Model minimization —An alternative to circumscription

Abstract

The idea underlying John McCarthy's notion of circumscription is interpreted, for formulas with finite models, as asking whether the conclusion C is true in all the minimal finite models of the premise T. A way of modifying one of the usual proof procedures for first-order logic (the tableau method) is given which captures this idea. The result is shown to differ from the consequences of McCarthy's circumscription schema. The resulting proof procedure is extended to the case in which it is also required that the extensions of the primitive predicates are minimal. For formulas with only infinite models, the idea on which the concept of circumscription is based is tantamount to the author's idea of restricting models to minimal ones.