Frame Definability in Finitely-Valued Modal Logics (Guillermo Badia)

The Logic and Metaphysics Workshop will meet on February 7th from 4:15-6:15 (NY time) via Zoom for a talk by Guillermo Badia (Queensland).

Title: Frame Definability in Finitely-Valued Modal Logics

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, 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). 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 [B. Teheux. Modal definability for Łukasiewicz validity relations. Studia Logica 104 (2): 343–363 (2016)] 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.

Note: This is joint work with Carles Noguera and Xavier Caicedo.

Spring 2022 Schedule

The Logic and Metaphysics Workshop will be meeting on Mondays from 4:15 to 6:15 (NY time). Talks may be both virtual and in-person; the details will be announced for each talk individually. The provisional schedule is as follows:

Feb 7. Guillermo Badia (Queensland)

Feb 14. Ekaterina Kubyshkina (Campinas)

Feb 21. Noson Yanofsky (CUNY)

Feb 28. Michael Burton (Yale)

Mar 7. David Papineau (King’s)

Mar 14. Wilfrid Hodges (King’s)


Mar 28. Dongwoo Kim (CUNY)

Apr 4. Jenn McDonald (Columbia)

Apr 11. Justin Bledin (Johns Hopkins)


Apr 25. Tore Fjetland Øgaard (Bergen)

May 2. Elia Zardini (Madrid)

May 9. Friederike Moltmann (CNRS Nice)

May 16. Mircea Dumitru (Bucharest)