An Approach to Default Reasoning Based on a First-Order Conditional Logic

This paper presents an approach to default reasoning based on an extension to classical first-order logic. In this approach, first -order logic is augmented with a “variable conditional” operator for representing default statements. Truth in the resulting logic is based on a possible worlds semantics: the default statement C-P is true just when p is true in the least exceptional worlds in which 01 is true. This system provides a basis for representing and reasoning about default statements. Inferences of default properties of individuals rely on two assumptions: first that the world being modelled by a set of sentences is as uniform as consistently possible and, second, that sentences that may consistently be assumed to be irrele\.ant to a default inference -are, in fact.-irrelevant to the inference. Two formulations of default inferencing are proposed. The first involves extending the set of defaults to include all combinations of irrelevant properties. The second involves assuming that the world being modelled is among the simplest worlds consistent with the defaults and with what is contingently known. In the end. the second approach is argued to be superior to the first.