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The Relative Power of Semantics and Unification

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Programming Logics

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7797))

Abstract

The OSHL theorem proving method is an attempt to extend propositional theorem proving techniques to first-order logic by working entirely at the ground level. A disadvantage of this approach is that OSHL does not perform unifications between non-ground literals, as resolution does. However, OSHL has the capability to use natural semantics to guide the proof search. The question arises whether the advantage of proof guidance using semantics can make up for the loss of unification between non-ground literals that other methods employ. This question is studied and some evidence is given that a properly chosen semantics causes OSHL to implicitly perform unifications between non-ground levels, suggesting that OSHL may have some of the advantages of theorem proving methods based on unification as well as some of the efficiencies of propositional theorem provers. Some implementation results of OSHL with and without nontrivial semantics are also presented to illustrate its properties.

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Authors and Affiliations

  1. Department of Computer Science, UNC Chapel Hill, Chapel Hill, NC, 27599-3175, USA

    David A. Plaisted & Swaha Miller

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  1. David A. Plaisted
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  2. Swaha Miller
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Editors and Affiliations

  1. University of Manchester, Oxford Road, M13 9PL, Manchester, UK

    Andrei Voronkov

  2. Max-Planck-Institut für Informatik, Campus E1 4, 66123, Saarbrücken, Germany

    Christoph Weidenbach

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Plaisted, D.A., Miller, S. (2013). The Relative Power of Semantics and Unification. In: Voronkov, A., Weidenbach, C. (eds) Programming Logics. Lecture Notes in Computer Science, vol 7797. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37651-1_14

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  • DOI: https://doi.org/10.1007/978-3-642-37651-1_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37650-4

  • Online ISBN: 978-3-642-37651-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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