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.
Highlights
Substantial evidence of presence of quantum structures in processes connected with human behavior and cognition has been put forward in the last decade
Let us first analyze the situation where we look for a modeling solution in the Hilbert space H —which for our complete quantum model in Fock space will be the first sector of this Fock space, as we will show in detail later
Our experimental data on conjunctions and negations of natural concepts confirm that classical probability does not generally work when people combine concepts, as we have seen in the previous sections
Summary
Substantial evidence of presence of quantum structures in processes connected with human behavior and cognition has been put forward in the last decade Such quantum structures were identified in situations of decision making and in the structure of language (see e.g., Aerts, 2009; Khrennikov, 2010; Busemeyer and Bruza, 2012; Aerts et al, 2013b; Haven and Khrennikov, 2013; Pothos and Busemeyer, 2013; Wang et al, 2014). The main experimental challenges to traditional modeling approaches to concepts combinations are sketched in the following
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