From Answer Set Logic Programming to Circumscription via Logic of GK

We rst embed Pearce s equilibrium logic and Ferraris s propositional general logic programs in Lin and Shoham s logic of GK a nonmonotonic modal logic that has been shown to include as special cases both Reiter s default logic in the propositional case and Moore s autoepistemic logic From this embedding we obtain a mapping from Ferraris s propositional general logic programs to circumscription and show that this mapping can be used to check the strong equivalence between two propo sitional logic programs in classical logic We also show that Ferraris s propositional general logic programs can be extended to the rst order case and our mapping from Ferraris s propositional general logic programs to circumscription can be ex tended to the rst order case as well to provide a semantics for these rst order general logic programs