Growing empirical evidence reveals that traditional set-theoretic structures cannot in general be applied to cognitive phenomena. This has raised several problems, as illustrated, for example, by probability judgement errors and decision-making (DM) errors. We propose here a unified theoretical perspective which applies the mathematical formalism of quantum theory in Hilbert space to cognitive domains. In this perspective, judgements and decisions are described as intrinsically non-deterministic processes which involve a contextual interaction between a conceptual entity and the cognitive context surrounding it. When a given phenomenon is considered, the quantum-theoretic framework identifies entities, states, contexts, properties and outcome statistics, and applies the mathematical formalism of quantum theory to model the considered phenomenon. We explain how the quantum-theoretic framework works in a variety of judgement and decision situations where systematic and significant deviations from classicality occur.
Growing empirical evidence reveals that traditional set-theoretic structures cannot in general be applied to cognitive phenomena. This has raised several problems, as illustrated, for example, by probability judgement errors and decision-making (DM) errors. We propose here a unified theoretical perspective which applies the mathematical formalism of quantum theory in Hilbert space to cognitive domains. In this perspective, judgements and decisions are described as intrinsically non-deterministic processes which involve a contextual interaction between a conceptual entity and the cognitive context surrounding it. When a given phenomenon is considered, the quantum-theoretic framework identifies entities, states, contexts, properties and outcome statistics, and applies the mathematical formalism of quantum theory to model the considered phenomenon. We explain how the quantum-theoretic framework works in a variety of judgement and decision situations where systematic and significant deviations from classicality occur.
Classical models of decision-making under uncertainty, grounded in expected utility theory and Bayesian probability, often fail to account for systematic cognitive anomalies such as preference reversals, order effects, ambiguity aversion, and context-dependent choices. Quantum cognition models offer a novel theoretical framework that applies the mathematical principles of quantum probability—such as superposition, interference, and non-commutativity—to cognitive processes without assuming physical quantum mechanisms in the brain. By representing cognitive states as probabilistic superpositions that collapse through decision “measurements,” these models provide parsimonious explanations for violations of classical rationality. This paper examines how quantum cognition frameworks capture contextual influence, belief updating, and interference effects in uncertain decision environments. Drawing on findings from cognitive psychology and behavioral economics, the study highlights the relevance of quantum cognition for applications in economic choice modeling, legal decision analysis, and artificial intelligence. The analysis suggests that quantum probability offers a robust alternative to classical approaches when modeling human decision-making in complex, ambiguous, and context-sensitive situations.
Uncertainty is an intrinsic part of life; most events, affairs, and questions are uncertain. A key problem in behavioral sciences is how the mind copes with uncertain information. Quantum probability theory offers a set of principles for inference, which align well with intuition about psychological processes in certain cases: cases when it appears that inference is contextual, the mental state changes as a result of previous judgments, or there is interference between different possibilities. We motivate the use of quantum theory in cognition and its key characteristics. For each of these characteristics, we review relevant quantum cognitive models and empirical support. The scope of quantum cognitive models encompasses fallacies in decision-making (such as the conjunction fallacy or the disjunction effect), question order effects, conceptual combination, evidence accumulation, perception, over-/underdistribution effects in memory, and more. Quantum models often formalize psychological ideas previously expressed in heuristic terms, allow unified explanations of previously disparate findings, and have led to several surprising, novel predictions. We also cast a critical eye on quantum models and consider some of their shortcomings and issues regarding their further development.
Abstract We provide here a general mathematical framework to model attitudes towards ambiguity which uses the formalism of quantum theory as a “purely mathematical formalism, detached from any physical interpretation”. We show that the quantum-theoretic framework enables modelling of the Ellsberg paradox, but it also successfully applies to more concrete human decision-making tests involving financial, managerial and medical decisions. In particular, we elaborate a mathematical representation of various empirical studies which reveal that attitudes of managers towards uncertainty shift from ambiguity seeking to ambiguity aversion, and viceversa, thus exhibiting hope effects and fear effects. The present framework provides a promising direction towards the development of a unified theory of decisions in the presence of uncertainty.
There are two basic theories of probability and two scientific perspectives – classical and quantum. In this chapter, assumptions of both the classical and the quantum probability theories will be presented and confronted. The rules for quantum probabilities differ from those of classical probabilities. In this chapter, we will describe what is the difference between the quantum cognitive modelling different from traditional cognitive modelling. In quantum probability theory (QPT) states of individual quantum, systems are called pure states, which are represented as vectors in a vector space (the Hilbert space). Properties of the Hilbert space and vectors’ operations will be explained. Two aspects of quantum theory open the door to addressing problems facing cognition and decision in a totally new light. The first is known as “contextuality” of judgements and decisions: the context generated by making a first judgement or decision interferes with subsequent judgements or decisions to produce order effects, so that judgements and decisions are non-commutative. The second aspect relates to quantum entanglement – a phenomenon whereby making an observation on one part of the system instantaneously affects the state in another part of the system, even if the respective systems are separated by space-like distances. This opens the door to developing quantum-like models of cognitive phenomena which are not decompositional in nature. Examples of cognitive processes modelled using the quantum account and results on the previous studies will be presented. We will also discuss the quantum–classical boundary.
Human reasoning is traditionally modeled through rational-order frameworks that assume stability, separability, and coherence. Yet across judgment, valuation, perception, and social decision-making, empirical work consistently reveals patterned violations of these assumptions. These deviations intensify in real-world contexts shaped by institutional constraints, identity commitments, and collective narratives, where reasoning must navigate incompatible interpretive frames and interdependent evaluative pressures. Existing theories typically treat such phenomena as noise, bias, or bounded rationality, leaving no formal account of how rational-order rules interact with the variability inherent in social domains. This article proposes a structural framework that explains why these two regimes diverge and how their interaction produces systematic mismatches. Building on quantum probability theory, not as a physical metaphor but as a representational tool, it formalizes evaluative states that remain indeterminate until elicited, transform under contextual modulation, and become relationally coupled across agents and domains. Whereas, existing quantum-cognition models primarily address task-level effects such as conjunction errors or order dependence, this framework scales quantum principles to socially and institutionally embedded reasoning. The account identifies contradiction, interference, entanglement, and resolution as recurrent properties of real-world cognition and shows how quantum formalisms provide a coherent vocabulary for capturing these phenomena. To support cumulative progress, the article outlines a research agenda with empirically testable designs for distinguishing incompatible bases, assessing inseparability, modeling context-driven transformations, and integrating multi-level reasoning environments. This program positions quantum and classical approaches within a unified architecture and advances a broader science of reasoning.
This thesis is fundamentally about using conceptual and mathematical constructs from the area of Quantum Theory in Information Retrieval (IR). The need and motivation for this is two-fold – firstly, it has been increasingly shown in decision sciences that human decision-making does not always conform to the norms of traditional probability and logic framework. The quantum framework offers a generalised probability and logic framework which can model decisions or judgements under dynamic context and ambiguity. Secondly, there is a need in IR for theories and models which improve our understanding of user behaviour. Hence it is worth exploring the combination of the quantum framework and IR, especially focused on the user aspects of IR. The overarching research question is whether there is evidence of user behaviour in IR scenarios which warrants the need for a quantum based approach by way of showing the limitations of the traditional (classical) approach. The methodology involves analysing data to detect quantum-like phenomena of interference, contextuality, incompatibility, etc. from two common data sources in IR–standard datasets like query log data, and through crowdsourced user studies designed similar to some quantum physics or cognitive science experiments. While the evidence of quantum-like phenomena from standard datasets is not convincing, we find that some of the user studies reveal the quantum-like structure of document judgements. One of the key findings which has implication for IR is the dynamic interactions between the different dimensions of relevance. For example, a user’s judgement of reliability of a document depends significantly on whether they found it understandable or not. Thus, the consideration of one relevance dimension or document feature can provide a context for another dimension, contrary to the current IR models which consider these features to be independent of each other and an objective property of the document. The quantum framework has been especially designed to deal with such scenarios where properties of systems or objects do not exist independent of measurement context. The thesis concludes with suggestions about incorporating quantum mathematical constructs into state-of-art IR algorithms.