Defaults and Relevance in Model-Based Reasoning

Reasoning with model-based representations is an intuitive paradigm, which has been shown to be theoretically sound and to possess some computational advantages over reasoning with formula-based representations of knowledge. In this paper we present more evidence to the value of such representations. Our results hinge on the notion of relevance, and model based representations are shown to be useful in capturing relevant information, and in allowing to ignore irrelevant information. In particular, we consider situations where context-specific information is used in the process of reasoning. We show that reasoning with model-based representations can be done efficiently in the presence of varying context information. We then consider the task of default reasoning. We show that default reasoning is a generalization of reasoning within context, in which the reasoner has many ``context" rules, which may be conflicting. We develop model-based algorithms that handle efficiently fragments of Reiter''s default logic. Our intuition about relevance is best captured in the model for reasoning within context, where model-based representations enable us to filter out irrelevant information. Interestingly, default logic is somewhat in contrast with our intuition about relevance. Default rules do not tell us explicitly what the context information is. Instead, we have to figure out what are the possible ``extensions" and then use those as possible contexts. As we show, model-based representations capture all possible extensions in an accessible form, thereby supporting efficient default reasoning whenever possible. Lastly, we argue that these results support an incremental view of reasoning in a natural way. We discuss the Learning to Reason framework, which emphasizes this view, and the notion of relevance as manifested in it. In particular, we discuss results on Learning to Reason in which model-based representations are used to represent relevant knowledge.