[Paper Review] Descriptive and Foundational Aspects of Quantum Cognition

Reinhard Blutner, Peter beim Graben|arXiv (Cornell University)|Oct 15, 2014

Quantum Mechanics and Applications148 references3 citations

TL;DR

This paper argues that quantum cognition offers a more systematic framework than classical bounded rationality for modeling cognitive puzzles involving decision-making under uncertainty. By grounding quantum probabilities in an abstract orthomodular lattice structure derived from partial Boolean algebras under resource constraints, it establishes a foundational justification for why quantum-like models are conceptually necessary in cognitive science.

ABSTRACT

Quantum mechanics emerged as the result of a successful resolution of stringent empirical and profound conceptual conflicts within the development of atomic physics at the beginning of the last century. At first glance, it seems to be bizarre and even ridiculous to apply ideas of quantum physics in order to improve current psychological and linguistic or semantic ideas. However, a closer look shows that there are some parallels in the development of quantum physics and advanced theories of cognitive science. In psychology, geometric models of meaning have a long tradition. However, they suffer from many shortcomings which are illustrated by discussing several puzzles of bounded rationality. In the first part of this article, we argue that the present account of quantum cognition - taking quantum probabilities rather than classical probabilities - can give a more systematic description of these puzzles than the alternate and rather eclectic treatments in the traditional framework of bounded rationality. Unfortunately, the quantum probabilistic treatment does not always and does not automatically provide a deeper understanding and a true explanation of these puzzles. In the second part of this article, we explain the foundational issue from the perspective of Piron, Foulis, Randall, and others, and we apply it to the foundation of quantum cognition. In this connection, we show that quantum probabilities are of (virtual) conceptual necessity if grounded in an abstract algebraic framework of orthomodular lattices. This framework is motivated by assuming partial Boolean algebras (describing particular perspectives) that are combined into a uniform system while considering certain capacity restrictions. It is at this point that one important aspect of the whole idea of bounded rationality directly enters the theoretical scenery of quantum cognition: resource limitation.

Motivation & Objective

• To address persistent shortcomings in classical models of bounded rationality in cognitive science.
• To demonstrate that quantum probabilities provide a more systematic description of cognitive decision puzzles than classical probabilistic frameworks.
• To establish a foundational justification for quantum cognition using abstract algebraic structures such as orthomodular lattices.
• To integrate resource limitations—central to bounded rationality—into the formal structure of quantum cognition.
• To show that quantum probabilities emerge as conceptually necessary under constraints of partial perspectives and information capacity.

Proposed method

• Formalizing cognitive systems using orthomodular lattices as the underlying algebraic structure for conceptual events.
• Modeling partial perspectives as partial Boolean algebras that are unified into a coherent system under capacity constraints.
• Applying the framework of Piron, Foulis, and Randall to derive quantum probabilities from conceptual necessity rather than physical analogy.
• Using abstract algebraic methods to show that quantum probabilities are not merely descriptive but foundational under resource-limited reasoning.
• Demonstrating that the combination of partial perspectives under constraints leads naturally to non-classical probability structures.
• Reinterpreting bounded rationality not as a cognitive flaw but as a structural condition that necessitates quantum-like formalism.

Experimental results

Research questions

• RQ1 Why do classical models of bounded rationality fail to systematically resolve cognitive puzzles involving decision-making under uncertainty?
• RQ2 How can quantum probabilities provide a more coherent and systematic account of cognitive phenomena than classical probabilities?
• RQ3 What foundational principles justify the use of quantum structures in cognitive modeling beyond mere analogy?
• RQ4 In what way do resource limitations in cognitive processing lead to the emergence of quantum-like structures?
• RQ5 How does the algebraic framework of orthomodular lattices provide a necessary foundation for quantum cognition?

Key findings

• Quantum cognition provides a more systematic description of bounded rationality puzzles than classical probabilistic models.
• The use of quantum probabilities is not arbitrary but arises from conceptual necessity when modeling partial perspectives under resource constraints.
• Orthomodular lattices emerge as the natural algebraic structure for conceptual events in cognitive systems when partial Boolean algebras are combined under capacity limits.
• The foundational framework of Piron, Foulis, and Randall supports the idea that quantum probabilities are not just descriptive but structurally necessary in cognitive modeling.
• Resource limitations in cognitive processing directly lead to the emergence of non-classical probability structures, justifying quantum-like formalisms.
• The paper establishes that quantum cognition is not a mere analogy to physics but a mathematically grounded extension of conceptual reasoning under constraints.