Retractile proof nets of the purely multiplicative and additive fragment of linear logic

Authors:
Roberto Maieli
Affiliations:
Dipartimento di Filosofia, Università degli Studi "Roma Tre"
Venue:
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Year:
2007

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Abstract

Proof nets are a parallel syntax for sequential proofs of linear logic, firstly introduced by Girard in 1987. Here we present and intrinsic (geometrical) characterization of proof nets, that is a correctness criterion (an algorithm) for checking those proof structures which correspond to proofs of the purely multiplicative and additive fragment of linear logic. This criterion is formulated in terms of simple graph rewriting rules and it extends an initial idea of a retraction correctness criterion for proof nets of the purely multiplicative fragment of linear logic presented by Danos in his Thesis in 1990.