Declarative and Fixpoint Characterizations of Disjunctive Stable Models

The paper presents a new notion of unfounded set for disjunctive logic programs, which generalizes the analog notion given in classical (i.e., nondisjunctive) logic programming

Two declarative characterizations of stable models in terms of unfounded sets are given. The former shows that the set of stable models coincides with the family of unfounded-free models (i.e., a model is stable if it contains no unfounded atom). The second characterization proves that stable models can be equivalently defined by a property of their false literals, as a model is stable if and only if the set of its false literals coincides with its greatest unfounded set

Then, the well-founded Wp operator is generalized to disjunctive logic programs and a fixpoint semantics for disjunctive stable models is provided

The computational complexity of the main computational problems related to the presented concepts is also discussed

Most of the presented results generalize previous studies conducted by Saccá and Zaniolo [22] and by Van Gelder et al. [25] in the context of traditional logic programming