On the semantic readings of proof-nets

Philippe de Groote 1 Christian Retoré 1
1 CALLIGRAMME - Linear logic, proof networks and categorial grammars
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The goal of this paper is to demonstrate how the very rich notion of proof-net may be used, in the framework of categorial grammars, as a unique structure that allows the syntactic and semantic apsects of sentence analysis to be unified. We first explain how the intuitionistic multiplicative proof nets correspond exactly to the so-called linear lambda-terms. This allow us to interpret proof-nets not only as syntatic structures but also as sematnic readings à la van Benthem. The we generalize the correspondence between proof-nets and lambda-terms to the complete categorial hierarchy, and we show how Montague-like semantics may be handled in this framework.
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Philippe de Groote, Christian Retoré. On the semantic readings of proof-nets. Formal grammar 1996, 1996, Prague, Czech Republic. pp.57--70. ⟨hal-00823554⟩

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