Theoretical Computer Science
Phase semantics and sequent calculus for pure noncommutative classical linear propositional logic
Journal of Symbolic Logic
Proceedings of the workshop on Advances in linear logic
Proceedings of the workshop on Advances in linear logic
Linear logic: its syntax and semantics
Proceedings of the workshop on Advances in linear logic
Proceedings of the workshop on Advances in linear logic
A New Correctness Criterion for Cyclic Proof Nets
Journal of Logic, Language and Information
A Non-commutative Extension of Classical Linear Logic
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
A Complete Axiomatisation for the Inclusion of Series-Parallel Partial Orders
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
Towards Hilbert's 24th Problem: Combinatorial Proof Invariants
Electronic Notes in Theoretical Computer Science (ENTCS)
Information and Computation
A characterization of medial as rewriting rule
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
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We first extract the combinatorial result behind various proofs of the sequentialisation theorem for multiplicative proof-nets. This result is an inductive characterisation of graphs with a unique perfect matching.Extending these techniques, we give a definition of multiplicative proof-nets in which commutativity but also associativity of the multiplicative connectives is interpreted as equality. This is done by representing a sequent by a cograph and axioms by a perfect matching. The main advantage of this presentation is aesthetic: any such graph, without any further requirement is a proof-structure and the correctness criterion also is a natural graph-theoretical property.A direct and purely graph theoretical proof of these results is available as a research report in which more details can be found (C. Retoré, Handsome proof-nets: R&B-graphs, perfect matchings and series-parallel graphs, Rapport de Recherche RR-3652, INRIA, March 1999. http://www.inria.fr/RRRT/publications-eng.html).