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Conference Papers Year : 2001

Refutations as countermodels in intuitionistic linear logic


We propose to investigate and to reuse the semantics of intuitionistic linear logic (ILL), from an initial analysis of known semantics like phase semantics or Petri net 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 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 a concrete representation 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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inria-00100563 , version 1 (26-09-2006)


  • HAL Id : inria-00100563 , version 1


Dominique Larchey. Refutations as countermodels in intuitionistic linear logic. Semantic Foundations of Proof-search, D. Pym, E. Ritter, T. Streicher, 2001, Schloss Dagsthul/Germany. ⟨inria-00100563⟩
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