Transfer Theorems for Multimodal Logics
Kit Fine, Gerhard Schurz · 1997
Abstract Many of the modal logics that have been developed contain two or more modal operators. A notable example is the tense logic of Prior, which contains operators for both the past and the future. A more recent example is the logic of programs, which contains infinitely many operators, one for each program. A multimodal logic will have various monomodal fragments; and in the simplest case, it will be the join of these fragments-there will be no interactive axioms. Our concern in the present chapter is to investigate the question of when certain properties of the monomodal logics transfer to their join. To answer this question, we develop a very general proof method, which allows us to piece together models for different logics. The resulting theorems provide very general answers to our question, which are positive in most cases, but not in all.