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.

The gap between natural and artificial intelligence is often discussed in terms of creativity, contextual adaptability, and non-algorithmic decision-making capacities where human cognition appears fundamentally different from current AI systems. This paper argues that developing quantum and quantum-like models of cognition, decision-making, and AI provides a promising pathway for narrowing, and perhaps essentially bridging, this gap. Empirical studies of human cognition and decision-making reveal systematic deviations from classical probability, logic, and information theory—manifesting as contextuality, order effects, interference (such as conjunction and disjunction effects), task incompatibility, and apparent randomness. These phenomena are well captured by quantum probability theory and related quantum-like frameworks, which provide a rigorous mathematical formalism—Hilbert spaces, superposition, entanglement, and decoherence—for modeling cognitive states and their evolution. Such models go beyond metaphor, showing that aspects of human reasoning can be more faithfully represented using quantum-like rather than classical probabilistic structures. Although genuine quantum (based on quantum physics) and quantum-like approaches share the same mathematical foundation, they differ experimentally. Both stimulate the development of novel AI architectures: quantum AI (QAI) and quantum-like AI (QLAI). While QAI depends on advances in quantum computing, QLAI can be realized on classical digital or analog hardware. The advancement of both offers a promising route to reducing—and potentially bridging—the divide between natural and artificial intelligence. This paper sets out a conceptual program to unify natural and artificial intelligence via quantum/quantum-like models of consciousness/cognition and AI.

This work introduces a rigorous mathematical approach for producing entangled quantum states from classical stochastic dynamics. We show that any density matrix ρAB describing a composite quantum system can be reconstructed from the correlations of two foundational stochastic processes, X(t) and Y(t), which model the random behavior of the individual subsystems. The framework employs a dual temporal scale—micro and macro time—where quantum correlations naturally arise as emergent macro-level correlations derived from fine-grained micro-level interactions. We formulate the Double Covariance Model (DCM), which captures the essential features of quantum mechanics by interpreting the quantum state as a fourth-order statistical structure within an underlying classical probabilistic model.

This paper addresses a central conceptual challenge in Quantum-like Cognition and Decision-Making (QCDM) and the broader research program of Quantum-like Modeling (QLM): the interpretation of phases in quantum-like state superpositions. In QLM, system states are represented by normalized vectors in a complex Hilbert space, |ψ⟩=∑kXk|k⟩, where the squared amplitudes Pk=|Xk|2 are outcome probabilities. However, the meaning of the phase factors eiϕk in the coefficients Xk=Pkeiϕk has remained elusive, often treating them as purely phenomenological parameters. This practice, while successful in describing cognitive interference effects (the “interference of the mind”), has drawn criticism for expanding the model’s parameter space without a clear physical or cognitive underpinning. Building on a recent framework that connects QCDM to neuronal network activity, we propose a concrete interpretation. We argue that the phases in quantum-like superpositions correspond directly to the phases of random oscillations generated by neuronal circuits in the brain. This interpretation not only provides a natural, non-phenomenological basis for phase parameters within QCDM but also helps to bridge the gap between quantum-like models and classical neurocognitive frameworks, offering a consistent physical analogy for the descriptive power of QLM.

Artificial intelligence is typically formulated as an information-processing system composed of artificial neurons, where computation is understood as recursive operations connecting inputs and outputs. However, real neural systems are materially embodied and continuously reconfigured by metabolic and physical processes, suggesting that computation cannot be reduced to fixed causal structures. In this paper, we propose a theoretical framework that captures the interplay between informational and material processes as the interaction between two computational schemes: a vertical scheme, representing fixed cause-effect relations, and a horizontal scheme, representing transformations between such relations. We show that the vertical scheme corresponds to Bayesian inference, which updates probability distributions over a fixed hypothesis space, and is consistent with the free-energy minimization principle. In contrast, the horizontal scheme is formalized as inverse Bayesian inference, which modifies the hypothesis space itself by updating likelihood structures based on experienced data. We further demonstrate that the interplay between these schemes can be expressed algebraically as a process of continuously gluing Boolean algebras. This construction yields a non-distributive orthomodular lattice, i.e., quantum logic, without invoking Hilbert space formalism. In this view, quantum logic emerges not as a static logical system but as a structural consequence of dynamically reconfiguring causal contexts. This framework provides a unified perspective in which inference is understood not only as optimization within a fixed model but also as a process that generates and transforms the model itself. It offers a formal basis for describing open-ended computation and suggests a connection to approaches such as unconventional computing and Natural Born Intelligence, where computational structures evolve through interaction with material processes. Unlike existing approaches, this framework derives quantum-logic-like structure from the continual reconfiguration of causal contexts rather than from Hilbert-space assumptions or optimization within a fixed hypothesis space.

Over the past two decades, quantum-like modeling (QLM) has emerged as a powerful framework for describing non-classical features of cognition and decision-making. Rather than assuming physical quantum processes in the brain, QLM employs the Hilbert space formalism to model contextuality, incompatibility of mental observables, and entanglement-like correlations. In this paper, we develop a quantum-informational model of mental markers within the broader I-field (information field) approach. We propose that, under conditions of information overload and limited cognitive resources, individuals primarily respond not to detailed semantic content but to compact content labels - mental markers - carrying cognitive and affective components. We formalize mental markers as structured quantum-like states and analyze the nonclassical correlations between their cognitive and affective components using the Contextuality-Incompatibility-Entanglement triad. Special attention is given to intra-system entanglement between rational (cognitive) evaluation and emotional (affective) coloring, accounting for context-dependent judgments, order effects, and affect-driven decision shifts. Illustrative examples with psychological interpretation and experimental perspectives are provided. An Appendix briefly discusses neurobiological analogues of information overload in neural networks, highlighting structural parallels with the proposed marker-based framework; coupling to the origin and diagnostics of neurological diseases is analyzed. The paper contributes to QLM by distinguishing inter-system and intra-system entanglement and by demonstrating that cognitive - affective entanglement constitutes a fundamental structural feature of mental markers in socially mediated information environments.

We introduce a neurophysiological adaptation of the Double Covariance Model (DCM) to provide a generative, fourth-order statistical framework for brain dynamics. Moving beyond descriptive sliding-window methods, the proposed theory implements a two-scale temporal scheme that explicitly separates fast micro-time stochastic neural fluctuations from the macro-time scale of emergent cognitive states. By treating the variance of covariance as a first-class mathematical object, the model computes the fourth-order moment of localized micro-signals to directly reconstruct a complex-valued network density matrix ($\rho$). This architecture transitions classical neurophysiological data into a quantum-like state representation, enabling the direct application of quantum information measures—such as concurrence and von Neumann entropy—to model macroscopic integration. Ultimately, this framework establishes a principled, non-phenomenological link between low-level stochastic network dynamics and the unified macroscopic phenomenon of "mental entanglement".

We introduce a lattice-theoretic framework for composite information systems in which tensor-like composition and entanglement are defined without presupposing Hilbert spaces or quantum states. Starting from approximation operators induced by indiscernibility relations, we construct composite systems via interaction-dependent closure operators and characterize their fixed-point lattices. Entanglement is defined structurally as the impossibility of generating a fixed point of the composite system from local fixed points alone. This notion does not rely on non-distributive logic a priori and remains meaningful even when local lattices are Boolean. Non-distributive and orthomodular structures arise only under additional conditions and are treated as emergent properties rather than assumptions. The proposed framework generalizes the concept of entanglement as a property of composition and interaction, providing a unified information-theoretic perspective on non-separability beyond standard quantum-mechanical formalisms. By mapping quantum states to correlation patterns via row-set tensor products, we demonstrate that standard quantum entanglement can be understood as a stabilized structural constraint. In this context, maximally entangled states, such as Bell states, correspond to diagonal constraint sets that are non-generable from local components, confirming that the structural core of entanglement exists independently of linear or probabilistic interpretations. Beyond quantum mechanics, the framework admits a natural interpretation in terms of relational databases, where entanglement corresponds to irreducible global relations stabilized by interaction-induced fixed points.

We develop an interacting extension of the Double Covariance Model (DCM), a stochastic subquantum framework in which macroscopic quantum dynamics emerge through coarse-graining of correlated microscopic fluctuations. Starting from local stochastic differential equations on subsystem Hilbert spaces, we derive a closed evolution equation for a coarse-grained double covariance operator using multi-scale Itô calculus and sliding-window averaging. The construction explicitly incorporates two separated temporal scales: a fast microscopic fluctuation scale governing subquantum stochastic processes and a slower macroscopic observation scale associated with coarse-grained dynamics. Within the hydrodynamic limit, where the ratio between microscopic correlation time and averaging-window scale vanishes, rapidly fluctuating corrections disappear and the effective dynamics converges to a deterministic macroscopic transport equation. We show that the emergent macroscopic dynamics has the exact Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) form: coherent Hamiltonian evolution arises from deterministic subquantum flow, while dissipative channels emerge from quadratic noise correlations. The framework further demonstrates how non-separable interaction Hamiltonians can arise from strictly local, state-dependent stochastic feedback fields. In the fluctuation-free limit, the model reduces naturally to the standard von Neumann equation, providing a unified stochastic foundation for both open and closed quantum dynamics.

We describe a phase-adjusted realification procedure that embeds any finite set of rays in C3 into R6. By assigning an appropriate phase to each ray before applying the standard coordinatewise map, we can arrange that two rays are orthogonal in C3 if and only if their images are orthogonal in R6, so the construction yields a faithful orthogonal representation of the original complex configuration. As a concrete example, we consider the 165 projectively distinct rays used in a C3 Kochen-Specker configuration obtained from mutually unbiased bases, list these 165 rays explicitly in C3, and give for each of them its image in R6 under the canonical realification map. We also note that, because the original three-element contexts are no longer maximal in R6, the embedded configuration admits two-valued states even though its realization with maximal contexts in C3 is Kochen-Specker uncolorable.

Dendrogramic Holographic Theory (DHT) is a purely relational theory of information in which the primitive elements are events, and physical description is defined by an observer’s dendrogram: a hierarchical tree of binary questions that distinguishes events only through operationally accessible relations. The core postulate is an epistemic form of Leibniz’s Principle of the Identity of Indiscernibles: if two states of affairs cannot be distinguished by any admissible measurement for a given observer, they are identified for that observer. From each dendrogram we construct a views distribution over relational distances and define a one-particle wavefunction from that distribution; many distinct relational configurations can therefore map to the same distribution and the same wavefunction, so a particle is naturally an equivalence class of dendrograms sharing the same wavefunction. We then study two-particle sectors by embedding a pair of finite dendrograms into a host context consisting of one or two larger dendrograms, allowing both equal host and distinct-host comparisons and accommodating a range of size relations. When neither host can be embedded into the other, the host pair is space-like separated in a Minkowski-like parameter space, so exchange signatures arise purely from the relative organization of the embedded structures rather than from causal nesting. Our simulations show that bosonic versus fermionic exchange behaviour is not an intrinsic label of the embedded inputs, but an emergent invariant of the composite relational wiring diagram linking two, often non-relationally closed, information sets through cross-host correlations, reproducing exclusion-like and pile-up behaviour without postulating the Pauli principle. In this sense, DHT offers a unifying perspective on bosonic and fermionic fields: both arise from the same underlying relational degrees of freedom, and boson–fermion conversion corresponds to operations that break or restore relational closure, by changing host choice and embedding pattern, while leaving the one-particle state fixed—an analogue of supersymmetric unification that does not require a new particle spectrum. This suggests a unification of matter and forces at the level of relational organization without introducing new particles and while remaining compatible with a Minkowski-like spacetime encoding.

Quantum logic is usually presented as a non-classical departure from ordinary reasoning forced on us by quantum mechanics, with classical logic kept as the secure starting point. We argue for the opposite order of explanation in a finite and fully computable setting. The free orthomodular lattice on two generators has ninety-six elements, the direct product of a six-element non-distributive factor and a sixteen-element Boolean factor. Reading the first factor as a register of contexts and the second as Boolean content, we obtain a calculus whose elements are context–bit-vector pairs and whose operations act component by component. With this calculus we establish three results. First, we classify the six layers by commutativity, identifying the central kernel of context-neutral propositions together with a dual central layer in which all complementary contexts are present. Second, we show that orthocomplementation rearranges the layers exactly as the complementation of the small factor rearranges its elements, which makes the duality among the layers rigid rather than accidental. Third, we prove that the operation forgetting the context is a surjective homomorphism of orthocomplemented lattices whose quotient is the classical Boolean algebra, so that classical logic is a six-to-one, information-losing image of the contextual calculus.

This paper starts with surveying the evolution of quantum-like models of cognition and decision making, transitioning from static kinematic representations to a robust dynamical framework based on open quantum systems. We provide a comprehensive analysis of the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation's application in cognitive psychology and decision making, illustrating how it models mental state evolution as a dissipative process influenced by an informational environment. We categorize dynamical regimes into Passive and Active Hamiltonians, demonstrating how non-commutation with projections on decision basis serves as a mathematical signature of cognitive agency and Quantum Escape from classical equilibria. The utility of this framework is further explored through its ability to stabilize non-Nash outcomes in strategic games, such as the Prisoner's Dilemma. Building upon this dynamical foundation, we identify ``cognitive beats'' as a signature of the internal struggle between competing ``flows of mind'' deliberated at approximately equal frequencies. Distinct from the damped oscillations of simple interference, these beats emerge from a structural tension between Liouvillian channels that generates a secondary, slow-scale modulation of conviction. This beat envelope dictates the timing of peak readiness and hesitation, providing a mathematical map of the transition between conflicting cognitive states. By resolving these nested time scales, we provide a new spectral diagnostic for the depth of cognitive agency and the complexity of the underlying deliberation process. This paper develops a theoretical framework linking GKSL dynamics with quantum-like cognition and decision-making (QCDM), highlighting how dissipative quantum models can capture features of human thought and decision processes.

Over the past two decades, quantum-like modeling (QLM) has emerged as a powerful framework for describing non-classical features of cognition and decision-making. Rather than assuming physical quantum processes in the brain, QLM employs the Hilbert space formalism to model contextuality, incompatibility of mental observables, and entanglement-like correlations. In this paper, we develop a quantum-informational model of mental markers within the broader information field approach. We propose that, under conditions of information overload and limited cognitive resources, individuals primarily respond not to detailed semantic content but to compact content labels - mental markers - carrying cognitive and affective components. We formalize mental markers as structured quantum-like states and analyze the nonclassical correlations between their cognitive and affective components using the Contextuality-Incompatibility-Entanglement triad. Special attention is given to intra-system entanglement between rational (cognitive) evaluation and emotional (affective) coloring, accounting for context-dependent judgments, order effects, and affect-driven decision shifts. Illustrative examples with psychological interpretation and experimental perspectives are provided. Appendix B briefly discusses neurobiological analogues of information overload in neural networks, highlighting structural parallels with the proposed marker-based framework; coupling to the origin and diagnostics of neurological diseases is analyzed. The paper contributes to QLM by distinguishing inter-system and intra-system entanglement and by demonstrating that cognitive-affective entanglement constitutes a fundamental structural feature of mental markers in socially mediated information environments.

We develop the mathematical and physical formulation of cognitive cost optimization that underlies the path-integral model of consciousness. The goal-directed cognitive process is modeled as imaginary-time evolution (ITE) under a projector Hamiltonian that rewards configurations consistent with a target concept. We establish three results. First, this ITE coincides with a double-bracket flow and is therefore the Riemannian gradient flow of a Hilbert–Schmidt cost whose unique minimum is the solution. Second, a Wick rotation re-expresses this non-unitary descent as an equivalent unitary evolution on the same Hilbert space, which admits an exact discrete path-integral representation in which the oracle and the initial-state diffusion projector play the roles of potential and kinetic energy. Third, we identify the continuum from unconscious to conscious processing with the strength of the unitary interaction between the cognitive system and a neural-environment probe, recovering the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) decoherence model of Asano et al. in the Markovian weak-coupling limit, and the projective, reportable fixation of an optimized state in the strong-coupling limit, an insight-like “Aha” endpoint. Both regimes share the same ITE and path-integral structure, and only the measurement-interaction strength varies. The Wick rotation is therefore a technique of re-description, not a physical regime change.

This paper starts with surveying the evolution of quantum-like models of cognition and decision making, transitioning from static kinematic representations to a robust dynamical framework based on open quantum systems. We provide a comprehensive analysis of the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation's application in cognitive psychology and decision making, illustrating how it models mental state evolution as a dissipative process influenced by an informational environment. We categorize dynamical regimes into Passive and Active Hamiltonians, demonstrating how non-commutation with projections on decision basis serves as a mathematical signature of cognitive agency and Quantum Escape from classical equilibria. The utility of this framework is further explored through its ability to stabilize non-Nash outcomes in strategic games, such as the Prisoner's Dilemma. Building upon this dynamical foundation, we identify “cognitive beats” as a signature of the internal struggle between competing “flows of mind” deliberated at approximately equal frequencies. Distinct from the damped oscillations of simple interference, these beats emerge from a structural tension between Liouvillian channels that generates a secondary, slow-scale modulation of conviction. This beat envelope dictates the timing of peak readiness and hesitation, providing a mathematical map of the transition between conflicting cognitive states. By resolving these nested time scales, we provide a new spectral diagnostic for the depth of cognitive agency and the complexity of the underlying deliberation process. This paper develops a theoretical framework linking GKSL dynamics with quantum-like cognition and decision-making (QCDM), highlighting how dissipative quantum models can capture features of human thought and decision processes.

This article presents a concrete mathematical framework for the generation of entangled quantum states from classical stochastic processes. We demonstrate that any density operator ρ_AB of a composite system can be derived from the correlations between two underlying stochastic processes, X(t) and Y(t), representing the random fluctuations of its subsystems. This construction utilizes a two-scale temporal scheme - micro and macro time - where quantum correlations emerge as macro-correlations derived from underlying micro-correlations. We propose the Double Covariance Model (DCM), which reproduces the fundamental properties of quantum theory by treating the quantum state as the fourth-order moment structure of an underlying classical probability space.

Can a quantum structure be directly identified in laughter? Here, we show that the basic structure of quantum logic can be identified in standup comedies and sketches. We analyzed scripts from standup comedies and sketches, employing a method to reveal the algebraic structures hidden within the semantic relations of the utterances. Our findings revealed that quantum logic is present in many instances of laughter, including punchlines. Moreover, we taught this method to ChatGPT, which corroborated our findings, indicating that the result is objectively significant. Our method and results, which directly address contextual relationships and identify quantum logic, are groundbreaking. We provide a novel methodology for quantum cognitive science and open new directions for research on sensations and emotions in Artificial Intelligence. Our method identifies contextual quantum-logical structure, but does not aim to model human-level general intelligence.

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.

By uncovering the contrast between Artificial Intelligence and Natural-born Intelligence as a computational process, we define closed computing and open computing, and implement open computing within chemical reactions. This involves forming a mixture and invalidation of the computational process and the execution environment, which are logically distinct, and coalescing both to create a system that adjusts fluctuations. We model chemical reactions by considering the computation as the chemical reaction and the execution environment as the degree of aggregation of molecules that interact with the reactive environment. This results in a chemical reaction that progresses while repeatedly clustering and de-clustering, where concentration no longer holds significant meaning. Open computing is segmented into Token computing, which focuses on the individual behavior of chemical molecules, and Type computing, which focuses on normative behavior. Ultimately, both are constructed as an interplay between the two. In this system, Token computing demonstrates self-organizing critical phenomena, while Type computing exhibits quantum logic. Through their interplay, the recruitment of fluctuations is realized, giving rise to interactions between quantum logical subspaces corresponding to quantum coherence across different Hilbert spaces. As a result, spike waves are formed, enabling signal transmission. This occurrence may be termed quantum-like coherence, implying the source of enzymes responsible for controlling spike waves and biochemical rhythms.