Abstract Classical probability theory provides the standard foundation for rational inference, yet human probability judgments are known to systematically violate Kolmogorovian axioms through phenomena such as conjunction fallacies and question-order effects. Whether large language models (LLMs) exhibit structurally analogous departures from classical probability remains an important empirical question with broad implications for AI evaluation and cognitive science. Here, we report a controlled experimental investigation of the probabilistic structure of LLM responses under systematically varied contextual prompts, treating model outputs as behavioral observables of a high-dimensional inference system. Using paradigms drawn from cognitive decision research, we evaluated multiple LLMs across tasks, including ambiguity judgments, belief revision, order effects, conjunction fallacies, and base-rate reasoning. Our experiments reveal systematic violations of the law of total probability accompanied by pronounced order-dependent effects across all models. Critically, these deviations are not random: they exhibit a structured interference form characterized by a phase-dependent term and a non-trivial upper bound, and the observed scaling relation demonstrates that the resulting probability assignments cannot be embedded within any single Kolmogorov probability space. These findings are consistent with a constrained non-commutative probabilistic structure, formally analogous to quantum probability models previously proposed for human cognition, without implying that neural networks implement quantum-physical processes. Our results establish non-commutative probability as a principled descriptive framework for contextual inference in large-scale artificial systems, and highlight the need for structural, beyond accuracy-based evaluation of probabilistic reasoning in modern AI.
Abstract Classical probability theory provides the standard foundation for rational inference, yet human probability judgments are known to systematically violate Kolmogorovian axioms through phenomena such as conjunction fallacies and question-order effects. Whether large language models (LLMs) exhibit structurally analogous departures from classical probability remains an important empirical question with broad implications for AI evaluation and cognitive science. Here, we report a controlled experimental investigation of the probabilistic structure of LLM responses under systematically varied contextual prompts, treating model outputs as behavioral observables of a high-dimensional inference system. Using paradigms drawn from cognitive decision research, we evaluated multiple LLMs across tasks, including ambiguity judgments, belief revision, order effects, conjunction fallacies, and base-rate reasoning. Our experiments reveal systematic violations of the law of total probability accompanied by pronounced order-dependent effects across all models. Critically, these deviations are not random: they exhibit a structured interference form characterized by a phase-dependent term and a non-trivial upper bound, and the observed scaling relation demonstrates that the resulting probability assignments cannot be embedded within any single Kolmogorov probability space. These findings are consistent with a constrained non-commutative probabilistic structure, formally analogous to quantum probability models previously proposed for human cognition, without implying that neural networks implement quantum-physical processes. Our results establish non-commutative probability as a principled descriptive framework for contextual inference in large-scale artificial systems, and highlight the need for structural, beyond accuracy-based evaluation of probabilistic reasoning in modern AI.
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.
Purpose: Decision-making under uncertainty remains a foundational challenge in cognitive science and artificial intelligence. Classical Bayesian Probability Models (CBM) often fail to explain paradoxical cognitive behaviors such as order effects, ambiguity aversion, and context-dependent reasoning. This study seeks to compare Quantum Probability Theory (QPT) and Classical Bayesian Models in their ability to capture the dynamics of human decision-making. It aims to determine which framework more accurately reflects the cognitive mechanisms underlying reasoning under uncertainty. Methodology: A qualitative, exploratory research design was adopted, involving in-depth semi-structured interviews with 16 experts across psychology, philosophy, artificial intelligence, and cognitive neuroscience. Participants were purposively selected for their theoretical and empirical expertise in probabilistic reasoning. Data were analyzed using reflexive thematic analysis, guided by the Dual-Process Theory and Busemeyer’s Quantum Cognition framework. The analysis emphasized participants’ perspectives on theoretical assumptions, cognitive plausibility, and predictive utility between QPT and CBM paradigms. Findings: Thematic findings reveal that Quantum Probability Theory offers superior explanatory power in contexts involving cognitive ambiguity, contextual dependence, and non-commutativity of mental operations. Participants consistently reported that QPT better models real-world reasoning tasks where classical logic collapses, capturing the fluid and context-sensitive nature of human judgment. Conversely, while CBM remains effective in structured, low-uncertainty scenarios, it fails to accommodate superposition and interference effects inherent in human cognition. Unique Contribution to Theory, Practice, and Policy (Recommendations): The study contributes theoretically by demonstrating how quantum probabilistic models expand existing theories of bounded rationality and probabilistic reasoning in cognitive science. Practically, it encourages interdisciplinary collaboration between cognitive scientists, AI researchers, and philosophers to refine decision models that mirror human intuition more closely. Policy-wise, the findings support the integration of quantum-inspired approaches in the design of intelligent decision-support systems and cognitive architectures. The study recommends continued empirical validation of QPT within applied domains—such as behavioral economics, machine learning, and cognitive modeling—to strengthen its predictive and explanatory robustness.
We present the results of cognitive tests on conceptual combinations, performed using specific Large Language Models (LLMs) as test subjects. In the first test, performed with ChatGPT (GPT-5.5 Thinking) and Google Gemini Advanced (Gemini 1.5 Pro), we show that Bell's inequalities are significantly violated, which indicates the presence of a 'non-classical probability model' with probabilities that do not satisfy Kolmogorov's axioms. In the second test, also performed using ChatGPT and Gemini, we identify the presence of 'Bose-Einstein statistics', rather than the intuitively expected 'Maxwell-Boltzmann statistics', in the distribution of the words contained in large-size texts. Interestingly, these findings mirror the results previously obtained in both cognitive tests with human participants and information retrieval tests on large corpora. Taken together, they point to the 'systematic emergence of non-classical quantum-like structures in conceptual-linguistic domains', regardless of whether the cognitive agent is human or artificial. Although LLMs are classified as neural networks for historical reasons, we believe that a more essential form of knowledge organization takes place in the distributive semantic structure of vector spaces built on top of the neural network. It is this meaning-bearing structure that lends itself to a phenomenon of evolutionary convergence between human cognition and language, slowly established through biological evolution, and LLM cognition and language, emerging much more rapidly as a result of self-learning and training. We analyze various aspects and examples that contain evidence supporting the above hypothesis. We also advance a unifying framework that explains the pervasive quantum organization of meaning that we identify.
Cognitive neuroscience has accumulated robust findings (e.g., order effects in judgment, multi-path motor preparation, perceptual binding, attentional selection, and the recursive construction of self and time) that systematically resist explanation within classical probabilistic and causal frameworks. We argue that these are not anomalies but signatures of a deeper, non-commutative architecture of cognition and brain dynamics. We propose quantum probability theory together with contextual probability theory, not as metaphorical analogies but as rigorous translational languages for cognitive processes in which observation actively transforms underlying state spaces. Underlying this framework is the conjecture that neural network dynamics in the brain are intrinsically organized to generate quantum-like representations-rather than merely being described by quantum mathematics from the outside. Their structural primitives (i.e., superposition, entanglement, projection, and non-commutativity) map onto premotor population coding, long-range cortical synchrony, prefrontal state dynamics, and default-mode network activity. On this basis we sketch a new sub-domain (namely, Cognitive Structural Science) that treats the geometry and algebra of cognitive state spaces as primary explananda, and outline a research program combining homologous human-macaque experiments with quantum-computer simulation as a constrained testbed.
Contemporary discussions of the gap between natural and artificial intelligence often emphasize human capacities such as contextual reasoning, cognitive flexibility, and non-classical decision-making. This paper proposes that quantum and quantum-like models of cognition and decision processes offer a principled framework for addressing these differences. A growing body of empirical evidence shows that human reasoning systematically violates the assumptions of classical probability and logic, exhibiting contextuality, order effects, interference phenomena, and task incompatibility. Quantum probability theory and related quantum-like formalisms provide mathematically rigorous tools—based on Hilbert spaces, superposition, and entanglement—that capture these features more naturally than classical models. While quantum and quantum-like approaches share a common mathematical structure, they differ in physical implementation, motivating two complementary directions in artificial intelligence: quantum AI and quantum-like AI. Together, these approaches suggest a viable pathway toward narrowing, and potentially bridging, the divide between natural and artificial intelligence by grounding AI architectures in models aligned with the structure of human cognition.
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.