Introduction to the Theory of Computation
Introduction to the Theory of Computation
Graphic Apology for Symmetry and Implicitness
Graphic Apology for Symmetry and Implicitness
Handsome proof-nets: perfect matchings and cographs
Theoretical Computer Science - Linear logic
A system of interaction and structure
ACM Transactions on Computational Logic (TOCL)
Towards Hilbert's 24th Problem: Combinatorial Proof Invariants
Electronic Notes in Theoretical Computer Science (ENTCS)
A characterization of medial as rewriting rule
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Naming proofs in classical propositional logic
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
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Combinatorial proofs are abstract invariants for sequent calculus proofs, similarly to homotopy groups which are abstract invariants for topological spaces. Sequent calculus fails to be surjective onto combinatorial proofs, and here we extract a syntactically motivated closure of sequent calculus from which there is a surjection onto a complete set of combinatorial proofs. We characterize a class of canonical sequent calculus proofs for the full set of propositional tautologies and derive a new completeness theorem for combinatorial propositions. For this, we define a new mapping between combinatorial proofs and sequent calculus proofs, different from the one originally proposed, which explicitly links the logical flow graph of a proof to a skew fibration between graphs of formulas. The categorical properties relating the original and the new mappings are explicitly discussed.