Frame definability in finitely-valued modal logics

Guillermo Badia; Xavier Caicedo; Carles Noguera

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arXiv · 2206.12953

Frame definability in finitely-valued modal logics

Guillermo Badia·Xavier Caicedo·Carles Noguera

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Abstract

In this paper we study frame definability in finitely-valued modal logics and establish two main results via suitable translations: (1) in finitely-valued modal logics one cannot define more classes of frames than are already definable in classical modal logic (cf.~\citep[Thm.~8]{tho}), and (2) a large family of finitely-valued modal logics define exactly the same classes of frames as classical modal logic (including modal logics based on finite Heyting and \MV-algebras, or even \BL-algebras). In this way one may observe, for example, that the celebrated Goldblatt--Thomason theorem applies immediately to these logics. In particular, we obtain the central result from~\citep{te} with a much simpler proof and answer one of the open questions left in that paper. Moreover, the proposed translations allow us to determine the computational complexity of a big class of finitely-valued modal logics.

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BibTeX RIS

Guillermo Badia, Xavier Caicedo, Carles Noguera. 2022-06-26. Frame definability in finitely-valued modal logics. https://arxiv.org/abs/2206.12953

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