Prime Implicate Generation in Equational Logic

International audienceA procedure is proposed to efficiently generate sets of ground implicates of first-order formulas with equality. It is based on a tuning of the superposition calculus [Nieuwenhuis and Rubio, 2001], enriched with rules that add new hypotheses on demand during the proof search. Experimental results are presented , showing that the proposed approach is more efficient than state-of-the-art systems

A Generic Framework for Implicate Generation Modulo Theories

International audienceThe clausal logical consequences of a formula are called its implicates. The generation of these implicates has several applications, such as the identification of missing hypotheses in a logical specification. We present a procedure that generates the implicates of a quantifier-free formula modulo a theory. No assumption is made on the considered theory, other than the existence of a decision procedure. The algorithm has been implemented (using the solvers MiniSAT, CVC4 and Z3) and experimental results show evidence of the practical relevance of the proposed approach

Equality and Abductive Residua for Horn Clauses

One method of proving theorems in Horn clause theories is surface deduction (also known as the modification method). Surface deduction yields interpretations of unification failures in terms of residual hypotheses needed for unification to succeed. This suggests that it can be used for abductive reasoning with equality. In surface deduction the input clauses are first transformed to a flat form (involving no nested terms) and symmetrized (if necessary). They are then manipulated by binary resolution, a restricted version of factoring and compression. In this paper we partially characterize the deductive strength of surface deduction and show how it depends on the type of flattening used. This is used to show that some forms of surface deduction will yield all hypotheses preferred by parsimony when used as an abductive inference engine. The characterization of deductive strength suggests a new equational preference principle according to which honest explanations are preferred. In h..