Generalized predicate completion
Circumscription, proposed by McCarthy, is a formalism of non-monotonic reasoning. Predicate completion is an approach, proposed by Clark, to closed world reasoning which assumes that given sufficient conditions on a predicate are also necessary. Reiter has shown that for clausal sentences which are Horn in a predicate p, the circumscription of p logically subsumes the predicate completion of p. In this paper, we present a generalized completion of a predicate p, which is appropriate for clausal sentences which are not Horn in p. The main results of this paper are: (1) for non-overlapping clausal sentences (which may not necessarily be Horn in the predicate p), the circumscription of p logically subsumes the generalized completion of p; (2) for non-overlapping clausal sentences which are collapsible wrt (with respect to) the predicate p, the generalized completion of p is even logically equivalent to the circumscription of p.
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