On Reducing Parallel Circumscription

Abstract

Three levels of circumscription have been pro-posed by McCathy to formalize common sense knowledge and non-monotonic reasoning in general-purpose database and knowledge base sys-tems. That is, basic circumscription, parallel cir-cumscription, and priority circumscription. Basic circumscription is a special case of parallel cir-cumscription while parallel circumscription is a special case of priority circumscription. Lifschitz has reduced priority circumscription into parallel circumscription, i.e., represented priority cir-cumscription as a conjunction of some parallel cir-cumscription formulas. In this paper, we have reduced parallel circumscription into basic cir-cumscription 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. 1.