Learning Approximate Consistencies

In this paper, we present an abstract framework for learning a finite domain constraint solver modeled by a set of operators enforcing a consistency. The behavior of the consistency to be learned is taken as the set of examples on which the learning process is applied. The best possible expression of this operator in a given language is then searched. We present sufficient conditions for the learned solver to be correct and complete with respect to the original constraint. We instantiate this framework to the learning of bound-consistency in the indexical language of Gnu-Prolog.