Pointwise Circumscription: Preliminary Report

Vladimir Lifschitz

Circumscription is the minimization of predicates subject to restrictions expressed by predicate formulas. We propose a modified notion of circumscription so that, instead of being a single minimality condition, it becomes an "infinite conjunction" of "local" minimality conditions; each of these conditions expresses the impossibility of changing the value of a predicate from true to false at one point. We argue that this "pointwise" circumscription is conceptually simpler than the traditional "global" approach and, at the same time, leads to generalizations with the additional flexibility needed in applications to the theory of commonsense reasoning.

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