The Pet-Fish problem on the World-Wide Web

In Aerts & Gabora (2005a,b), we introduced a modeling scheme for concepts and their combinations that makes use of the mathematical formalism of quantum physics. This quantum modeling scheme has been further worked out in Aerts (2009a) and Aerts (2010a,b). The experimental data we used to create our modeling scheme were data collected in experiments with human subjects that were conducted within the framework of concepts research in psychology (Hampton 1988a,b). These experiments required human subjects to estimate typicalities of exemplars of concepts and their combinations. The results of these estimations were in conflict with how combinations of concepts such as'conjunction' and'disjunction' were expected to behave classically, as prescribed by classical logic or set theory. Hampton called these deviations from classical behavior'overextension' and'underextension', depending on their relation to the classically expected values of typicality (Hampton 1988a,b).