On the comparison of theories: preferring the most specific explanation

Default reasoning is reasoning with generalised knowledge which we want to use if there is no more specific knowledge also applicable. This pa-per presents a formal, model-theoretic characterisation of default reasoning. Defaults are treated as possible hypotheses in a “scientific ” theory to explain the results. One of the problems with systems that reason with defaults oc-curs when two answers can be produced, and one is preferred. In terms of our default logic, we define a semantic characterisation of the notion of the more specific theory. This overcomes many of the problems which moti-vated non-normal defaults, and provides a semantics for correct inheritance in inheritance systems, where we want choose the result supported by the most specific knowledge. We also show how to produce a general computa-tional mechanism in terms of normal first order predicate calculus deduction systems.