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Unified Classical Logic Completeness

A Coinductive Pearl

  • Conference paper
Automated Reasoning (IJCAR 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8562))

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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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Author information

Authors and Affiliations

  1. Fakultät für Informatik, Technische Universität München, Germany

    Jasmin Christian Blanchette, Andrei Popescu & Dmitriy Traytel

  2. Institute of Mathematics Simion Stoilow of the Romanian Academy, Bucharest, Romania

    Andrei Popescu

Authors
  1. Jasmin Christian Blanchette
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  2. Andrei Popescu
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  3. Dmitriy Traytel
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Editor information

Editors and Affiliations

  1. CNRS,, New York University &amp, USA

    Stéphane Demri

  2. Department of Computer Science, University of New Mexico, 87131-0001, Albuquerque, NM, USA

    Deepak Kapur

  3. Max Planck Institute for Informatics, Campus E1 4, 66123, Saarbrücken, Germany

    Christoph Weidenbach

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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. https://doi.org/10.1007/978-3-319-08587-6_4

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  • DOI: https://doi.org/10.1007/978-3-319-08587-6_4

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08586-9

  • Online ISBN: 978-3-319-08587-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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