Combinatorial Proofs and Decomposition Theorems for First-order Logic
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 a...
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| Veröffentlicht in: | Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science S. 1 - 13 |
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| Hauptverfasser: | , , |
| Format: | Tagungsbericht |
| Sprache: | Englisch |
| Veröffentlicht: |
IEEE
29.06.2021
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| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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. |
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| DOI: | 10.1109/LICS52264.2021.9470579 |