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On the relation between coherence semantics and multiplicative proof nets

Christian Retoré 1
1 MEIJE - Concurrency, Synchronization and Real-time Programming
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : It is known that (mix) proof nets admits a coherence semantics, computed as a set of experiments. We prove here the converse: a proof structure is shown to be a proof net whenever its sets of experiments is a semantical object --- a clique of the corresponding coherence space. Moreover the interpretation of atomic formulae can be restricted to a given coherent space with three tokens in its web. This is done by transforming \tt cut links into \tt tensor links. Dealing directly with non-cut-free proof structure we characterise the deadlock freeness of the reduced proof structure. These results are especially convenient for Abramsky's proof expressions, and can be extended to the pomset calculus.
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Submitted on : Wednesday, May 24, 2006 - 2:51:02 PM
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Christian Retoré. On the relation between coherence semantics and multiplicative proof nets. RR-2430, INRIA. 1994. ⟨inria-00074245⟩

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