Failure of completeness properties of intuitionistic predicate logic for constructive models
Daniel Leivant (1976)
Annales scientifiques de l'Université de Clermont. Mathématiques
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Daniel Leivant (1976)
Annales scientifiques de l'Université de Clermont. Mathématiques
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Andrzej Grzegorczyk (1968)
Compositio Mathematica
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Javier Legris, Jorge A. Molina (2001)
Philosophia Scientiae
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In this paper we analyze the consideration of intuitionistic logic as an extension of classical logic. This — at first sight surprising — point of view has been sustained explicitly by Jan Łukasiewicz on the basis of a mapping of classical propositional logic into intuitionistic propositional logic by Kurt Gödel in 1933. Simultaneously with Gödel, Gerhard Gentzen had proposed another mapping of Peano´s arithmetic into Heyting´s arithmetic. We shall discuss these mappings in connection...
George Boolos (1980)
Fundamenta Mathematicae
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Tinko Tinchev, Dimiter Vakarelov (1988)
Banach Center Publications
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Krister Segerberg (1982)
Banach Center Publications
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Jan Štěpán (1989)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Došen, Kosta (1984)
Publications de l'Institut Mathématique. Nouvelle Série
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Zofia Kostrzycka (2020)
Bulletin of the Section of Logic
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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, whereas variables and other positive sentences remain as they are. The proposed translation preserves fragments of the Rieger-Nishimura lattice which is the Lindenbaum algebra of monadic formulas in INT. Unfortunately, INT is not embedded...