Quantum structure of negation and conjunction in human thought

Abstract

We analyze in this paper the data collected in a set of experiments investigating how people combine natural concepts. We study the mutual influence of conceptual conjunction and negation by measuring the membership weights of a list of exemplars with respect to two concepts, e.g., Fruits and Vegetables, and their conjunction Fruits And Vegetables, but also their conjunction when one or both concepts are negated, namely, Fruits And Not Vegetables, Not Fruits And Vegetables, and Not Fruits And Not Vegetables. Our findings sharpen and advance existing analysis on conceptual combinations, revealing systematic deviations from classical (fuzzy set) logic and probability theory. And, more important, our results give further considerable evidence to the validity of our quantum-theoretic framework for the combination of two concepts. Indeed, the representation of conceptual negation naturally arises from the general assumptions of our two-sector Fock space model, and this representation faithfully agrees with the collected data. In addition, we find a new significant and a priori unexpected deviation from classicality, which can exactly be explained by assuming that human reasoning is the superposition of an “emergent reasoning” and a “logical reasoning,” and that these two processes are represented in a Fock space algebraic structure.

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“…Hence, the feature of 'typicality' behaves weirdly with respect to the conjunction, in the sense that the conjunction 'pet-fish' rates higher in typicality than the single components 'pet' and 'fish', for specific entities such as a 'guppy' or a 'gold-fish'. In our Brussels group, we have worked out quantum models for the guppy effect in great detail, and we believe that it is an archetype for what happens when the conjunction fallacy manifests in experimental situations, leading to a much better understanding of the phenomenon than in traditional explanations, where it is merely classified as a probability judgment error [26,27,28,29]. This also because, a much less known probabilistic variant of the original pet-fish problem, using 'membership weights' instead of 'typicalities', has also been abundantly tested, giving rise to analogous behaviors for the conjunction [30,31,32].…”

“…The authors of the above-mentioned study disagree with this view and claim that their experiments show that double conjunction fallacies are no exception and appear abundantly whenever some specific cognitive situations arise. What is interesting is that in the quantum model of the pet-fish situation that we developed in our group [17,26,27,28,29], the single and double conjunction fallacies can be modeled in a very natural way, and result both from a same fundamental mechanism, which we plan to use also as an explanation for, and to further the analysis of, the situations put forward in [34].…”