Abstract

Modal Logic’s theorems and rules are valid in possible worlds but Relevant Logic’s theorems and rules are valid, respectively, in logical worlds and situations. Robert Meyer in 1974 removed this asymmetry between the theorems and the rules of Relevant Logic by establishing a logical system, whose theorems and rules are valid in all situations. Introducing a new kind of truth and falsity operators, the authors in this article sketch a logical system defined on the basis of Relevant Logic. Such a system can not only preserve symmetry, but also remove some inconsistency between Modern Classical Logic and Relevant Logic, because the latter, like the former, puts possible worlds as a criterion for validity.