A Calculus for Generating Ground Explanations

  • Mnacho Echenim
  • Nicolas Peltier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7364)


We present a modification of the superposition calculus that is meant to generate explanations why a set of clauses is satisfiable. This process is related to abductive reasoning, and the explanations generated are clauses constructed over so-called abductive constants. We prove the correctness and completeness of the calculus in the presence of redundancy elimination rules, and develop a sufficient condition guaranteeing its termination; this sufficient condition is then used to prove that all possible explanations can be generated in finite time for several classes of clause sets, including many of interest to the SMT community. We propose a procedure that generates a set of explanations that should be useful to a human user and conclude by suggesting several extensions to this novel approach.


Inference Rule Unit Clause Abductive Reasoning Empty Clause Ground Substitution 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Mnacho Echenim
    • 1
  • Nicolas Peltier
    • 1
  1. 1.University of Grenoble, (LIG, Grenoble INP/CNRS)France

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