Update by means of inference rules

Katsuno and Mendelzon have distinguished two abstract frameworks for reasoning about change: theory revision and theory update. Theory revision involves a change in knowledge or belief with respect to a static world. By contrast, theory update involves a change of knowledge or belief in a changing world. In this paper, we are concerned with theory update. Winslett has shown that theory update should be computed “one model at a time.” Accordingly, we focus exclusively on the update of interpretations. We begin with a study of revision programming, introduced by Marek and Truszcyński to formulize interpretation update in a language similar to logic programming. While revision programs provide a useful and natural definition of interpretation update, they are limited to a fairly restricted set of update rules. Accordingly, we introduce the more general notion of rule update—interpretation update by arbitrary sets of inference rules. We show that Winslett's approach to update by means of arbitrary sets of formulas corresponds to a simple subclass of rule update. We also specify a simple embedding of rule update in Reiter’s default logic, obtained by augmenting the original update rules with default rules encoding the commonsense law of inertia—the principle that things change only when they are made to.