A SEMANTICS FOR MODAL CALCULI
J. V. Ivlev · 2005
Our approach to a construction of semantics for modal calculi consists in interpretation of modal statement in terms of necessary and possible truths as well as in terms of necessary and possible falsity. It supposes also some actual (ontological) and logical necessity, chance and possibility. In this paper there are given semantics for a number of calculi of actual and logical modalities. We have constructed the calculi of actual modalities in the beginning of the seventies. Classical sentential logic (CSL) which is the base of many other calculi contains connectives “¬” (negation) and “ ” (implication). The remaining connectives are introduced on the base of adequate definitions. As the symbols for actual necessity and possibility there are, respectively, used 2 and 3. The calculus Smin is the axiomatic strengthening of sentential calculus with axiom schemas (CSL) with the following axioms: