Abstract

Many interesting philosophical principles include two kinds of modalities, e.g. epistemic and doxastic, alethic and epistemic, or alethic and deontic modalities.The purpose of this essay is to describe a set of bimodal systems, i.e. systems that include two kinds of modal operators, in which it is possible to investigate some formalizations of such principles. All in all we will consider 4,194,304 logics. All logics are described semantically and proof theoretically. We use possible world semantics to characterize the logics semantically, and both axiomatic systems and semantic tableaux to characterize them proof theoretically. We show that all systems are sound and complete with respect to their semantics and we consider some relationships between the various systems.