A Most General Reenement Operator for Reduced Sentences

Many learning systems use the space of logic formulas as the search space of hypotheses. To build eecient systems, the set of rst order logic formulas can be reduced in many ways. Most systems restrict themselves to (subsets of) Horn clauses. In this paper we investigate the space of reduced rst order sentences, which has the same expressive power as an arbritrary rst order logic. Shapiro 6] has used the subset of reduced rst order sentences to deene a most general reenement operator. His operator is claimed to be complete, i.e., all reduced sentences are derivable from the empty sentence. In this article we will show that his operator is not complete and propose a new, complete reenement operator for reduced rst order sentences.