Naming Proofs in Classical Propositional Logic

  • François Lamarche
  • Lutz Straßburger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3461)

Abstract

We present a theory of proof denotations in classical propositional logic. The abstract definition is in terms of a semiring of weights, and two concrete instances are explored. With the Boolean semiring we get a theory of classical proof nets, with a geometric correctness criterion, a sequentialization theorem, and a strongly normalizing cut-elimination procedure. This gives us a “Boolean” category, which is not a poset. With the semiring of natural numbers, we obtain a sound semantics for classical logic, in which fewer proofs are identified. Though a “real” sequentialization theorem is missing, these proof nets have a grip on complexity issues. In both cases the cut elimination procedure is closely related to its equivalent in the calculus of structures.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • François Lamarche
    • 1
  • Lutz Straßburger
    • 2
  1. 1.LORIA & INRIA-Lorraine, Projet CalligrammeVillers-lès-NancyFrance
  2. 2.Informatik — ProgrammiersystemeUniversität des SaarlandesSaarbrückenGermany

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