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Naming Proofs in Classical Propositional Logic

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Typed Lambda Calculi and Applications (TLCA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3461))

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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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Author information

Authors and Affiliations

  1. LORIA & INRIA-Lorraine, Projet Calligramme, 615, rue du Jardin Botanique, 54602, Villers-lès-Nancy, France

    François Lamarche

  2. Informatik — Programmiersysteme, Universität des Saarlandes, Postfach 15 11 50, 66041, Saarbrücken, Germany

    Lutz Straßburger

Authors
  1. François Lamarche
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  2. Lutz Straßburger
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Editor information

Editors and Affiliations

  1. Institute of Informatics, University of Warsaw, Poland

    Paweł Urzyczyn

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Lamarche, F., Straßburger, L. (2005). Naming Proofs in Classical Propositional Logic. In: Urzyczyn, P. (eds) Typed Lambda Calculi and Applications. TLCA 2005. Lecture Notes in Computer Science, vol 3461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11417170_19

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  • DOI: https://doi.org/10.1007/11417170_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25593-2

  • Online ISBN: 978-3-540-32014-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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