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A semantic characterisation of the correctness of a proof net

Published online by Cambridge University Press:  01 October 1997

CHRISTIAN RETORÉ
CHRISTIAN RETORÉ
Affiliation:
Projet Calligramme, INRIA-Lorraine & CRIN-C.N.R.S., 615 rue du Jardin Botanique, B.P. 101, F-54602 Villers lès Nancy Cedex, France. Email: retore@loria.fr
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Abstract

The purpose of this note is to show that the correctness of a multiplicative proof net with mix is equivalent to its semantic correctness: a proof structure is a proof net if and only if its semantic interpretation is a clique, where one given finite coherence space interprets all propositional variables.

This is just an example of what can be done with these kinds of semantic techniques; for more information and further results, the reader is referred to Retoré (1994).

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 7 , Issue 5 , October 1997 , pp. 445 - 452
Copyright
1997 Cambridge University Press

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