Priestley Duality for SHn-algebras and Applications to the Study of Kripke-style Models for SHn-logics
Viorica Sofronie-Stokkermans · 2000
The main goal of this paper is to show that the Priestley duality for SHn-algebras can help to establish a link between the algebraic and Kripke-style semantics for SHn-logics. We present a Priestley duality theorem for SHn-algebras, and note that the dual space of an SHn-algebra satisfies in particular the properties of a Kripke model for SHn-logics. We then show that Priestley duality can help in proving the soundness and completeness of SHn-logics with respect to the class of SHn-frames in a direct way, by using only soundness and completeness of SHn-logics with respect to the variety of SHn-algebras.