On Reducing Parallel Circumscription

Li Yan Yuan, Cheng Hui Wang

Three levels of circumscription have been proposed by McCathy to formalize common sense knowledge and non-monotonic reasoning in general-purpose database and knowledge base systems. That is, basic circumscription, parallel circumscription, and priority circumscription. Basic circumscription is a special case of parallel circumscription while parallel circumscription is a special case of priority circumscription. Lifschitz has reduced priority circumscription into parallel circumscription, i.e., represented priority circumscription as a conjunction of some parallel circumscription formulas. In this paper, we have reduced parallel circumscription into basic circumscription under some restriction, i.e., parallel circumscription of a Z-conflict free first order logic formula can be represented as a conjunction of some basic circumscription formulea.

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