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 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.Comment: 39 pages, 3 figure

Hierarchical conceptual spaces for concept combination

AbstractWe introduce a hierarchical framework for conjunctive concept combination based on conceptual spaces and random set theory. The model has the flexibility to account for composition of concepts at various levels of complexity. We show that the conjunctive model includes linear combination as a special case, and that the more general model can account for non-compositional behaviours such as overextension, non-commutativity, preservation of necessity and impossibility of attributes and to some extent, attribute loss or emergence. We investigate two further aspects of human concept use, the conjunction fallacy and the ‘guppy effect’