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Quantum-Like Cognition and Rationality: Biological and Artificial Intelligence Systems

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Quantum Computing in the Arts and Humanities

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Abstract

This is a short introductory review on quantum-like modeling of cognition with applications to decision-making and rationality. The aim of the review is twofold: (a) to present briefly the apparatus of quantum information and probability theory useful for such modeling; (b) to motivate applications of this apparatus in cognitive studies and artificial intelligence, psychology, decision-making, social and political sciences. We define quantum rationality as decision-making that is based on quantum information processing. Quantumly and classically rational agents behaves differently. A quantum-like agent can violate the Savage Sure Thing Principle, the Aumann theorem on impossibility of agreeing to disagree. Such an agent violates the basic laws of classical probability, e.g., the law of total probability and the Bayesian probability inference. In some contexts, “irrational behavior” (from the viewpoint of classical theory of rationality) can be profitable, especially for agents who are overloaded by a variety of information flows. Quantumly rational agents can save a lot of information processing resources. At the same time, this sort of rationality is the basis for quantum-like socio-political engineering, e.g., social laser. This rationality plays the important role in the process of decision-making not only by biosystems, but even by AI-systems. The latter equipped with quantum(-like) information processors would behave irrationally, from the classical viewpoint. As for biosystems, quantum rational behavior of AI-systems has its advantages and disadvantages. Finally, we point out that quantum-like information processing in AI-systems can be based on classical physical devices, e.g., classical digital or analog computers.

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Notes

  1. 1.

    Of course, non-Bayesian probability updates are not reduced to quantum, given by state transformations in the complex Hilbert space. One may expect that human decision-making violates not only classical, but even quantum rationality.

  2. 2.

    Comment: earthquakes nearby Tokyo happen often; in some periods things in room shake practically everyday. Amplitudes vary day to day; of course each time I estimated their strength. But this is difficult to do subjectively....

  3. 3.

    Although in quantum physics the magnitudes of these numbers play an important role, in quantum information theory the eigenvalues are merely formal labels encoding information which can be extracted from a state with the aid of an observable. In the case of dichotomous answers, we can simply use zero to encode “no” and one to encode “yes”.

  4. 4.

    We state again that in the classical probability model the states of the world are encoded by points of \(\Omega .\) Take one fixed state \(\omega .\) Since information representation of each agent is a partition of \(\Omega ,\) for each i there exists an element of partition, say \(P_j^{(i)},\) containing this \(\omega .\) For this state of the world, the ith agent should definitely get the answer \(a_j^{(i)}\) corresponding the element \(P_j^{(i)}\). Thus any agent is able to resolve uncertainty at least for her/his information representation (although she/he is not able to completely resolve uncertainty about the state of the world). In the quantum case, an agent is not able to resolve uncertainty even at the level of her/his information representation. And the prior probability is updated in this uncertainty context.

  5. 5.

    For example, the state space H is four dimensional with the orthonormal basis \((e_1,e_2, e_3, e_4),\) the projectors \(P_1\) and \(P_2\) project H onto the subspaces with the bases \((e_1,e_2)\) and \((e_3, e_4),\) respectively. Here \((P_1, P_2)\) is information representation of an agent. Let E be the projector onto the subspace with the basis \((e_1, e_4)\) and let \(\Psi =(e_1+e_4)/\sqrt{2}.\) Then \(Q_\Psi = I,\) the unit operator. Hence, E is not known for this agent, although it belongs to \(H_E.\)

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  1. International Center for Mathematical Modeling in Physics and Cognitive Sciences, Linnaeus University, 351 95, Växjö, Sweden

    Andrei Khrennikov

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  1. Interdisciplinary Centre for Computer Music Research (ICCMR), University of Plymouth, Plymouth, UK

    Eduardo Reck Miranda

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Khrennikov, A. (2022). Quantum-Like Cognition and Rationality: Biological and Artificial Intelligence Systems. In: Miranda, E.R. (eds) Quantum Computing in the Arts and Humanities. Springer, Cham. https://doi.org/10.1007/978-3-030-95538-0_4

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