An approach to default reasoning based on a first-order conditional logic: Revised report

摘要

An approach to default reasoning based on an extension to classical first-order logic is presented. In this approach, first-order logic is augmented with a “variable conditional” operator, ⇒, for representing default statements. The statement α ⇒ β is read as “if α then normally β”. Truth in the resulting logic is based on a possible worlds semantics: α ⇒ β is true just when β is true in the least exceptional worlds in which α 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 is as unexceptional as consistently possible and, second, that sentences that may consistently be assumed to be irrelevant to a default inference are, in fact, irrelevant to the inference. Two formulations of default inferencing are developed. The first involves extending the set of default statements 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 two approaches prove to be equivalent with respect to their respective set of default inferences. Finally, it is shown how the approach treats two current problems in default reasoning. The first problem concerns the ordering of default statements. The second concerns a problem of Hanks and McDermott for dealing with “multiple extensions” of a set of defaults.