Representation Theorems for Lattice-ordered Modal Algebras and their Axiomatic Extensions*

Article type: Research Article

Authors: Radzikowska, Anna Maria^†

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: In this paper we present relational representation theorems for lattice-based modal algebras and their axiomatic extensions taking into account well-known schemas of modal logics. The underlying algebraic structures are bounded, not necessarily distributive lattices. Our approach is based on the Urquhart’s result for non-distributive lattices and Allwein and Dunn developments for algebras of liner logics.

Keywords: Representation theorems, Modal algebras, Algebraic semantics, Kripke-style semantics, Duality theory

DOI: 10.3233/FI-2016-1327

Journal: Fundamenta Informaticae, vol. 144, no. 2, pp. 183-203, 2016