Computing perfect and stable models using ordered model trees

Abstract

Ordered Model trees were introduced as a normal form for disjunctive deductive databases. They were also used to facilitate the computation of minimal models for disjunctive theories by exploiting the order imposed on the Herbrand base of the theory. In this work we show how the order on the Herbrand base can be used to compute perfect models of a disjunctive strati ed nite theory. We are able to compute the stable models of a general nite theory by combining the order on the elements of the Herbrand base with previous results that had shown that the stable models of a theory T can be computed as the perfect models of a corresponding disjunctive theory ET resulting from applying the so called evidential transformation to T . While other methods consider many models that are rejected at the end, the use of atom ordering allows us to guarantee that every model generated belongs to the class of models being computed. As for negation-free databases, the ordered tree serves as the canonical representation of the database.