Elsevier

Artificial Intelligence

Volume 31, Issue 2, February 1987, Pages 201-211
Artificial Intelligence

Research note
Circumscribing with sets

https://doi.org/10.1016/0004-3702(87)90020-8Get rights and content

Abstract

Sets can play an important role in circumscription's ability to deal in a general way with certain aspects of commonsense reasoning. A result of Kueker indicates that sentences that intuitively one would want circumscription to prove are nonetheless not so provable in a formal setting devoid of sets. Furthermore, when sets are introduced, first-order circumscription handles these cases very easily, obviating the need for second-order circumscription. The “Aussonderungs” axiom of ZF set theory plays an intuitive role in this shift back to a first-order language

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