The Logic and Metaphysics Workshop will meet on February 14th from 4:15-6:15 (NY time) via Zoom for a talk by Ekaterina Kubyshkina (Campinas).

Title: Ignorance as an excuse, formally

Abstract: In the current literature on epistemology there is a lively debate on which type of ignorance may provide a moral excuse. A good candidate is the one in which an agent has never considered or thought about a true proposition p. From a logical perspective, it is usual to model situations involving ignorance by means of epistemic logic. However, no formal analysis was provided for ignorance as an excuse. First, we will argue that if ignorance is expressed via standard modalities of knowledge and belief, one is unable to represent ignorance as an excuse. Secondly, we fill this gap by providing an original logical setting for modelling this type of ignorance. In particular, we introduce a complete and sound logic in which ignorance is expressed as a primitive modality. Semantically, the logic is characterized by Kripke semantics with possibly incomplete worlds. Moreover, in order to consider the conditions of a possible change of an agent’s ignorance, we will extend the setting by considering public announcements.

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.

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 (at the Graduate Center, Room 5382); 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. NO MEETING

Feb 28. Michael Burton (Yale)

Mar 7. David Papineau (King’s)

Mar 14. Wilfrid Hodges (Queen Mary)

Mar 21. Noson Yanofsky (CUNY)

Mar 28. Dongwoo Kim (CUNY)

Apr 4. Jenn McDonald (Columbia)

Apr 11. Justin Bledin (Johns Hopkins)

Apr 18. NO MEETING

Apr 25. Tore Fjetland Øgaard (Bergen)

May 2. Elia Zardini (Madrid)

May 9. Friederike Moltmann (CNRS Nice) Julian Schlöder (UConn)

May 16. Mircea Dumitru (Bucharest)