Core c-Representations and c-Core Closure for Conditional Belief Bases

Marco Wilhelm, Gabriele Kern-Isberner, Christoph Beierle

Abstract: c-Representations constitute a family of ranking models of symbolic conditional belief bases with outstanding inference properties. In this paper, we identify the subclass of core c-representations which inherit all beneficial properties from c-representations but are stratified, hence, easier to compute. Moreover, this class provides a unique minimal representative, the minimal core c-representation of a conditional belief base. Based on that, we define a novel inference operation, c-core closure, analyze its properties, and compare it to System P, System Z, and skeptical c-inference. Like skeptical c-inference, c-core closure satisfies syntax splitting and does not suffer from the drowning problem. In addition, it satisfies rational monotony and inductive enforcement.