Syntax Splitting and Reasoning from Weakly Consistent Conditional Belief Bases with c-Inference

Jonas Haldimann, Christoph Beierle, Gabriele Kern-Isberner

Abstract: It has been shown that c-inference is an inductive inference operator, mapping belief bases to inference relations, that exhibits many desirable properties put forward for nonmonotonic reasoning. It is based on c-representations which are a special kind of ranking function. However, the definition of c-representation only takes belief bases into account that satisfy a rather strong notion of consistency requiring every world to be at least somewhat plausible. In this paper, we employ the concepts of strong and weak consistency for conditional belief bases and extend the notions of c-representation and c-inference to also cover weakly consistent belief bases. We adapt a constraint satisfaction problem characterizing c-inference so that it captures extended c-inference and provides a basis for its implementation. Furthermore, we show various properties of extended c-inference and in particular, we prove that the extended notion of c-inference fully satisfies syntax splitting.