Nested Abnormality Theories

We propose a new approach to the use of circumscription for representing knowledge. Nested abnormality theories are similar to simple abnormality theories introduced by McCarthy, except that their axioms may have a nested structure , with each level corresponding to another application of the circumscription operator. The new style of applying circumscription sometimes leads to more economical and elegant formalizations. Mathematical properties of nested abnormality theories may be easier to investigate. These advantages are demonstrated by recasting several familiar applications of circumscription in the new format, including some examples of inheritance hierarchies, the domain closure assumption and causal minimization. Nested abnormality theories provide also a convenient representation for the explanation closure approach to the frame problem developed by Schubert.