Disjunctive Programs with Set Constraints

We study an extension of disjunctive logic programs called set constraint disjunctive (SCD) programs where the clauses of the program are allowed to have a disjunction of monotone set constraints in their head and arbitrary monotone and antimonotone set constraints in their body. We introduce new class of models called selector stable models which represent all models which can be computed by an analogue the Gelfond-Lifschitz transform. We show that the stable models of disjunctive logic programs can be defined in terms of selector stable models and then extend this result to SCD logic programs. Finally we show that there is a natural proof theory associated with selector stable models.