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Conditional term rewriting and first-order theorem proving

  • Theorem-Proving and Normal Form Languages
  • Conference paper
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Conditional Term Rewriting Systems (CTRS 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 656))

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Abstract

We survey some basic issues in first-order theorem proving and their implications for conditional term-rewriting systems. In particular, we discuss the propositional efficiency of theorem proving strategies, goal-sensitivity, and the use of semantics. We give several recommendations for theorem proving strategies to enable them to properly treat these issues. Although few current theorem provers implement these recommendations, we discuss the clause linking theorem proving method and its extension to equality and semantics as examples of methods that satisfy most or all of our recommendations. Implicit induction theorem provers meet our recommendations, to some extent. We also discuss correctness and efficiency issues involved in the use of semantics in first-order theorem proving. Finally, we discuss issues of efficiency and semantics in conditional term-rewriting.

This research was partially supported by the National Science Foundation under grant CCR-9108904; Fachbereich Informatik, Universitaet Kaiserslautern, Kaiserslautern, Germany; and the Max-Planck-Institut fuer Informatik, Saarbruecken, Germany

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Authors and Affiliations

  1. Department of Computer Science, University of North Carolina at Chapel Hill, 27599-3175, Chapel Hill, NC

    David A. Plaisted, Geoffrey D. Alexander, Heng Chu & Shie-Jue Lee

Authors
  1. David A. Plaisted
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  2. Geoffrey D. Alexander
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  3. Heng Chu
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  4. Shie-Jue Lee
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Michaël Rusinowitch Jean-Luc Rémy

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© 1993 Springer-Verlag Berlin Heidelberg

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Plaisted, D.A., Alexander, G.D., Chu, H., Lee, SJ. (1993). Conditional term rewriting and first-order theorem proving. In: Rusinowitch, M., Rémy, JL. (eds) Conditional Term Rewriting Systems. CTRS 1992. Lecture Notes in Computer Science, vol 656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56393-8_19

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  • DOI: https://doi.org/10.1007/3-540-56393-8_19

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  • Print ISBN: 978-3-540-56393-8

  • Online ISBN: 978-3-540-47549-1

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