Automating the Computation of Nested Abnormality Theories

Nested Abnormality Theories (NATs) were introduced by Lifschitz to use circumscription for representing knowledge. We describe a program CS (Circumscription Simpli er) for computing NATs. The main part of CS is SCAN, developed by Engel and Ohlbach for the elimination of second-order quanti ers. Our addition to SCAN is a new interface that allows us to use it to simplify NATs. CS takes a NAT as input and if it terminates, the output is a set of formulas whose conjunction is logically equivalent to the NAT we used as input. In many cases, the resulting formulas are rst-order.