A New Correctness Criterion for Cyclic Proof Nets

We define proof nets for cyclic multiplicative linear logic as edge bi-coloured graphs. Our characterization is purely graph theoretical and works without further complication for proof nets with cuts, which are usually harder to handle in the non-commutative case. This also provides a new character...

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Bibliographic Details
Published in:Journal of logic, language, and information language, and information, 1998-10, Vol.7 (4), p.449-459
Main Authors: Abrusci, V. Michele, Maringelli, Elena
Format: Article
Language:English
Subjects:
Lambek calculus
Linear logic
Mathematical logic
Mathematical theorems
Sequent calculus
Sequents
Terminology
Vertices
Online Access:Get full text
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Summary:We define proof nets for cyclic multiplicative linear logic as edge bi-coloured graphs. Our characterization is purely graph theoretical and works without further complication for proof nets with cuts, which are usually harder to handle in the non-commutative case. This also provides a new characterization of the proof nets for the Lambek calculus (with the empty sequence) which simply are a restriction on the formulas to be considered (which are asked to be intuitionistic).
ISSN:0925-8531
1572-9583
DOI:10.1023/A:1008354130493