Duality via Truth for Information Algebras Based on De Morgan Lattices*

Abstract

Duality via truth is a kind of correspondence between a class of algebras and a class of relational systems (frames). These classes are viewed as two kinds of semantics for some logic: algebraic semantics and Kripke-style semantics, respectively. Having defined the notion of truth, the duality principle states that a sequent/formula is true in one semantics if and only if it is true in the other one. In consequence, the algebras and their corresponding frames express equivalent notion of truth. In this paper we develop duality via truth between modal algebras based on De Morgan lattices and their corresponding frames. Some axiomatic extensions of these algebras are considered. Basing on these results we present duality via truth between some classes of latticebased information algebras and their corresponding frames.