A description logic framework for commonsense conceptual combination integrating typicality, probabilities and cognitive heuristics

We propose a nonmonotonic Description Logic of typicality able to account for the phenomenon of the combination of prototypical concepts. The proposed logic relies on the logic of typicality (Formula presented.), whose semantics is based on the notion of rational closure, as well as on the distributed semantics of probabilistic Description Logics, and is equipped with a cognitive heuristic used by humans for concept composition. We first extend the logic of typicality (Formula presented.) by typicality inclusions of the form (Formula presented.), whose intuitive meaning is that ‘we believe with degree (Formula presented.) about the fact that typical Cs are Ds’. As in the distributed semantics, we define different scenarios containing only some typicality inclusions, each one having a suitable probability. We then exploit such scenarios in order to ascribe typical properties to a concept (Formula presented.) obtained as the combination of two prototypical concepts. We also show that reasoning in the proposed Description Logic is ExpTime-complete as for the underlying standard Description Logic (Formula presented.).