Quantum Structure of Negation and Conjunction in Human Thought

TL;DR

This paper presents a quantum-theoretic framework to analyze how humans combine concepts involving negation and conjunction, revealing deviations from classical logic and supporting a superposition model of reasoning.

Contribution

It introduces a quantum Fock space model that accurately represents conceptual negation and conjunction, providing a novel explanation for non-classical reasoning patterns.

Findings

Deviations from classical fuzzy logic and probability theory in concept combination

Quantum model accurately fits experimental data on concept negation and conjunction

Evidence for superposition of emergent and logical reasoning in human thought

Abstract

We analyse in this paper the data collected in a set of experiments performed on human subjects on the combination of natural concepts. We investigate 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 existing analysis on conceptual combinations, revealing systematic and remarkable 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 further significant deviation and a priori unexpected 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 can be successfully represented in a Fock space algebraic structure.