Conjunction and negation of natural concepts: A quantum-theoretic modeling

Abstract

We perform two experiments with the aim to investigate the effects of negation on the combination of natural concepts. In the first experiment, we test the membership weights of a list of exemplars with respect to two concepts, e.g., Fruits and Vegetables, and their conjunction Fruits And Vegetables. In the second experiment, we test the membership weights of the same list of exemplars with respect to the same two concepts, but negating the second, e.g., Fruits and Not Vegetables, and again their conjunction Fruits And Not Vegetables. The collected data confirm existing results on conceptual combination, namely, they show dramatic deviations from the predictions of classical (fuzzy set) logic and probability theory. More precisely, they exhibit conceptual vagueness, gradeness of membership, overextension and double overextension of membership weights with respect to the given conjunctions. Then, we show that the quantum probability model in Fock space recently elaborated to model Hampton’s data on concept conjunction (Hampton, 1988a) and disjunction (Hampton, 1988b) faithfully accords with the collected data. Our quantum-theoretic modeling enables to describe these non-classical effects in terms of genuine quantum aspects, namely ‘contextuality’, ‘superposition’, ‘interference’ and ‘emergence’. The obtained results confirm and strengthen the analysis in Aerts (2009a) and Sozzo (2014) on the identification of quantum structures in experiments on conceptual vagueness. And, more, they can be inserted within the general research on the identification of quantum structures in cognitive processes.