, Volume 38, Issue 3, pp 297-311

A modal calculus analogous to K4W, based on intuitionistic propositional logic, Iℴ

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Abstract

This paper treats a kind of a modal logic based on the intuitionistic propositional logic which arose from the “provability” predicate in the first order arithmetic. The semantics of this calculus is presented in both a relational and an algebraic way.

Completeness theorems, existence of a characteristic model and of a characteristic frame, properties of FMP and FFP and decidability are proved.