From answer set logic programming to circumscription via logic of GK

Authors:
Fangzhen Lin;Yi Zhou
Affiliations:
Department of Computer Science, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong;School of Computing and Mathematics, University of Western Sydney, Penrith South DC, NSW 1797, Australia
Venue:
Artificial Intelligence
Year:
2011

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Abstract

We first 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 propositional logic programs in classical logic. We also show that Ferraris's propositional general logic programs can be extended to the first-order case, and our mapping from Ferraris's 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.