Affiliations: Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland. [email protected]
Correspondence:
[†]
Address for correspondence: Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland.
Note: [*] This work has been supported by the grant N N206 399134 of Polish Ministry of Science and Higher Education.
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 lattice-based information algebras and their corresponding frames.
Keywords: Algebraic semantics, Kripke-style semantics, Modal algebras, De Morgan lattices, Information algebras, Duality theory
