Experimental Evidence for Quantum Structure in Cognition

TL;DR

This paper demonstrates that experimental data on concept membership weights, affected by overextension effects, cannot be modeled with classical measure theory, and suggests quantum models as a better alternative.

Contribution

It proves a no-go theorem showing classical measure structures cannot account for certain cognitive data and introduces a geometric criterion to identify non-classicality in membership weights.

Findings

Experimental data violate classical measure-theoretic models.

A geometric criterion reveals non-classicality in concept membership data.

Quantum formalism can model cognitive phenomena that classical models cannot.

Abstract

We proof a theorem that shows that a collection of experimental data of membership weights of items with respect to a pair of concepts and its conjunction cannot be modeled within a classical measure theoretic weight structure in case the experimental data contain the effect called overextension. Since the effect of overextension, analogue to the well-known guppy effect for concept combinations, is abundant in all experiments testing weights of items with respect to pairs of concepts and their conjunctions, our theorem constitutes a no-go theorem for classical measure structure for common data of membership weights of items with respect to concepts and their combinations. We put forward a simple geometric criterion that reveals the non classicality of the membership weight structure and use experimentally measured membership weights estimated by subjects in experiments to illustrate our geometrical criterion. The violation of the classical weight structure is similar to the violation of the well-known Bell inequalities studied in quantum mechanics, and hence suggests that the quantum formalism and hence the modeling by quantum membership weights can accomplish what classical membership weights cannot do.