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Resource models and proof-search in Intuitionistic Linear Logic

Didier Galmiche 1 Dominique Larchey-Wendling 1
1 TYPES - Logic, proof Theory and Programming
LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : In this paper, we propose to investigate and to revise the semantics of Intuitionistic Linear Logic (\ILL), from an unified analysis of known semantics like phase semantics or Petri nets semantics. Thus, we focus on notions like quantale, closure and resource frames and we define a new semantics of \ILL\ that is called resource semantics. The completeness and the finite model property are proved from a based-on proof-search method in which countermodels are obtained from refutation trees. Moreover, we define a new preordered monoid semantics from an adequate choice of pretopology. As Petri nets can be seen as concrete representations of preordered monoids, such a choice also leads to a new Petri nets semantics for \ILL\ with new results like completeness and finite model property. From these semantical considerations, we obtain some results about non-provability in \ILL\ and then we can expect to develop methods for the generation of countermodels.
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Submitted on : Tuesday, September 26, 2006 - 8:52:39 AM
Last modification on : Friday, February 26, 2021 - 3:28:08 PM


  • HAL Id : inria-00099314, version 1



Didier Galmiche, Dominique Larchey-Wendling. Resource models and proof-search in Intuitionistic Linear Logic. [Intern report] A00-R-341 || galmiche00g, 2000, 39 p. ⟨inria-00099314⟩



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