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Reports Year : 1994

On the relation between coherence semantics and multiplicative proof nets

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.

Domains

Other [cs.OH]
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Dates and versions

inria-00074245 , version 1 (24-05-2006)

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  • HAL Id : inria-00074245 , version 1

Cite

Christian Retoré. On the relation between coherence semantics and multiplicative proof nets. RR-2430, INRIA. 1994. ⟨inria-00074245⟩
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