Priestley Duality for SHn-algebras and Applications to the Study of 
Kripke-style Models for SHn-logics

Sofronie-Stokkermans, Viorica

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Priestley Duality for SHn-algebras and Applications to the Study of Kripke-style Models for SHn-logics

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Sofronie-Stokkermans, Viorica
Automation of Logic, MPI for Informatics, Max Planck Society;
Programming Logics, MPI for Informatics, Max Planck Society;

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Citation

Sofronie-Stokkermans, V. (2000). Priestley Duality for SHn-algebras and Applications to the Study of Kripke-style Models for SHn-logics. Multiple-Valued Logic - an International Journal, 5(4), 281-305.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-3458-E

Abstract

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.