Positive modal logic beyond distributivity

Bezhanishvili, Nick, Dmitrieva, Anna ORCID: https://orcid.org/0000-0001-7551-6122, de Groot, Jim and Moraschini, Tommaso (2024) Positive modal logic beyond distributivity. Annals of Pure and Applied Logic, 175 (2). ISSN 0168-0072

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Abstract

We develop a duality for (modal) lattices that need not be distributive, and use it to study positive (modal) logic beyond distributivity, which we call weak positive (modal) logic. This duality builds on the Hofmann, Mislove and Stralka duality for meet-semilattices. We introduce the notion of Π1-persistence and show that every weak positive modal logic is Π1-persistent. This approach leads to a new relational semantics for weak positive modal logic, for which we prove an analogue of Sahlqvist’s correspondence result.

Item Type:	Article
Additional Information:	Data availability statement: No data was used for the research described in the article.
Uncontrolled Keywords:	duality,modal logic,non-distributive positive logic,sahlqvist correspondence,weak positive logic,logic ,/dk/atira/pure/subjectarea/asjc/2600/2609
Faculty \ School:	Faculty of Science Faculty of Science > School of Mathematics (former - to 2024)
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	30 May 2024 15:31
Last Modified:	11 Oct 2024 00:14
URI:	https://ueaeprints.uea.ac.uk/id/eprint/95345
DOI:	10.1016/j.apal.2023.103374

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