Combinatorial Proofs and Decomposition Theorems for First-order Logic

Autor:	Hughes, Dominic, Straßburger, Lutz, Wu, Jui-Hsuan
Rok vydání:	2021
Předmět:	Computer Science - Logic in Computer Science
Druh dokumentu:	Working Paper
Popis:	We uncover a close relationship between combinatorial and syntactic proofs for first-order logic (without equality). Whereas syntactic proofs are formalized in a deductive proof system based on inference rules, a combinatorial proof is a syntax-free presentation of a proof that is independent from any set of inference rules. We show that the two proof representations are related via a deep inference decomposition theorem that establishes a new kind of normal form for syntactic proofs. This yields (a) a simple proof of soundness and completeness for first-order combinatorial proofs, and (b) a full completeness theorem: every combinatorial proof is the image of a syntactic proof. Comment: To be published in LICS 2021. This is the author version of the paper with full proofs in the appendix
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2104.13124 Zobrazit plný text záznamu View this record from Arxiv