Title: Inference behaviour semantics for all* connectives in two-dimensional sequent calculi

Abstract: In this talk, I present inference behaviour semantics (IBS) for connectives in two-dimensional sequent calculi. IBS is a novel approach to proof-theoretic semantics (PTS) that emphasises Wittgenstein’s conception of ‘meaning as use’, alongside Gentzen’s idea of operational rules as connective definitions. The core idea of IBS is to explore how proof rules determine the way we use connectives.

To implement this idea, I analyse all rule parameters that affect connective usage by proving global harmony in minimal derivability relations. This method allows me to define IBS for any connective definable in two-dimensional sequent calculi. The findings offer a meaning-theoretic explanation for the co-determination effects recently observed by Dicher and offer a fresh perspective on the relationships between connectives and their logics.

Ultimately, IBS opens a new avenue for PTS, providing a fine-grained local analysis of connective use and meaning, with the potential to evolve our understanding of the connectives.