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Proofs, denotational semantics and observational equivalences in Multiplicative Linear Logic

Published online by Cambridge University Press:  01 April 2007

MICHELE PAGANI
MICHELE PAGANI*
Affiliation:
Dipartimento di Filosofia – Università Roma Tre, Via Ostiense 234 – 00146 Roma – Italy Email: pagani@uniroma3.it
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We study full completeness and syntactical separability of MLL proof nets with the mix rule. The general method we use consists of first addressing these two questions in the less restrictive framework of proof structures, and then adapting the results to proof nets.

At the level of proof structures, we find a semantical characterisation of their interpretations in relational semantics, and define an observational equivalence that is proved to be the equivalence induced by cut elimination. Hence, we obtain a semantical characterisation (in coherent spaces) and an observational equivalence for the proof nets with the mix rule.

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Paper
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Mathematical Structures in Computer Science , Volume 17 , Issue 2 , April 2007 , pp. 341 - 359
Copyright
Copyright © Cambridge University Press 2007

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