A Calculus for Generating Ground Explanations

Mnacho Echenim (1) , Nicolas Peltier (1)

1 CAPP - Calculs algorithmes programmes et preuves

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.

Domaines: Logique en informatique [cs.LO]

Mnacho Echenim, Nicolas Peltier. A Calculus for Generating Ground Explanations. IJCAR 2012 - International Joint Conference on Automated Reasoning, Jun 2012, Manchester, United Kingdom. pp.194-209, ⟨10.1007/978-3-642-31365-3_17⟩. ⟨hal-00933272⟩