Proof Diagrams for Multiplicative Linear Logic: Syntax and Semantics
Proof nets are a syntax for linear logic proofs which gives a coarser notion of proof equivalence with respect to syntactic equality together with an intuitive geometrical representation of proofs. In this paper we give an alternative 2-dimensional syntax for multiplicative linear logic derivations. The syntax of string diagrams authorizes the definition of a framework where the sequentializability of a term, i.e. deciding whether the term corresponds to a correct derivation, can be verified in linear time. Furthermore, we can use this syntax to define a denotational semantics for multiplicative linear logic with units by means of equivalence classes of proof diagrams modulo a terminating rewriting.
KeywordsString diagrams Liner logic Proof semantics Monoidal categories
Mathematics Subject Classification18D10 03b47 18C50 03B70
I would like to thank Michele Alberti, Marianna Girlando, Giulio Guerrieri, Paolo Pistone and Lionel Vaux for the fruitful exchanges during the redaction of this work. A special acknowledgment to Yves Guiraud who wrote (and upgraded for the scope) the latex package for string diagrams representations  employed in the present manuscript. Thank to reviewers for carefull readings, useful remark and constructive observations.
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