Semantic bridges between first order c-representations and cost-based semantics: an initial perspective

Weighted-knowledge bases and cost-based semantics represent a recent formalism introduced by Bienvenu et al. for Ontology Mediated Data Querying in the case where a given knowledge base is inconsistent. This is done by adding a weight to each statement in the knowledge base (KB), and then giving each DL interpretation a cost based on how often it breaks rules in the KB. In this paper we compare this approach with c-representations, a form of non-monotonic reasoning originally introduced by Kern-Isberner. c-Representations describe a means to interpret defeasible concept inclusions of the form C ⊏∼ D (read “instances of C are usually instances of D”) in the first-order case. This is done by assigning a numerical ranking to each interpretations via penalties for each violated conditional. We compare these two approaches on a semantic level. In particular, we show that under certain conditions a weighted knowledge base and a set of defeasible conditionals can generate the same ordering on interpretations, and therefore an equivalence of semantic structures up to relative cost. Moreover, we compare entailment described in both cases, where certain notions are equivalently expressible in both formalisms. Our results have the potential to benefit further work on both cost-based semantics and c-representations.