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Special relations in automated deduction

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Automata, Languages and Programming (ICALP 1985)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 194))

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Abstract

Two deduction rules are introduced to give streamlined treatment to relations of special importance in an automated theorem-proving system. These rules, the relation replacement and relation matching rules, generalize to an arbitrary binary relation the paramodulation and E-resolution rules, respectively, for equality, and may operate within a nonclausal or clausal system. The new rules depend on an extension of the notion of polarity to apply to subterms as well as to subsentences, with respect to a given binary relation. The rules allow us to eliminate troublesome axioms, such as transitivity and monotonicity, from the system; proofs are shorter and more comprehensible, and the search space is correspondingly deflated.

This research was supported in part by the National Science Foundation under grants MCS-82-14523 and MCS-81-05565, by the Defense Advanced Research Projects Agency under contract N00039-84-C-0211, by the United States Air Force Office of Scientific Research under contract AFOSR-81-0014, by the Office of Naval Research under contract N00014-84-C-0706, and by a contract from the International Business Machines Corporation.

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Author information

Authors and Affiliations

  1. Computer Science Department, Stanford University, USA

    Zohar Manna

  2. Artificial Intelligence Center SRI International, USA

    Richard Waldinger

Authors
  1. Zohar Manna
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  2. Richard Waldinger
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Editor information

Wilfried Brauer

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© 1985 Springer-Verlag Berlin Heidelberg

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Manna, Z., Waldinger, R. (1985). Special relations in automated deduction. In: Brauer, W. (eds) Automata, Languages and Programming. ICALP 1985. Lecture Notes in Computer Science, vol 194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015767

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  • DOI: https://doi.org/10.1007/BFb0015767

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15650-5

  • Online ISBN: 978-3-540-39557-7

  • eBook Packages: Springer Book Archive

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