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AC-superposition with constraints: No AC-unifiers needed

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Automated Deduction — CADE-12 (CADE 1994)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 814))

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Abstract

We prove the completeness of (basic) deduction strategies with constrained clauses modulo associativity and commutativity (AC). Here each inference generates one single conclusion with an additional equality s=AC t in its constraint (instead of one conclusion for each minimal AC-unifier, i.e. exponentially many). Furthermore, computing AC-unifiers is not needed at all. A clause C〚 T〛 is redundant if the constraint T is not AC-unifiable. If C is the empty clause this has to be decided to know whether C〚 T 〛 denotes an inconsistency. In all other cases any sound method to detect unsatisfiable constraints can be used.

Both authors upported by the Esprit Working Group CCL, ref. 6028

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Authors and Affiliations

  1. Technical University of Catalonia, Pau Gargallo 5, 08028, Barcelona, Spain

    Robert Nieuwenhuis & Albert Rubio

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  1. Robert Nieuwenhuis
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  2. Albert Rubio
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Alan Bundy

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© 1994 Springer-Verlag Berlin Heidelberg

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Nieuwenhuis, R., Rubio, A. (1994). AC-superposition with constraints: No AC-unifiers needed. In: Bundy, A. (eds) Automated Deduction — CADE-12. CADE 1994. Lecture Notes in Computer Science, vol 814. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58156-1_40

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  • DOI: https://doi.org/10.1007/3-540-58156-1_40

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58156-7

  • Online ISBN: 978-3-540-48467-7

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