### Generalized Modal Logic

NAGAHASHI, Hideo
Department of Mathematical Sciences

New Mexico State University

Las Cruces, New Mexico 88003

USA

E-mail: hnagahas@nmsu.edu

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.