Circumscribing equality

Abstract

One important facet of common-sense reasoning is the ability to draw default conclusions about the state of the world. Such an abili ty enables one to assume, for example, that a given bird flies in the absence of information to the contrary. One drawback of the circumscriptive approach to common-sense reasoning has been its inability to produce default conclusions about equality. For example, generally one cannot tentatively conclude that President (USA) ≠ Fido using circumscription. In this paper we give a second-order axiom and model theory for circumscribing equality, and prove that they are equivalent.