Unified Classical Logic Completeness

A Coinductive Pearl
  • Jasmin Christian Blanchette
  • Andrei Popescu
  • Dmitriy Traytel
Conference paper

DOI: 10.1007/978-3-319-08587-6_4

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8562)
Cite this paper as:
Blanchette J.C., Popescu A., Traytel D. (2014) Unified Classical Logic Completeness. In: Demri S., Kapur D., Weidenbach C. (eds) Automated Reasoning. IJCAR 2014. Lecture Notes in Computer Science, vol 8562. Springer, Cham

Abstract

Codatatypes are absent from many programming and specification languages. We make a case for their importance by revisiting a classical result: the completeness theorem for first-order logic established through a Gentzen system. The core of the proof establishes an abstract property of possibly infinite derivation trees, independently of the concrete syntax or inference rules. This separation of concerns simplifies the presentation. The abstract proof can be instantiated for a wide range of Gentzen and tableau systems as well as various flavors of first-order logic. The corresponding Isabelle/HOL formalization demonstrates the recently introduced support for codatatypes and the Haskell code generator.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Jasmin Christian Blanchette
    • 1
  • Andrei Popescu
    • 1
    • 2
  • Dmitriy Traytel
    • 1
  1. 1.Fakultät für InformatikTechnische Universität MünchenGermany
  2. 2.Institute of Mathematics Simion Stoilow of the Romanian AcademyBucharestRomania

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