Theoretical Computer Science
A Non-commutative Extension of Classical Linear Logic
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
LINK: A Proof Environment Based on Proof Nets
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Concurrent Constraint Programming and Non-commutative Logic
CSL '97 Selected Papers from the11th International Workshop on Computer Science Logic
Natural Deduction for Intuitionistic Non-communicative Linear Logic
TLCA '99 Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications
Implicit exchange in multiplicative proofnets
Mathematical Structures in Computer Science
Two-dimensional proof-structures and the exchange rule
Mathematical Structures in Computer Science
Permutative additives and exponentials
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Rewriting systems for the surface classification theorem
Mathematical Structures in Computer Science
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Recent work establishes a direct link between the complexity of a linear logic proof in terms of the exchange rule and the topological complexity of its corresponding proof net, expressed as the minimal rank of the surfaces on which the proof net can be drawn without crossing edges. That surface is essentially computed by sequentialising the proof net into a sequent calculus which is derived from that of linear logic by attaching an appropriate structure to the sequents. We show here that this topological calculus can be given a better-behaved logical status, when viewed in the variety-presentation framework introduced by the first author. This change of viewpoint gives rise to permutative logic, which enjoys cut elimination and focussing properties and comes equipped with new modalities for the management of the exchange rule. Moreover, both cyclic and linear logic are shown to be embedded into permutative logic. It provides the natural logical framework in which to study and constrain the topological complexity of proofs, and hence the use of the exchange rule.