From Proof Nets to the Free *-Autonomous Category

Details From Proof Nets to the Free *-Autonomous Category From Proof Nets to the Free *-Autonomous Category

2006-05-12

arxiv.org/abs/cs/0605054v3

LMCS 2 (4:3) 2006

Computer Science

Logic in Computer Science

LaTeX, 44 pages, final version for LMCS; v2: updated bibliography

Scientific paper

10.2168/LMCS-2(4:3)2006

In the first part of this paper we present a theory of proof nets for full multiplicative linear logic, including the two units. It naturally extends the well-known theory of unit-free multiplicative proof nets. A linking is no longer a set of axiom links but a tree in which the axiom links are subtrees. These trees will be identified according to an equivalence relation based on a simple form of graph rewriting. We show the standard results of sequentialization and strong normalization of cut elimination. In the second part of the paper we show that the identifications enforced on proofs are such that the class of two-conclusion proof nets defines the free *-autonomous category.

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