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Automated deduction with associative commutative operators

  • Part II Selected Contributions
  • Conference paper
  • First Online:
Fundamentals of Artificial Intelligence Research (FAIR 1991)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 535))

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Abstract

We propose a new inference system for automated deduction with equality and associative commutative operators. This system is an extension of the ordered paramodulation strategy. However, rather than using associativity and commutativity as the other axioms, they are handled by the AC unification algorithm. Moreover, we prove the refutational completeness of this system without needing the functional reflexive axioms or AC axioms. Such a result is obtained by semantic tree techniques, assuming that terms are compared with an AC-compatible and complete simplification ordering.

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Philippe Jorrand Jozef Kelemen

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© 1991 Springer-Verlag Berlin Heidelberg

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Rusinowitch, M., Vigneron, L. (1991). Automated deduction with associative commutative operators. In: Jorrand, P., Kelemen, J. (eds) Fundamentals of Artificial Intelligence Research. FAIR 1991. Lecture Notes in Computer Science, vol 535. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54507-7_15

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  • DOI: https://doi.org/10.1007/3-540-54507-7_15

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54507-1

  • Online ISBN: 978-3-540-38420-5

  • eBook Packages: Springer Book Archive

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