AC-superposition with constraints: No AC-unifiers needed

  • Robert Nieuwenhuis
  • Albert Rubio
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 814)


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=ACt 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 CT〛 is redundant if the constraint T is not AC-unifiable. If C is the empty clause this has to be decided to know whether CT 〛 denotes an inconsistency. In all other cases any sound method to detect unsatisfiable constraints can be used.


Inference Rule Theorem Prove Horn Clause Ground Term Ground Instance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Robert Nieuwenhuis
    • 1
  • Albert Rubio
    • 1
  1. 1.Technical University of CataloniaBarcelonaSpain

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