Clark's completion is a simple nonmonotonic formalism and a special case of several non-monotonic logics. Recently there has been work on extending completion with "loop formulas" so that general cases of nonmonotonic logics such as logic programs (under the answer set semantics) and McCain-Turner causal logic can be characterized by propositional logic in the form of "completion loop formulas." In this paper, we show that the idea is applicable to McCarthy's circumscription in the propositional case, with Lifschitz's pointwise circumscription playing the role of completion. We also show how to embed propositional circumscription in logic programs and in causal logic, inspired by the uniform characterization of "completion loop formulas."

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In Proceedings of National Conference on Artificial Intelligence (AAAI), pp. 281-286 2004.

@Inproceedings{lee04, title={Loop Formulas for Circumscription}, author={Joohyung Lee and Fangzhen Lin}, booktitle={Proceedings of National Conference on Artificial Intelligence (AAAI)}, pages={281-286}, url="http://www.cs.utexas.edu/users/ai-lab?lee04", year={2004} }