A Two-Stage Approach to First Order Default Reasoning

Abstract

Our subject is the representation and analysis of simple first-order default statements of ordinary language, such as “normally, birds fly”. There are, among other approaches, two kinds of analysis, both semantic in style. One interprets “normally, birds fly” along the lines of “for every item x in the domain of discourse, the most normal models of “x is a bird” are models of “x flies””. This is the preferential models approach, first outlined by Bossu/Siegel and Shoham, and studied by Kraus, Lehmann, Magidor and others. The other interprets “normally, birds fly” along the lines of “there is an important subset of the birds, all of whose elements fly”. This is the generalized quantifier approach, formulated and developed by the author. The purpose of the present paper is to show how the two approaches may usefully be combined into a single two-stage approach, and how such a combination provides an elegant account of certain problematic examples.