticisms of our defense of a socially conscious moral intuitionism. We respond to these criticisms, defending our claim that social factors enhance the epistemic credentials of moral intuitions, answering worries pertaining to the reliability of the moral intuition practice, and addressing concerns about both the individuation of (...)
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  35. Intuitions in 21st-Century Ethics: Why Ethical Intuitionism and Reflective Equilibrium Need Each Other.Ernesto V. Garcia - 2021 - In Discipline filosofiche XXXI 2 2021 ( L’intuizione e le sue forme. Prospettive e problemi dell’intuizionismo). pp. 275-296.
    In this paper, I attempt to synthesize the two most influential contemporary ethical approaches that appeal to moral intuitions, viz., Rawlsian reflective equilibrium and Audi’s moderate intuitionism. This paper has two parts. First, building upon the work of Audi and Gaut, I provide a more detailed and nuanced account of how these two approaches are compatible. Second, I show how this novel synthesis can both (1) fully address the main objections to reflective equilibrium, viz., that it provides neither necessary nor (...)
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  36.  43
    Natural deduction for intuitionistic linear logic.A. S. Troelstra - 1995 - Annals of Pure and Applied Logic 73 (1):79-108.
    The paper deals with two versions of the fragment with unit, tensor, linear implication and storage operator of intuitionistic linear logic. The first version, ILL, appears in a paper by Benton, Bierman, Hyland and de Paiva; the second one, ILL+, is described in this paper. ILL has a contraction rule and an introduction rule !I for the exponential; in ILL+, instead of a contraction rule, multiple occurrences of labels for assumptions are permitted under certain conditions; moreover, there is a (...)
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  37.  68
    Possibility Semantics for Intuitionistic Logic.M. J. Cresswell - 2004 - Australasian Journal of Logic 2:11-29.
    The paper investigates interpretations of propositional and firstorder logic in which validity is defined in terms of partial indices; sometimes called possibilities but here understood as non-empty subsets of a set W of possible worlds. Truth at a set of worlds is understood to be truth at every world in the set. If all subsets of W are permitted the logic so determined is classical first-order predicate logic. Restricting allowable subsets and then imposing certain closure conditions provides a modelling for (...)
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  38.  90
    Godel's interpretation of intuitionism.William Tait - 2006 - Philosophia Mathematica 14 (2):208-228.
    Gödel regarded the Dialectica interpretation as giving constructive content to intuitionism, which otherwise failed to meet reasonable conditions of constructivity. He founded his theory of primitive recursive functions, in which the interpretation is given, on the concept of computable function of finite type. I will (1) criticize this foundation, (2) propose a quite different one, and (3) note that essentially the latter foundation also underlies the Curry-Howard type theory, and hence Heyting's intuitionistic conception of logic. Thus the Dialectica interpretation (...)
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  39.  43
    A Characteristic Frame for Positive Intuitionistic and Relevance Logic.Yale Weiss - 2020 - Studia Logica 109 (4):687-699.
    I show that the lattice of the positive integers ordered by division is characteristic for Urquhart’s positive semilattice relevance logic; that is, a formula is valid in positive semilattice relevance logic if and only if it is valid in all models over the positive integers ordered by division. I show that the same frame is characteristic for positive intuitionistic logic, where the class of models over it is restricted to those satisfying a heredity condition. The results of this article (...)
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  40. Univocity of Intuitionistic and Classical Connectives.Branden Fitelson & Rodolfo C. Ertola-Biraben - forthcoming - Bulletin of Symbolic Logic.
    In this paper, we show (among other things) that the conditional in Frege's Begriffsschrift is ambiguous.
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  41.  14
    Kuhn’s World Change and Mathematical Intuitionism.Eduardo Castro - forthcoming - International Studies in the Philosophy of Science.
    This paper argues for the following conditional: if mathematical intuitionism is a scientific revolution, then there is a world change. It contends that the intuitionistic mathematical revolution brings about an ontic world change. The paper presents examples of mathematical types and tokens that change within the intuitionistic mathematical revolution. It also addresses Michael Dummett’s semantic view regarding the realism vs. anti-realism dispute in mathematics. Contrary to Dummett, I argue that the metaphysical realism vs. anti-realism dispute precedes the (...)
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  42.  35
    Errata Corrige to “Pragmatic and dialogic interpretation of bi-intuitionism. Part I”.Gianluigi Bellin, Massimiliano Carrara, Daniele Chiffi & Alessandro Menti - 2016 - Logic and Logical Philosophy 25 (2):225-233.
    The goal of [3] is to sketch the construction of a syntactic categorical model of the bi-intuitionistic logic of assertions and hypotheses AH, axiomatized in a sequent calculus AH-G1, and to show that such a model has a chirality-like structure inspired by the notion of dialogue chirality by P-A. Melliès [8]. A chirality consists of a pair of adjoint functors L ⊣ R, with L: A → B, R: B → A, and of a functor (.)* : A → (...)
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  43.  81
    Pragmatic and dialogic interpretations of bi-intuitionism. Part 1.Gianluigi Bellin, Massimiliano Carrara, Daniele Chiffi & Alessandro Menti - 2014 - Logic and Logical Philosophy 23 (4):449-480.
    We consider a “polarized” version of bi-intuitionistic logic [5, 2, 6, 4] as a logic of assertions and hypotheses and show that it supports a “rich proof theory” and an interesting categorical interpretation, unlike the standard approach of C. Rauszer’s Heyting-Brouwer logic [28, 29], whose categorical models are all partial orders by Crolard’s theorem [8]. We show that P.A. Melliès notion of chirality [21, 22] appears as the right mathematical representation of the mirror symmetry between the intuitionistic and (...)
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  44.  52
    Preservation of structural properties in intuitionistic extensions of an inference relation.Tor Sandqvist - 2018 - Bulletin of Symbolic Logic 24 (3):291-305.
    The article approaches cut elimination from a new angle. On the basis of an arbitrary inference relation among logically atomic formulae, an inference relation on a language possessing logical operators is defined by means of inductive clauses similar to the operator-introducing rules of a cut-free intuitionistic sequent calculus. The logical terminology of the richer language is not uniquely specified, but assumed to satisfy certain conditions of a general nature, allowing for, but not requiring, the existence of infinite conjunctions and (...)
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  45. Conditionals, probability, and nontriviality.Charles G. Morgan & Edwin D. Mares - 1995 - Journal of Philosophical Logic 24 (5):455-467.
    We show that the implicational fragment of intuitionism is the weakest logic with a non-trivial probabilistic semantics which satisfies the thesis that the probabilities of conditionals are conditional probabilities. We also show that several logics between intuitionism and classical logic also admit non-trivial probability functions which satisfy that thesis. On the other hand, we also prove that very weak assumptions concerning negation added to the core probability conditions with the restriction that probabilities of conditionals are conditional probabilities are (...)
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  46. The Logic of Conditional Negation.John Cantwell - 2008 - Notre Dame Journal of Formal Logic 49 (3):245-260.
    It is argued that the "inner" negation $\mathord{\sim}$ familiar from 3-valued logic can be interpreted as a form of "conditional" negation: $\mathord{\sim}$ is read '$A$ is false if it has a truth value'. It is argued that this reading squares well with a particular 3-valued interpretation of a conditional that in the literature has been seen as a serious candidate for capturing the truth conditions of the natural language indicative conditional (e.g., "If Jim went to the party (...)
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  47.  98
    Dummett's intuitionism is not strict finitism.Samuel William Mitchell - 1992 - Synthese 90 (3):437 - 458.
    Michael Dummett's anti-realism is founded on the semantics of natural language which, he argues, can only be satisfactorily given in mathematics by intuitionism. It has been objected that an analog of Dummett's argument will collapse intuitionism into strict finitism. My purpose in this paper is to refute this objection, which I argue Dummett does not successfully do. I link the coherence of strict finitism to a view of confirmation — that our actual practical abilities cannot confirm we know what would (...)
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  48.  57
    Empirical meaningfulness and intuitionistic logic.John Myhill - 1972 - Philosophy and Phenomenological Research 33 (2):186-191.
    CONSIDER A NON EMPTY BUT OTHERWISE ARBITRARY SET OF\nPROPERTIES CALLED OBSERVATION-PROPERTIES (O-PROPERTIES).\nCALL A PROPERTY P A MEANINGFUL PROPERTY (M-PROPERTY) IF IT\nIS EQUIVALENT TO A (FINITE OR INFINITE) DISJUNCTION OF\nO-PROPERTIES--I.E., A NECESSARY AND SUFFICIENT CONDITION\nFOR P IS THAT AT LEAST ONE OBSERVATION-PROPERTY IN A\nCERTAIN SET O(P) BE TRUE. OBVIOUSLY THE CONJUNCTION AND\nDISJUNCTION OF TWO M-PROPERTIES IS AN M-PROPERTY; IN\nGENERAL THE NEGATION OF AN M-PROPERTY IS NOT AN M-PROPERTY.\nHOWEVER WE CAN DEFINE THE PSEUDO NEGATION OF AN M-PROPERTY\nP AS THE POSSESSION OF SOME (...)
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  49. Natural Semantics: Why Natural Deduction is Intuitionistic.James W. Garson - 2001 - Theoria 67 (2):114-139.
    In this paper investigates how natural deduction rules define connective meaning by presenting a new method for reading semantical conditions from rules called natural semantics. Natural semantics explains why the natural deduction rules are profoundly intuitionistic. Rules for conjunction, implication, disjunction and equivalence all express intuitionistic rather than classical truth conditions. Furthermore, standard rules for negation violate essential conservation requirements for having a natural semantics. The standard rules simply do not assign a meaning to the negation sign. (...) negation fares much better. Not only do the intuitionistic rules have a natural semantics, that semantics amounts to familiar intuitionistic truth conditions. We will make use of these results to argue that intuitionistic connectives, rather than standard ones have a better claim to being the truly logical connectives. (shrink)
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  50. Existence Assumptions and Logical Principles: Choice Operators in Intuitionistic Logic.Corey Edward Mulvihill - 2015 - Dissertation, University of Waterloo
    Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in (...)
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