First-Order Expressibility and Boundedness of Disjunctive Logic Programs / 1198

*Heng Zhang, Yan Zhang*

In this paper, the fixed point semantics developed in [Lobo et al., 1992] is generalized to disjunctive logic programs with default negation and over arbitrary structures, and proved to coincide with the stable model semantics. By using the tool of ultraproducts, a preservation theorem, which asserts that a disjunctive logic program without default negation is bounded with respect to the proposed semantics if and only if it has a first-order equivalent, is then obtained. For the disjunctive logic programs with default negation, a sufficient condition assuring the first-order expressibility is also proposed.