General Quantum Modeling of Combining Concepts: A Quantum Field Model in Fock Space

TL;DR

This paper develops a quantum field theoretical model in Fock space to accurately predict how items combine concepts, explaining experimental deviations from classical logic through quantum interference and superposition effects.

Contribution

It introduces a novel quantum field model in Fock space for concept combination, extending previous Hilbert space models and matching experimental data with high precision.

Findings

Quantum interference explains overextension and underextension in concept disjunctions.

Superpositions of different number states are essential for accurate modeling.

The model achieves perfect prediction of Hampton's experimental results.

Abstract

We extend a quantum model in Hilbert space developed in Aerts (2007a) into a quantum field theoric model in Fock space for the modeling of the combination of concepts. Items and concepts are represented by vectors in Fock space and membership weights of items are modeled by quantum probabilities. We apply this theory to model the disjunction of concepts and show that the predictions of our theory for the membership weights of items regarding the disjunction of concepts match with great accuracy the complete set of results of an experiment conducted by Hampton (1988b). It are the quantum effects of interference and superposition of that are at the origin of the effects of overextension and underextension observed by Hampton as deviations from a classical use of the disjunction. It is essential for the perfect matches we obtain between the predictions of the quantum field model and Hampton's experimental data that items can be in superpositions of `different numbers states' which proves that the genuine structure of quantum field theory is needed to match predictions with experimental data.