Nondistributivity of human logic and violation of response replicability effect in cognitive psychology

TL;DR

This paper advocates for using quantum logic to analyze human reasoning, demonstrating that testing response replicability effects can serve as an experimental test for nondistributivity in cognitive processes, within a state-dependent framework.

Contribution

It introduces a simple test for response replicability effects as a means to empirically examine nondistributivity in human logic, advancing quantum-like modeling in cognitive psychology.

Findings

Response replicability testing is equivalent to testing nondistributivity.

State-dependent framework allows improved analysis of question order and response effects.

Quantum logical nondistributivity can be tested experimentally in cognitive psychology.

Abstract

The aim of this paper is to promote quantum logic as one of the basic tools for analyzing human reasoning. We compare it with classical (Boolean) logic and highlight the role of violation of the distributive law for conjunction and disjunction. It is well known that nondistributivity is equivalent to incompatibility of logical variables -- the impossibility to assign jointly the two-valued truth values to these variables. A natural question arises as to whether quantum logical nondistributivity in human logic can be tested experimentally. We show that testing the response replicability effect (RRE) in cognitive psychology is equivalent to testing nondistributivity -- under the prevailing conjecture that the mental state update generated by observation is described as orthogonal projection of the mental state vector (the projective update conjecture of Wang and Busemeyer). A simple test of RRE is suggested. In contrast to the previous works in quantum-like modeling, we proceed in the state-dependent framework; in particular, distributivity, compatibility, and RRE are considered in a fixed mental state. In this framework, we improve the previous result on the impossibility to combine question order and response replicability effects by using (von Neumann-L\"uders) projective measurements.