The homogeneous form of logic programs with equality.

Abstract

Let P be a Horn clause logic program. The homogeneous form of a clause p (t 1 , ..., t n )←B 1 , ..., B q is p(x 1 , ..., x n )←x 1 =t 1 , ..., x n =t n , B 1 , ..., B q . The homogeneous form P' of P is the set of homogeneous forms of clauses of P. Let T be a set of axioms asserting the reflexivity, symmetry, transitivity, and congruence of =. Then P∪T is goal equivalent to P'∪{x=x}; i.e., for any goal G. P∪T∪{G} is unsatisfiable iff P'∪{x=x}∪{G} is unsatisfiable. The main interest of the paper lies in its construction of the Herbrand model M and in the proof that M is the minimal Herbrand model of both P∪T and P'∪{x=x}