Speaker: Amanda Vidal (IIIA – CSIC)
Date and Time: Thursday, June 15th 2023, 16:30-18:00
Venue: KdVI seminar room F3.20 in Science Park 107 and online
Title: Computability for some modal many-valued logics.
Abstract.
Modal logic is one of the most developed and studied non-classical logics, yielding a beautiful equilibrium between complexity and expressivity. On the other hand, substructural (and as a particular case, many- valued) logics provide a formal framework to manage vague and resource sensitive information in a very general (and so, adaptable) fashion. Many-valued modal logics, combining the notions of modal operators with logics over richer algebraic structures is a field in ongoing development. While the first publications on the topic can be traced back to some seminal works by Fitting in the 90s, it has been only in the latter years when a more systematic work has been done.
In this talk we present some results for these logics, focused on their decidability and axiomatizability, and compare their behaviour to classical modal logics and the corresponding propositional substructural logics. In particular, we exhibit a family of undecidable non-classical (global) modal logics, including two of the three better known fuzzy logics (namely modal expansions of Łukasiewicz and Product logics). Moreover, we will see how we can further exploit undecidability to show that these logics are not even recursively enumerable, thus not being axiomatizable in the usual sense. This contrasts to what happens in their propositional counterparts, and places they nearer to the behavior of the corresponding FO logics (eg. validity in FO [0, 1]L is not R.E. either).