8 December 2020, The Utrecht Logic in Progress Series (TULIPS), Bogdan Dicher

Abstract:
Proof-theoretic semantics aims to explain the meaning of the logical constants in terms of the inference rules that govern their behaviour in proofs. One of its central concepts is that of harmony: roughly, the match between the rules stipulating the conditions for introducing a logical constant in a proof and those for eliminating it from a proof. There are many accounts of harmony, most of them are developed against a background that assumes the rules of Identity and Cut, taken to codify the reflexivity and transitivity of logical consequence. We have argued elsewhere that the proof-theoretic project should be approached relative to a logic, i.e., relative to a consequence relation, and that the consequence relation relevant for proof-theoretic semantics is the one given by the sequent-to-sequent derivability relation in Gentzen systems. This relation is always reflexive, monotonic, and transitive, but it being so does not depend on the availability of sequent rules codifying these properties. In this talk we investigate the prospects for an account of harmony adequate for logics that lack the structural rules of Identity and Cut.​

The talk will take place on MS Teams. Please contact the organizers for information about how to join the online meeting.