Logic and Logical Philosophy
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A deductive-reductive form of logic: Intuitionistic S4 modalities
DOI: http://dx.doi.org/10.12775/LLP.2002.005
Abstract
The paper is a continuation of A deductive-reductive form of logic: general theory and intuitionistic case ([1]) and considers the problem of definability of modal operators on the intuitionistic base. Contrary to the classical case, it seems that the fact whether the connective is Heyting’s or Brouwerian is essential for the intuitionistic logic. The connective of possibility has the classical interpretation, if it is defined on the base of the logic with Brouwerian connective of coimplication.
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Łukowski, P., “A deductive-reductive form of logic: general theory and intuitionistic case”, this volume. DOI: http://dx.doi.org/10.12775/LLP.2002.004
Rauszer, C., “An algebraic and Kripke-style approach to a certain extension of intuitionistic logic”, Dissertationes Mathematicae CLXVII, PWN Warszawa 1980.
Suszko, R., “Abolition of the Fregean Axiom”, Lectures Notes in Mathematics, No. 453, 1975, pp. 169–239.
Wójcicki, R., “Dual counterparts of consequence operation”, Bulletin of the Section of Logic 2/1, 54–57 (1973).
Print ISSN: 1425-3305
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