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1 — 50 / 916
  1. added 2020-05-25
    Paracomplete Logics Which Are Dual to the Paraconsistent Logics L3A and L3B.Alejandro Hernández-Tello, Verónica Borja-Macı́as & Marcelo E. Coniglio - 2020 - LANMR 2019: Proceedings of the 12th Latin American Workshop on Logic/Languages, Algorithms and New Methods of Reasoning.
    In 2016 Beziau, introduce a more restricted concept of paraconsistency, namely the genuine paraconsistency. He calls genuine paraconsistent logic those logic rejecting φ, ¬φ |- ψ and |- ¬(φ ∧ ¬φ). In that paper the author analyzes, among the three-valued logics, which of these logics satisfy this property. If we consider multiple-conclusion consequence relations, the dual properties of those above mentioned are: |- φ, ¬φ, and ¬(ψ ∨ ¬ψ) |- . We call genuine paracomplete logics those rejecting the mentioned properties. (...)
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  2. added 2020-04-14
    Constructive Mathematics and Equality.Bruno Bentzen - 2018 - Dissertation, Sun Yat-Sen University
    The aim of the present thesis is twofold. First we propose a constructive solution to Frege's puzzle using an approach based on homotopy type theory, a newly proposed foundation of mathematics that possesses a higher-dimensional treatment of equality. We claim that, from the viewpoint of constructivism, Frege's solution is unable to explain the so-called ‘cognitive significance' of equality statements, since, as we shall argue, not only statements of the form 'a = b', but also 'a = a' may contribute to (...)
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  3. added 2020-02-11
    Mystic, Geometer, and Intuitionist. The Life of L. E. J. Brouwer. Volume 1. The Dawning Revolution.Jan von Plato - 2001 - Bulletin of Symbolic Logic 7 (1):62-65.
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  4. added 2020-02-11
    The Method of Axiomatic Rejection for the Intuitionistic Propositional Logic.Rafal Dutkiewicz - 1989 - Studia Logica 48 (4):449-459.
    We prove that the intuitionistic sentential calculus is Ł-decidable, i.e. the sets of these of Int and of rejected formulas are disjoint and their union is equal to all formulas. A formula is rejected iff it is a sentential variable or is obtained from other formulas by means of three rejection rules. One of the rules is original, the remaining two are Łukasiewicz's rejection rules: by detachement and by substitution. We extensively use the method of Beth's semantic tableaux.
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  5. added 2020-01-25
    Boxes and Diamonds. An Open Introduction to Modal Logic.Richard Zach - 2019
    A textbook for modal and other intensional logics based on the Open Logic Project. It covers normal modal logics, relational semantics, axiomatic and tableaux proof systems, intuitionistic logic, and counterfactual conditionals.
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  6. added 2019-10-14
    Conservativity of Transitive Closure Over Weak Operational Set Theory.Laura Crosilla & Andrea Cantini - 2012 - In Ulrich Berger, Hannes Diener, Peter Schuster & Monika Seisenberger (eds.), Logic, Construction, Computation. De Gruyter.
    Constructive set theory a' la Myhill-Aczel has been extended in (Cantini and Crosilla 2008, Cantini and Crosilla 2010) to incorporate a notion of (partial, non--extensional) operation. Constructive operational set theory is a constructive and predicative analogue of Beeson's Inuitionistic set theory with rules and of Feferman's Operational set theory (Beeson 1988, Feferman 2006, Jaeger 2007, Jaeger 2009, Jaeger 1009b). This paper is concerned with an extension of constructive operational set theory (Cantini and Crosilla 2010) by a uniform operation of Transitive (...)
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  7. added 2019-09-28
    Modelling Combinatorial Auctions in Linear Logic.Daniele Porello & Ulle Endriss - 2010 - In Principles of Knowledge Representation and Reasoning: Proceedings of the Twelfth International Conference, {KR} 2010, Toronto, Ontario, Canada, May 9-13, 2010.
    We show that linear logic can serve as an expressive framework in which to model a rich variety of combinatorial auction mechanisms. Due to its resource-sensitive nature, linear logic can easily represent bids in combinatorial auctions in which goods may be sold in multiple units, and we show how it naturally generalises several bidding languages familiar from the literature. Moreover, the winner determination problem, i.e., the problem of computing an allocation of goods to bidders producing a certain amount of revenue (...)
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  8. added 2019-09-28
    Modelling Multilateral Negotiation in Linear Logic.Daniele Porello & Ulle Endriss - 2010 - In {ECAI} 2010 - 19th European Conference on Artificial Intelligence, Lisbon, Portugal, August 16-20, 2010, Proceedings. pp. 381--386.
    We show how to embed a framework for multilateral negotiation, in which a group of agents implement a sequence of deals concerning the exchange of a number of resources, into linear logic. In this model, multisets of goods, allocations of resources, preferences of agents, and deals are all modelled as formulas of linear logic. Whether or not a proposed deal is rational, given the preferences of the agents concerned, reduces to a question of provability, as does the question of whether (...)
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  9. added 2019-08-19
    A Binary Quantifier for Definite Descriptions in Intuitionist Negative Free Logic: Natural Deduction and Normalisation.Nils Kürbis - 2019 - Bulletin of the Section of Logic 48 (2):81-97.
    This paper presents a way of formalising definite descriptions with a binary quantifier ι, where ιx[F, G] is read as ‘The F is G’. Introduction and elimination rules for ι in a system of intuitionist negative free logic are formulated. Procedures for removing maximal formulas of the form ιx[F, G] are given, and it is shown that deductions in the system can be brought into normal form.
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  10. added 2019-08-05
    Proof Theory for Positive Logic with Weak Negation.Marta Bílková & Almudena Colacito - forthcoming - Studia Logica:1-38.
    Proof-theoretic methods are developed for subsystems of Johansson’s logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems. In particular, cut-free complete sequent calculi are introduced and used to provide a proof of the fact that the systems satisfy the Craig interpolation property. Alternative versions of the calculi are later obtained by means of an appropriate loop-checking history mechanism. Termination of the new calculi is proved, and (...)
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  11. added 2019-07-04
    Peter Geach: A Few Personal Remarks.Arthur Gibson - 2015 - Philosophical Investigations 38 (1-2):25-33.
    Personal biographical outline of being taught by, and encounters with, Peter Geach.
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  12. added 2019-07-03
    Algebraic and Topological Semantics for Inquisitive Logic Via Choice-Free Duality.Nick Bezhanishvili, Gianluca Grilletti & Wesley H. Holliday - 2019 - In Rosalie Iemhoff, Michael Moortgat & Ruy de Queiroz (eds.), Logic, Language, Information, and Computation. WoLLIC 2019. Lecture Notes in Computer Science, Vol. 11541. Springer. pp. 35-52.
    We introduce new algebraic and topological semantics for inquisitive logic. The algebraic semantics is based on special Heyting algebras, which we call inquisitive algebras, with propositional valuations ranging over only the ¬¬-fixpoints of the algebra. We show how inquisitive algebras arise from Boolean algebras: for a given Boolean algebra B, we define its inquisitive extension H(B) and prove that H(B) is the unique inquisitive algebra having B as its algebra of ¬¬-fixpoints. We also show that inquisitive algebras determine Medvedev’s logic (...)
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  13. added 2019-06-07
    Kuroda Sigekatu. Sûgaku no tyokkansei to sono mu-muzyunsei ni tuite . Kisokagaku, vol. 1 no. 2 , pp. 33–44.Kuroda Sigekatu. Aristotle no ronri to Brouwer no ronri ni tuite . Kagaku, vol. 18 no. 1 , pp. 2–10.Kuroda Sigekatu. Intuitionistische Untersuchungen der formalistischen Logik. Nagoya mathematical journal, vol. 2 , pp. 35–47. [REVIEW]M. Ohnishi - 1956 - Journal of Symbolic Logic 21 (2):196-196.
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  14. added 2019-06-06
    Review: L. E. J. Brouwer, D. Van Dalen, Brouwer's Cambridge Lectures on Intuitionism. [REVIEW]R. J. Grayson - 1983 - Journal of Symbolic Logic 48 (1):214-215.
  15. added 2019-06-06
    Zucker J. I.. The Adequacy Problem for Classical Logic. Journal of Philosophical Logic, Vol. 7 , Pp. 517–535.Zucker J. I. And Tragesser R. S.. The Adequacy Problem for Inferential Logic. Journal of Philosophical Logic, Pp. 501–516.Prawitz Dag. Proofs and the Meaning and Completeness of the Logical Constants. Essays on Mathematical and Philosophical Logic, Proceedings of the Fourth Scandinavian Logic Symposium and of the First Soviet-Finnish Logic Conference, Jyväskyla, Finland, June 29-July 6,1976, Edited by Hintikka Jaakko, Niiniluoto Ilkka, and Saarinen Esa, Synthese Library, Vol. 122, D. Reidel Publishing Company, Dordrecht, Boston, and London, 1979, Pp. 25–40.Prawitz Dag. Meaning and Proofs: On the Conflict Between Classical and Intuitionistic Logic. Theoria, Vol. 43 , Pp. 2–40.Dummett M. A. E.. The Justification of Deduction. Proceedings of the British Academy, Vol. 59 , Pp. 201–232.Dummett Michael. The Philosophical Basis of Intuitionistic Logic. Logic Colloquium '73, Proceedings. [REVIEW]Richard E. Grandy - 1982 - Journal of Symbolic Logic 47 (3):689-694.
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  16. added 2019-06-06
    Elements of Intuitionism.Michael Dummett - 1977 - Oxford University Press.
    This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics, for example Brouwer's proof of the Bar Theorem, valuation systems, and the completeness of intuitionistic first-order logic, have been completely revised.
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  17. added 2019-06-06
    A Bridge to Advanced Mathematics.H. B. Enderton & Dennis Sentilles - 1976 - Journal of Symbolic Logic 41 (3):699.
  18. added 2019-06-06
    Existence and Description in Formal Logic.Alonzo Church, Dana Scott & Ralph Schoenman - 1973 - Journal of Symbolic Logic 38 (1):166.
  19. added 2019-06-06
    Kac Mark and Ulam Stanislaw M.. Mathematics and Logic. Retrospect and Prospects. Praeger Frederick A., Publishers, New York, Washington, and London 1968, Ix + 170 Pp.; Also a Paperbound Reprint, A Mentor Book, Published by The New American Library, New York and Toronto 1969, 222 Pp. [REVIEW]David Booth - 1971 - Journal of Symbolic Logic 36 (4):677.
  20. added 2019-06-06
    The Gentle Art of Mathematics.Alonzo Church, Dan Pedoe & Griselda El Tayeb - 1966 - Journal of Symbolic Logic 31 (4):675.
  21. added 2019-06-06
    Britzelmayr Wilhelm. Interpretation von Kalkülen. Synthese, Vol. 7 , Pp. 50–57.Roderick M. Chisholm - 1951 - Journal of Symbolic Logic 16 (4):292-292.
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  22. added 2019-06-06
    D. A. T. Gasking. Mathematics and the World. The Australasian Journal of Psychology and Philosophy, Vol. 18 , Pp. 97–116. [REVIEW]Morton G. White - 1941 - Journal of Symbolic Logic 6 (2):66-67.
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  23. added 2019-06-05
    Intuitionism and the Modal Logic of Vagueness.Susanne Bobzien & Ian Rumfitt - 2020 - Journal of Philosophical Logic 49 (2):221-248.
    Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptance has been hampered by two factors. First, the lack of an accepted semantics for languages containing vague terms has led even philosophers sympathetic to intuitionism to complain that no explanation has been given of why intuitionistic logic is the correct logic for such languages. Second, switching from classical to intuitionistic logic, while it may help with the Sorites, does not appear to offer any advantages when dealing with the (...)
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  24. added 2019-06-05
    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 as a logic of assertions and conjectures: looking at the (...)
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  25. added 2019-06-05
    The Logic of Partitions: Introduction to the Dual of the Logic of Subsets: The Logic of Partitions.David Ellerman - 2010 - Review of Symbolic Logic 3 (2):287-350.
    Modern categorical logic as well as the Kripke and topological models of intuitionistic logic suggest that the interpretation of ordinary “propositional” logic should in general be the logic of subsets of a given universe set. Partitions on a set are dual to subsets of a set in the sense of the category-theoretic duality of epimorphisms and monomorphisms—which is reflected in the duality between quotient objects and subobjects throughout algebra. If “propositional” logic is thus seen as the logic of subsets of (...)
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  26. added 2019-06-05
    An Algebraic Approach to Canonical Formulas: Intuitionistic Case: An Algebraic Approach to Canonical Formulas.Guram Bezhanishvili - 2009 - Review of Symbolic Logic 2 (3):517-549.
    We introduce partial Esakia morphisms, well partial Esakia morphisms, and strong partial Esakia morphisms between Esakia spaces and show that they provide the dual description of homomorphisms, homomorphisms, and homomorphisms between Heyting algebras, thus establishing a generalization of Esakia duality. This yields an algebraic characterization of Zakharyaschev’s subreductions, cofinal subreductions, dense subreductions, and the closed domain condition. As a consequence, we obtain a new simplified proof of Zakharyaschev’s theorem that each intermediate logic can be axiomatized by canonical formulas.
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  27. added 2019-06-05
    Some Weak Fragments of {${\Rm HA}$} and Certain Closure Properties.Morteza Moniri & Mojtaba Moniri - 2002 - Journal of Symbolic Logic 67 (1):91-103.
    We show that Intuitionistic Open Induction iop is not closed under the rule DNS(∃ - 1 ). This is established by constructing a Kripke model of iop + $\neg L_y(2y > x)$ , where $L_y(2y > x)$ is universally quantified on x. On the other hand, we prove that iop is equivalent with the intuitionistic theory axiomatized by PA - plus the scheme of weak ¬¬LNP for open formulas, where universal quantification on the parameters precedes double negation. We also show (...)
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  28. added 2019-06-05
    Five Observations Concerning the Intended Meaning of the Intuitionistic Logical Constants.Gustavo Fernández Díez - 2000 - Journal of Philosophical Logic 29 (4):409-424.
    This paper contains five observations concerning the intended meaning of the intuitionistic logical constants: (1) if the explanations of this meaning are to be based on a non-decidable concept, that concept should not be that of 'proof'; (2) Kreisel's explanations using extra clauses can be significantly simplified; (3) the impredicativity of the definition of → can be easily and safely ameliorated; (4) the definition of → in terms of 'proofs from premises' results in a loss of the inductive character of (...)
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  29. added 2019-06-05
    Propositional Quantification in the Monadic Fragment of Intuitionistic Logic.Tomasz Połacik - 1998 - Journal of Symbolic Logic 63 (1):269-300.
    We study the monadic fragment of second order intuitionistic propositional logic in the language containing the standard propositional connectives and propositional quantifiers. It is proved that under the topological interpretation over any dense-in-itself metric space, the considered fragment collapses to Heyting calculus. Moreover, we prove that the topological interpretation over any dense-in-itself metric space of fragment in question coincides with the so-called Pitts' interpretation. We also prove that all the nonstandard propositional operators of the form q $\mapsto \exists$p ), where (...)
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  30. added 2019-06-05
    An Inside View of Exp; or, The Closed Fragment of the Provability Logic of $I\Delta0 + \Omega1$ with a Propositional Constant for $\Operatorname{Exp}$. [REVIEW]Albert Visser - 1992 - Journal of Symbolic Logic 57 (1):131-165.
    In this paper I give a characterization of the closed fragment of the provability logic of $I \triangle_0 + \mathrm{EXP}$ with a propositional constant for $\mathrm{EXP}$. In three appendices many details on arithmetization are provided.
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  31. added 2019-06-05
    Finite Kripke Models of HA Are Locally PA.E. C. W. Krabbe - 1986 - Notre Dame Journal of Formal Logic 27:528-532.
  32. added 2019-06-05
    Individual Concepts as Propositional Variables in "ML"V"+1.Alberto Zanardo - 1984 - Notre Dame Journal of Formal Logic 25:332-346.
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  33. added 2019-06-05
    Some Applications of Kripke Models to Formal Systems of Intuitionistic Analysis.Scott Weinstein - 1979 - Annals of Pure and Applied Logic 16 (1):1.
  34. added 2019-06-05
    On modal logic with an intuitionistic base.Gisèle Fischer Servi - 1977 - Studia Logica 36:141.
    A definition of the concept of "Intuitionist Modal Analogue" is presented and motivated through the existence of a theorem preserving translation from MIPC to a bimodal S₄-S₅ calculus.
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  35. added 2019-06-05
    Kripke Models and the Intuitionistic Theory of Species.D. H. J. de Jongh - 1976 - Annals of Pure and Applied Logic 9 (1):157.
  36. added 2019-06-05
    Extensions of Kripke's Embedding Theorem.Jonathan Stavi - 1975 - Annals of Pure and Applied Logic 8 (4):345.
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  37. added 2019-06-05
    Formal Systems for Some Branches of Intuitionistic Analysis.G. Kreisel - 1970 - Annals of Pure and Applied Logic 1 (3):229.
  38. added 2019-06-04
    S. C. Kleene. An Addendum. The Journal of Symbolic Logic, Vol. 28 No. 2 , Pp. 154–156.T. Thacher Robinson - 1964 - Journal of Symbolic Logic 29 (3):146.
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  39. added 2019-06-03
    G. Kreisel. A Remark on Free Choice Sequences and the Topological Completeness Proofs. The Journal of Symbolic Logic, Vol. 23 No. 4 , Pp. 369–388. [REVIEW]Joan Rand Moschovakis - 1967 - Journal of Symbolic Logic 32 (2):283-283.
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  40. added 2019-06-03
    G. Kreisel. Elementary Completeness Properties of Intuitionistic Logic with a Note on Negations of Prenex Formulae. The Journal of Symbolic Logic, Vol. 23 No. 3 , Pp. 317–330. [REVIEW]Joan Rand Moschovakis - 1967 - Journal of Symbolic Logic 32 (2):282-283.
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  41. added 2019-05-21
    Wilfrid Hodges. Elementary Predicate Logic. Handbook of Philosophical Logic, Volume I, Elements of Classical Logic, Edited by D. Gabbay and F. Guenthner, Synthese Library, Vol. 164, D. Reidel Publishing Company, Dordrecht, Boston, and Lancaster, 1983, Pp. 1–131. [REVIEW]H. B. Enderton - 1989 - Journal of Symbolic Logic 54 (3):1089-1090.
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  42. added 2019-05-15
    Edsger W. Dijkstra and Carel S. Scholten. Predicate Calculus and Program Semantics. Texts and Monographs in Computer Science. Springer-Verlag, New York, Berlin, Heidelberg, Etc., 1990, Xi + 220 Pp. [REVIEW]Egon Börger - 1994 - Journal of Symbolic Logic 59 (2):673-678.
  43. added 2019-03-17
    On Dummett’s Pragmatist Justification Procedure.Hermógenes Oliveira - forthcoming - Erkenntnis:1-27.
    I show that propositional intuitionistic logic is complete with respect to an adaptation of Dummett’s pragmatist justification procedure. In particular, given a pragmatist justification of an argument, I show how to obtain a natural deduction derivation of the conclusion of the argument from, at most, the same assumptions.
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  44. added 2019-03-08
    Undecidability of the Real-Algebraic Structure of Models of Intuitionistic Elementary Analysis.Miklós Erdélyi-Szabó - 2000 - Journal of Symbolic Logic 65 (3):1014-1030.
    We show that true first-order arithmetic is interpretable over the real-algebraic structure of models of intuitionistic analysis built upon a certain class of complete Heyting algebras. From this the undecidability of the structures follows. We also show that Scott's model is equivalent to true second-order arithmetic. In the appendix we argue that undecidability on the language of ordered rings follows from intuitionistically plausible properties of the real numbers.
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  45. added 2019-03-07
    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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  46. added 2019-03-04
    Inference Rules and the Meaning of the Logical Constants.Hermógenes Oliveira - 2019 - Dissertation, Eberhard Karls Universität Tübingen
    The dissertation provides an analysis and elaboration of Michael Dummett's proof-theoretic notions of validity. Dummett's notions of validity are contrasted with standard proof-theoretic notions and formally evaluated with respect to their adequacy to propositional intuitionistic logic.
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  47. added 2018-12-15
    Elementary Constructive Operational Set Theory.Andrea Cantini & Laura Crosilla - 2010 - In Ways of Proof Theory.
    We introduce an operational set theory in the style of [5] and [16]. The theory we develop here is a theory of constructive sets and operations. One motivation behind constructive operational set theory is to merge a constructive notion of set ([1], [2]) with some aspects which are typical of explicit mathematics [14]. In particular, one has non-extensional operations (or rules) alongside extensional constructive sets. Operations are in general partial and a limited form of self{application is permitted. The system we (...)
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  48. added 2018-12-15
    Constructive Set Theory with Operations.Andrea Cantini & Laura Crosilla - 2008 - In Logic Colloquium 2004.
    We present an extension of constructive Zermelo{Fraenkel set theory [2]. Constructive sets are endowed with an applicative structure, which allows us to express several set theoretic constructs uniformly and explicitly. From the proof theoretic point of view, the addition is shown to be conservative. In particular, we single out a theory of constructive sets with operations which has the same strength as Peano arithmetic.
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  49. added 2018-11-21
    On the Concept of a Notational Variant.Alexander W. Kocurek - 2017 - In Alexandru Baltag, Jeremy Seligman & Tomoyuki Yamada (eds.), Logic, Rationality, and Interaction (LORI 2017, Sapporo, Japan). pp. 284-298.
    In the study of modal and nonclassical logics, translations have frequently been employed as a way of measuring the inferential capabilities of a logic. It is sometimes claimed that two logics are “notational variants” if they are translationally equivalent. However, we will show that this cannot be quite right, since first-order logic and propositional logic are translationally equivalent. Others have claimed that for two logics to be notational variants, they must at least be compositionally intertranslatable. The definition of compositionality these (...)
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  50. added 2018-11-20
    Intuitionistic Mereology.Paolo Maffezioli & Achille C. Varzi - forthcoming - Synthese:1-26.
    Two mereological theories are presented based on a primitive apartness relation along with binary relations of mereological excess and weak excess, respectively. It is shown that both theories are acceptable from the standpoint of constructive reasoning while remaining faithful to the spirit of classical mereology. The two theories are then compared and assessed with regard to their extensional import.
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1 — 50 / 916