Skeptical Inference Based on C-Representations and Its Characterization as a Constraint Satisfaction Problem

The axiomatic system P is an important standard for plausible, nonmonotonic inferences that is, however, known to be too weak to solve benchmark problems like irrelevance, or subclass inheritance (so-called Drowning Problem). Spohn’s ranking functions which provide a semantic base for system P have often been used to design stronger inference relations, like Pearl’s system Z, or c-representations. While each c-representation shows excellent inference properties and handles particularly irrelevance and subclass inheritance properly, it is still an open problem which c-representation is the best. In this paper, we focus on the generic properties of c-representations and consider the skeptical inference relation (c-inference) that is obtained by taking all c-representations of a given knowledge base into account. In particular, we show that c-inference preserves the properties of solving irrelevance and subclass inheritance which are met by every single c-representation. Moreover, we characterize skeptical c-inference as a constraint satisfaction problem so that constraint solvers can be used for its implementation.