The principle of reflection and nested sequents

Mathematics and Philosophy Seminar

• Speaker: Hidenori Kurokawa (Kanazawa University, Japan)

All welcome!

For more information please contact the convenor, Salvatore Florio.

Abstract

This talk will address Sambin, Battilotti and Faggian’s proposal in proof theoretic semantics (broadly considered) for introducing logical constants via a method they refer to as “the principle of reflection." By this method, logical constants are first introduced by a sequent formulation of biconditionals, operational rules for traditional sequent calucli are then derived via reflexivity and cut, and the whole process is justified by proving cut elimination. I will propose a modification of this method based on nested sequents, which uniformizes it and extend it to a wider range of non-classical logics. Nested sequents have traditionally been understood as closely related to Kripke semantics for modal logic. But I will argue that it is possible to provide an alternative motivation in relation to Sambin et al.'s principle of reflection.