Can Completion Entail Circumscription (Sometimes)?

概要

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Circumscription, a form of non-monotonic reasoning, proposed by J.McCarthy, of first-order predicate symbols are second-order formula. The formulas derivable from a theory T augmented by the circumscription of a predicate symbol P are just those true in all models of T minimal in P. In order to achieve this kind of minimal derivation, it is very important to find out some suitable first-order instances of circumscription. As there is actually such instances, we say the theory T is circumscriptively reducible wrt the predicate symbol P. Completion of a theory, proposed by Keith L. Clark, is one way to represent closed world assumption by assuming given sufficient condition about a predicate is also necessary. Shown in ,circumscription of a predicate symbol P in a theory T Horn in P implies the completion of T wrt P. Here we will show that the completion of T wrt P entails the circumscription of P in T in the model-theoretical viewpoint.
一般社団法人情報処理学会の論文
1988-09-12