Partial Evidential Stable Models for Disjunctive Deductive Databases

. In this paper we consider the basic semantics of stable and partial stable models for disjunctive deductive databases (with default negation), cf. [9,16]. It is well--known that there are disjunctive deductive databases where no stable or partial stable models exist, and these databases are called inconsistent w.r.t. the basic semantics. We define a consistent variant of each class of models, which we call evidential stable and partial evidential stable models. It is shown that if a database is already consistent w.r.t. the basic semantics, then the class of evidential models coincides with the basic class of models. Otherwise, the set of evidential models is a subset of the set of minimal models of the database. This subset is non-empty, if the database is logically consistent. It is determined according to a suitable preference relation, whose underlying idea is to minimize the amount of reasoning by contradiction. The technical ingredients for the construction of the new classes..