Characterization of an auto-compatible default theory

In this paper, an equivalence condition for deciding whether a default theory is an auto-compatible default one is presented. Under the condition, the existence of extension of an auto-compatible default theory is a natural result. By introducing a well-ordering over the set D of default rules, the extensions of an auto-compatible default theory (D, W) can be computed directly. The condition represents clearly the characterization of an auto-compatible default theory, and some properties about auto-compatible default theory, such as semi-monotonicity, become natural corollaries. Based on the characterization, the revision of default beliefs is discussed to ensure the existence of extension of the default theory, and the method is applied to investigate stable models of a general logic program.