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 of models are two transformations of disjunctive deductive databases. First, the evidential transformation is used to realize the preference relation, and to define evidential stable models. Secondly, based on the tu-transformation the result is lifted to the three-valued case, that is, partial evidential stable models are defined.