From answer set logic programming to circumscription via logic of GK Original Research Article

We first embed Pearceʹs equilibrium logic and Ferrarisʹs propositional general logic programs in Lin and Shohamʹs logic of GK, a nonmonotonic modal logic that has been shown to include as special cases both Reiterʹs default logic in the propositional case and Mooreʹs autoepistemic logic. From this embedding, we obtain a mapping from Ferrarisʹs propositional general logic programs to circumscription, and show that this mapping can be used to check the strong equivalence between two propositional logic programs in classical logic. We also show that Ferrarisʹs propositional general logic programs can be extended to the first-order case, and our mapping from Ferrarisʹs propositional general logic programs to circumscription can be extended to the first-order case as well to provide a semantics for these first-order general logic programs.