This paper compares weighted knowledge bases (KBs) and cost-based semantics, recent formalisms for ontology-mediated data querying of inconsistent knowledge bases (KBs), with c-representations, a form of non-monotonic reasoning first introduced by Kern-Isberner. Weighted knowledge bases assign weights to each proposition in the KB and assign a cost to each DL interpretation based on the frequency with which it violates the KB's rules. c-representations assign numerical ranks to each interpretation by penalizing violated conditions to interpret weakenable concept inclusions in first-order logic. This paper compares these two approaches at the semantic level, showing that, under certain conditions, weighted knowledge bases and sets of weakenable conditions produce equivalent orderings in interpretations and exhibit semantic structural equivalence based on their relative costs. We also compare the implications in both cases, suggesting that certain concepts can be expressed identically in both formalisms.
