Generalized Modal Logic


Department of Mathematical Sciences
New Mexico State University
Las Cruces, New Mexico 88003

Abstract: We present the well known Sahlqvist correspondence results within the framework of a generalized modal algebra (and logic), which is meant to be a DLO (distributive lattice with operators) whose operators are unary. This gives us a natural way of defining a Kripke-style semantics in a large class of extensions of the generalized modal logic where the canonicity and hence the completeness hold. In particular, the class contains most of distributive logics such as (classical) modal logic, positive modal logic, intuitionistic logic and more. Algebraic point of view is stressed throughout.