MODAL COMPANIONS OF SUPERINTUITIONISTIC LOGICS: SYNTAX, SEMANTICS, AND PRESERVATION THEOREMS

Abstract

This paper studies the class of superintuitionistic logics and the class of normal extensions of the modal system S4, and the syntactic and semantic connections between the two classes, given by the mapping (which assigns to every modal logic its superintuitionistic fragment) and by the mappings and (which assign to every superintuitionistic logic its smallest and its greatest companion, respectively). It is shown that from classes of relational models with respect to which a logic is complete, one can construct a class of models with respect to which the logics and are complete. The relationship of inference (of canonical formulas) in logics , , and is also described. As a consequence, preservation theorems are obtained for finite approximability, for Kripke completeness and for the disjunction property at the transition from to , and also for decidability at the transition to and .Bibliography: 21 titles.