Semantics for Default Rules

It is well-known that default rules require a nonmonotonic logic. Veltman proposed one dynamic theory which interprets default rules in such a way that correct inferences can be made at each information state. But his theory has some problems. First, this theory excludes the possibility that a default rule can be true of false. Second, his representation of an information state makes it difficult to interpret a default rule embedded in another sentence. Third, the notion of a frame which is introduced in the interpretation of a default rule and the adjustment of inferential expectation has a more complex structure than is necessary, In this paper, I propose a truth-conditional theory of default rules in which the meaning of a default rule is defined as a truth-condition in a possible world and which assumes a simpler structure of a frame. This makes it possible to interpret a default rule embedded in a sentence. A dynamic theory for default rules is also proposed for correct inferences based on default rules.