Exploiting Data Dependencies in Many-Valued Logics

The purpose of this paper is to make some practically relevant results in automated theorem proving available to many-valued logics with suitable modifications. We are working with a notion of many-valued first-order clauses which any finitely-valued logic formula can be translated into and that has been used several times in the literature, but in an ad hoc way. We give a many-valued version of polarity which in turn leads to natural many-valued counterparts of Horn formulas, hyperresolution, and a Davis-Putnam procedure. We show that the many-valued generalizations share many of the desirable properties of the classical versions. Our results justify and generalize several earlier results on theorem proving in many-valued logics.