Yuri Kazakov’s presentation “Modal logic from Proof-Theoretic Semantics Perspective”

Intern researcher at IL LLFP, Yuri Kazakov, gave a presentation at the research seminar “From the Logical Point of View,” which took place on May 30.

Abstract

In addition to the traditional representation of modal logic through Kripke models, there is a long tradition of researching proof theories for the corresponding class of logics. At the same time, the question of the possibility and expediency of describing modal connectives through proof-based constructions has rarely been raised in logical semantics. For some logics, such a description seems more natural or even indispensable, for example, for intuitionistic or substructural ones. But are the corresponding results portable to the class of modal logics? My research is devoted to this issue. I will try to introduce some of the basic ideas of proof-theoretic semantics as a complete program, justify the use of sequences as basic proof constructions, and demonstrate the results obtained for modal logics.