The unbearable richness of proof-theoretic semantics

Tuesday, February 13, 2024 - 12:30 to 14:00

Title of Presentation: The unbearable richness of proof-theoretic semantics
CISCL Philosophy Seminars: Antonio Piccolomini D'Aragona

Abstract: Proof-theoretic semantics, a constructive framework stemming from Prawitz’s normalisation results for Gentzen’s Natural Deduction, provides a fine-grained treatment of such basic notions of logic as validity and consequence. In my talk, I claim that this richness depends on a combinatorial interplay of four choices for defining the concept of proof, and that the resulting combinations are symmetric, i.e., that they are permutations of sequences of some primitive ingredients involved in this concept. I also claim that the proof-theoretic diagram thereby obtained is complete, i.e., any other sequence of the primitive ingredients is either void, or else equivalent to one of the four already contained in the diagram. I conclude by suggesting that the diagram can be extended to one of higher-level, in which nodes are not definitions of the concept of proof, but consequence relations.