arXiv Open Access 2022

Positive Modal Logic Beyond Distributivity

Nick Bezhanishvili Anna Dmitrieva Jim de Groot Tommaso Moraschini

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Abstrak

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 $Π_1$-persistence and show that every weak positive modal logic is $Π_1$-persistent. This approach leads to a new relational semantics for weak positive modal logic, for which we prove an analogue of Sahlqvist correspondence result.

Topik & Kata Kunci

math.LO cs.LO

Penulis (4)

Nick Bezhanishvili

Anna Dmitrieva

Jim de Groot

Tommaso Moraschini

Format Sitasi

APA MLA BibTeX

Bezhanishvili, N., Dmitrieva, A., Groot, J.d., Moraschini, T. (2022). Positive Modal Logic Beyond Distributivity. https://arxiv.org/abs/2204.13401

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Informasi Jurnal

Tahun Terbit: 2022
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓