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An Investigation into Intuitionistic Logic with Identity
, 2019 We define Kripke semantics for propositional intuitionistic logic with Suszko’s identity (ISCI). We propose sequent calculus for ISCI along with cut-elimination theorem.
Szymon Chlebowski +1 more
semanticscholar +1 more source
Proof-search of propositional intuitionistic logic sequents by means of classical logic calculus
Lietuvos Matematikos Rinkinys, 2008 In the paper, we define some classes of sequents of the propositional intuitionistic logic. These are classes of primarily and α-primarily reducible sequents. Then we show how derivability of these sequents in a propositional intuitionistic logic sequent
Romas Alonderis
doaj +1 more source
Intersection Logic in sequent calculus style [PDF]
Electronic Proceedings in Theoretical Computer Science, 2011 The intersection type assignment system has been designed directly as deductive system for assigning formulae of the implicative and conjunctive fragment of the intuitionistic logic to terms of lambda-calculus.
Simona Ronchi Della Rocca +3 more
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Monadic Fragments of Intuitionistic Control Logic [PDF]
, 2016 We investigate monadic fragments of Intuitionistic Control Logic (ICL), which is obtained from Intuitionistic Propositional Logic (IPL) by extending language of IPL by a constant distinct from intuitionistic constants.
Glenszczyk, Anna
core +2 more sources
Uniform Definability in Propositional Dependence Logic
, 2016 Both propositional dependence logic and inquisitive logic are expressively complete. As a consequence, every formula with intuitionistic disjunction or intuitionistic implication can be translated equivalently into a formula in the language of ...
Yang, Fan
core +1 more source
Co-constructive Logics for Proofs and Refutations
Studia Humana, 2015 This paper considers logics which are formally dual to intuitionistic logic in order to investigate a co-constructive logic for proofs and refutations. This is philosophically motivated by a set of problems regarding the nature of constructive truth, and
Trafford James
doaj +1 more source
Intuitionistic Linear Temporal Logics [PDF]
ACM Transactions on Computational Logic, 2019 We consider intuitionistic variants of linear temporal logic with “next,” “until,” and “release” based on expanding posets : partial orders equipped with an order-preserving transition function. This class of structures gives rise to a logic that we denote ITL e , and by imposing additional ...
Philippe Balbiani +3 more
openaire +5 more sources
Philosophical Foundations of Intuitionistic Logic [PDF]
Metaphysics, 2013 Intuitionistic logic, as a non-classical logic, encompasses the principles of logical reasoning which were used by L. E. J. Brouwer in developing his intuitionistic mathematics.
L Nabavi, MA Hojati, H Alaeenezhad
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From Intuitionism to Brouwer's Modal Logic
Bulletin of the Section of Logic, 2020 We try to translate the intuitionistic propositional logic INT into Brouwer's modal logic KTB. Our translation is motivated by intuitions behind Brouwer's axiom p →☐◊p The main idea is to interpret intuitionistic implication as modal strict implication ...
Zofia Kostrzycka
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'Unless' is 'Or', Unless '¬A Unless A' is Invalid
Dialectica, 2022 The proper translation of "unless" into intuitionistic formalisms is examined. After a brief examination of intuitionistic writings on "unless", and on translation in general, and a close examination of Dummett's use of "unless" in Elements of ...
Roy Cook
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