Disjunctive logic programs with existential quantification in rule heads

We consider disjunctive logic programs without function symbols but with existential quantification in rule heads, under the semantics of general stable models. There are at least two interesting prospects in these programs. The first is that a program can be made more succinct by using existential variables, and the second is on the potential in representing defeasible ontological knowledge by these logic programs. This paper studies some of the properties of these programs. First, we show a simple yet intuitive definition of stable models for these programs that does not resort to second-order logic. Second, the stable models of these programs can be characterized by an extension of progression for disjunctive programs, which provides a native characterization of justification for stable models. We then study the decidability issue. While the stable model existence problem for safe disjunctive programs is decidable, with existential quantification allowed in rule heads the problem becomes undecidable. We identify an interesting decidable fragment by exploring a new notion of stratification over existential quantification.