Representation of Lattices with Modal Operators in Two-Sorted Frames

Article type: Research Article

Authors: Hartonas, Chrysafis^{a; *} | Orłowska, Ewa^b

Affiliations: [a] University of Thessaly, Larissa, Greece. hartonas@teilar.gr | [b] National Institute of Telecommunications, Szachowa 1, 04-894 Warsaw, Poland. E.Orlowska@itl.waw.pl

Correspondence: [*] Address for correspondence: University of Thessaly, 41110 Larissa, Greece.

Abstract: We study general lattices with normal unary operators for which we prove relational representation and duality results. Similar results have appeared in print, using Urquhart’s lattice representation, by the second author with Vakarelov, Radzikowska and Rewitzky. We base our approach in this article on the Hartonas and Dunn lattice duality, proven by Gehrke and Harding to deliver a canonical lattice extension, and on recent results by the first author on the relational representation of normal lattice operators. We verify that the operators at the representation level (appropriately generated by relations) are the canonical extensions of the lattice operators, in Gehrke and Harding’s sense.

DOI: 10.3233/FI-2019-1793

Journal: Fundamenta Informaticae, vol. 166, no. 1, pp. 29-56, 2019