NESTED ABNORMALITY THEORIES

We propose a new approach to the use of circumscription for representi ng knowledge. Nested abnormality theories are similar to simple abnorm ality theories introduced by McCarthy, except that their axioms may ha ve a nested structure, with each level corresponding to another applic ation of the circumscription operator. The new style of applying circu mscription sometimes leads to more economical and elegant formalizatio ns. Mathematical properties of nested abnormality theories may be easi er to investigate. These advantages are demonstrated by recasting seve ral familiar applications of circumscription in the new format, includ ing some examples of inheritance hierarchies, the domain closure assum ption and causal minimization. Nested abnormality theories provide als o a convenient representation for the explanation closure approach to the frame problem developed by Schubert.