Coupling quantum-like cognition with the neuronal networks within generalized probability theory

TL;DR

This paper introduces a novel quantum-like model of neuronal networks using generalized probability theory, aiming to connect cognitive phenomena with neurophysiological processes and enabling applications in medical diagnostics.

Contribution

It develops a GPT-based quantum-like representation of neuronal networks, bridging phenomenological models with neurophysiological foundations and demonstrating key quantum-like effects.

Findings

Reproduces order, non-repeatability, and disjunction effects in neuronal networks

Models neurological conditions like depression and epilepsy using quantum-like frameworks

Provides a flexible approach applicable to biological and social networks

Abstract

The past few years have seen a surge in the application of quantum theory methodologies and quantum-like modeling in fields such as cognition, psychology, and decision-making. Despite the success of this approach in explaining various psychological phenomena such as order, conjunction, disjunction, and response replicability effects there remains a potential dissatisfaction due to its lack of clear connection to neurophysiological processes in the brain. Currently, it remains a phenomenological approach. In this paper, we develop a quantum-like representation of networks of communicating neurons. This representation is not based on standard quantum theory but on generalized probability theory (GPT), with a focus on the operational measurement framework. Specifically, we use a version of GPT that relies on ordered linear state spaces rather than the traditional complex Hilbert spaces. A network of communicating neurons is modeled as a weighted directed graph, which is encoded by its weight matrix. The state space of these weight matrices is embedded within the GPT framework, incorporating effect observables and state updates within the theory of measurement instruments a critical aspect of this model. This GPT based approach successfully reproduces key quantum-like effects, such as order, non-repeatability, and disjunction effects (commonly associated with decision interference). Moreover, this framework supports quantum-like modeling in medical diagnostics for neurological conditions such as depression and epilepsy. While this paper focuses primarily on cognition and neuronal networks, the proposed formalism and methodology can be directly applied to a wide range of biological and social networks.