Representing Defaults as Sentences with Reduced Priority

We distinguish between two ways of thinking about defaults. The rst way, in which defaults augment known premises by`strengthening' the underlying logic, is the traditional approach taken by most existing formalisms. In the second way, defaults are represented in the set of premises, but obtain their default status by having a reduced priority relative to the known premises. In this paper we: 1. Compare and contrast the approaches. We argue that the second approach makes for simpler representation of defaults and their interactions. 2. Describe a syntax and semantics for the second, less well-known approach; we introduce the notion of ordered theory presentation (OTP) to represent theories with defaults. 3. Show how ordered theory presentations can represent familiar examples of interacting defaults in an intuitively clear and simple way; we give the Tweety example and the Yale Shooting example. We also show that the OTP framework is particularly well suited to inheritance examples. 4. Show formal properties of OTPs, in particular cu-mulativity, and suggest connections with circumscrip-tion. 5. Show how OTPs may be used to model belief revision and compare the result with the standard theory.