On Stein's paper: resolving ambiguity in nonmonotonic inheritance hierarchies

Abstract

Inheritance hierarchies provide a simple encoding of common sense knowledge. Though attracted by the simplicity of hierarchies, the artificial intelligence community does not agree on how to deal with the ambiguities caused by the nonmonotonicity of these hierarchies. Stein (1992) presents a theory of multiple defeasible inheritance which is different from the theory of Touretzky et al. (1990, 1991, 1994). We show here that her way of defining an extension with respect to a focus node and as a subgraph of the inheritance graph is very attractive and compatible with Touretzky et al.'s theoretic framework, but that her definition of admissibility is not intuitively satisfactory. Nevertheless, her polynomial algorithm for computing the ideally skeptical conclusion set according to this definition of admissibility provides an interesting heuristic to compute a really skeptical conclusion set, i.e. a subset of the ideally skeptical one. In Touretzky et al.'s theory, ideal skepticism is NP-hard.