Superintuitionistic companions of classical modal logics

Studia Logica 58 (2):229-259 (1997)
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Abstract

This paper investigates partitions of lattices of modal logics based on superintuitionistic logics which are defined by forming, for each superintuitionistic logic L and classical modal logic , the set L[] of L-companions of . Here L[] consists of those modal logics whose non-modal fragments coincide with L and which axiomatize if the law of excluded middle p V p is added. Questions addressed are, for instance, whether there exist logics with the disjunction property in L[], whether L[] contains a smallest element, and whether L[] contains lower covers of . Positive solutions as concerns the last question show that there are (uncountably many) superclean modal logics based on intuitionistic logic in the sense of Vakarelov [28]. Thus a number of problems stated in [28] are solved. As a technical tool the paper develops the splitting technique for lattices of modal logics based on superintuitionistic logics and ap plies duality theory from [34].

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Citations of this work

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References found in this work

Some embedding theorems for modal logic.David Makinson - 1971 - Notre Dame Journal of Formal Logic 12 (2):252-254.
Klassische und nichtklassische Aussagenlogik.Wolfgang Rautenberg - 1980 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 11 (2):405-407.
Intuitionistic tense and modal logic.W. B. Ewald - 1986 - Journal of Symbolic Logic 51 (1):166-179.

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