A Description Logic Framework for Commonsense Conceptual Combination Integrating Typicality, Probabilities and Cognitive Heuristics
This work addresses the challenge of modeling human-like concept composition in AI, though it appears incremental as it builds on existing logics like ALC TR and probabilistic Description Logics.
The authors tackled the problem of concept combination in commonsense reasoning by proposing a nonmonotonic Description Logic that integrates typicality, probabilities, and cognitive heuristics, resulting in a framework that maintains EXPTIME-complete reasoning complexity as in the underlying ALC logic.
We propose a nonmonotonic Description Logic of typicality able to account for the phenomenon of concept combination of prototypical concepts. The proposed logic relies on the logic of typicality ALC TR, 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 ALC TR by typicality inclusions whose intuitive meaning is that "there is probability p 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 focus on those scenarios whose probabilities belong to a given and fixed range, and we exploit such scenarios in order to ascribe typical properties to a concept C 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 ALC.