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Unified Classical Logic Completeness

A Coinductive Pearl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8562)

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.

Keywords

Proof System Proof Theory Completeness Theorem Derivation Tree Rule System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Fakultät für InformatikTechnische Universität MünchenGermany
  2. 2.Institute of Mathematics Simion Stoilow of the Romanian AcademyBucharestRomania

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