Строго импликативные формулы в модальных логиках, близких к интуиционистской.

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A.V. Chagrov

Abstract

In this paper some questions about strict implication in modal systems \textbf{S3} and \textbf{S4} are discussed. The first theorem shows that strict implication fragments of these logics have different properties: the fragment of \textbf{S4} is equivalent (but is not coincided) with the implication fragment of intuitionistic logic, but the fragment of \textbf{S3} is not such one. The second theorem of the paper is connected with an open question [8] on description of one variable strict implication fragment of \textbf{S3}: this fragment contains at least 24 non-equivalent formulas. The third theorem refutes a result of [13]: all the implication logics of the sequence [13] are coincided with implication fragment of intuitionistic logic, but in [13] it is «proved» that these logics form a strictly decreasing chain.

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