Mind-Internal Computational System

• Mind-Internal Computational Systems are rigorously formalizable architectures that implement cognitive functions via modular, layered structures and nested-stack memory models.
• They employ finite-state control and hierarchical memory to capture complex abilities like language parsing, planning, and meta-cognition with measurable computational constraints.
• Applications span neuroscience and AI, where designs leveraging self-modeling, second-order perception, and meta-level planning advance our understanding of natural and synthetic minds.

A mind-internal computational system is a rigorously formalizable architecture that instantiates the information-processing substrate of a mind, whether biological or artificial. It encompasses the abstract modules, mathematical operations, representational formats, control flows, and learning dynamics underlying cognition, self-modeling, memory, and behavior. Recent theoretical and empirical work across neuroscience, artificial intelligence, and formal logic reveals that minds can be captured by layered, modular computational architectures embedding both domain-specific and meta-cognitive competencies. The sections below detail prominent abstractions and experimental realizations of such systems, with an emphasis on formal structure, computational constraints, and measurable consequences.

1. Foundational Formalisms and Model Classes

At the intersection of computational neuroscience and mathematical logic, the human mind’s computational core can be formalized as a finite-state control system augmented by a nested-stack (indexed grammar) memory structure. This model captures the “all-and-only” cognitive abilities observed in humans—namely, hierarchical language parsing, extended working memory, and complex planning—not achievable by systems limited to context-free memory, yet strictly below the Turing machine model in power. The canonical formal model is a tuple

$$\mathbb{M}_\text{mind} = (Q, \Sigma, \Gamma, \delta, q_0, F)$$

with $Q$ (control states), $\Sigma$ (input alphabet), $\Gamma$ (stack alphabet), and a hierarchical stack transition function. The memory subsystem allows $k$-th order stacks, with operations $\text{push}_k(x), \text{pop}_k(), \text{top}_k()$, providing combinatorially rich but anatomically constrained storage. Empirical and neuroanatomical data restrict human cognition, in effect, to “indexed” automata—the precise class of nested-stack automata—precluding Turing completeness for unaided mental computation (Granger, 2020).

In broader computational and philosophical treatments, a mind-internal computational system may be cast as any causal network of modules that together realize (i) representation of the external world, (ii) prediction and simulation, and (iii) explicit or implicit meta-modeling of the system’s own internal states and processes. For artificial systems, this includes neural, symbolic, or hybrid architectures with explicit planning, self-monitoring, memory, and belief-updating subroutines (Adami, 2017, Fitz, 30 Nov 2025).

2. Modular Architectures and Layered Processing

Contemporary frameworks universally emphasize modular decomposition and layered processing as critical motifs. In biological systems, cognition is organized in parallel and hierarchical sensory–motor streams, each with generative–inverse model pairs learned at multiple abstraction levels (Kawato et al., 2021). Meta-cognitive executive modules—such as the cognitive reality monitoring network (CRMN) in prefrontal cortex—compute responsibility signals, orchestrating attention, gating learning, and enabling explicit monitoring.

In machine systems, this modularization is formalized in structured agentic flows (Kim, 22 Jul 2025) and cognitive architectures such as MIDCA (Cox et al., 2022), which delineate tightly interleaved cycles of object-level (perception, planning, action) and meta-level (monitoring, discrepancy detection, self-modification) modules, all operating on well-defined declarative state records and transition functions. The cascading, message-passing structure is mirrored in models of consciousness that emphasize the integration and transmission of discrete informational packets across abstraction, self-evaluation, narrative and theory-of-mind modules (Gillon, 2 Oct 2025).

Table: Example Modular Decomposition (selection of models)

Architecture	Modules/Subsystems	Key Formalism
Modular Consciousness Theory	Filtering, Abstraction, Narration, Evaluation…	Discrete IIS, density-vector tagging
MIDCA (Metacognitive Agent)	Perceive, Interpret, Plan, Act, Monitor, Learn	Declarative state/action tuples, traces
Agentic Flow	Retrieval, Cognition, Control, Action, Memory	Recurrent control loop, formal update eqs.

3. Second-Order Perception, Reflexivity, and Self-Modeling

A distinguishing property of advanced mind-internal computational systems is the implementation of second-order perception: the capacity not only to represent the world but to represent, track, and integrate the system’s own representations and decision processes (Fitz, 30 Nov 2025). This reflexivity is structurally realized through explicit self-models (e.g., data-base entries encoding “having an impression of mind” (Adami, 2017)), meta-level planning traces (Cox et al., 2022), and responsibility/entropy signals reflecting the internal status and coherence of modular subcomponents (Kawato et al., 2021, Gillon, 2 Oct 2025).

Layers of agents in distributed systems communicate compressed self-predictions in a constrained channel, iteratively adjusting internal codes so that a coherent, collective self-model emerges (Fitz, 30 Nov 2025). In symbolic systems, the “Self-Watcher” explicitly records and reports on inferences drawn by the inference engine, introducing self-referential data structures (Adami, 2017).

The formal content of consciousness and self-modeling is further operationalized through communicative alignment (measured by mutual information, integration, and topological invariants) in distributed neural-agent substrates (Fitz, 30 Nov 2025), and through entropy of modular responsibility allocation in meta-cognitive control networks (Kawato et al., 2021).

4. Learning, Memory, and Information Compression

Learning is universally cast as either incremental adaptation or compositional synthesis, systematically pushing the system towards more parsimonious representations of sensory history or action repertoires. Models such as the “growing circuits” paradigm explicitly encode each concept as a lambda expression composed of earlier, simpler nodes, with new circuits added only when repeated experience yields compositional compression over existing nodes—a process guided by upper bounds on Kolmogorov complexity (Panigrahy et al., 2012).

Within neural network perspectives, learning equates to the solution of coupled, nonlinear equations via trial-and-error adaptation, governed by implicit or explicit cost functions minimized by gradient-like rules (Schad, 2019). Biologically, this yields a continuous adaptation landscape where “unconscious” computation reflects transient, non-converged solution searching; the “conscious” state emerges only when the system dynamics converge to an attractor with outputs above awareness thresholds.

In modular and meta-cognitive frameworks, learning applies both at the base-level (tuning perception and action) and at the meta-level (altering strategies, operator models, or memory structures based on detected performance discrepancies (Cox et al., 2022)). Memory systems range from nested stack architectures for symbolic working memory (Granger, 2020) to distributed, persistently updated log structures in agentic flows (Kim, 22 Jul 2025).

5. Theory-of-Mind, Representation of Others, and Decision Modeling

Sophisticated mind-internal computational systems explicitly represent and reason about the mental states (beliefs, intentions, goals) of other agents, whether human or synthetic. This capacity is formalized in several recent frameworks:

• The cognitive event calculus (CEC) introduces high-expressivity quantified modal logic with sorts for agent, time, events, fluents, and modal operators for perception, knowledge, belief, desire, and intention, enabling a CAIS to track and correct false or missing beliefs in human users, with strong formal guarantees of knowledge alignment (Peveler et al., 2017).
• Deep interpretable models of theory-of-mind modularize latent belief, intent, and action plans, enforce human-interpretable concept representations via whitening transformations, and achieve both predictive accuracy and explanatory transparency (Oguntola et al., 2021).
• Computable game-theoretic frameworks encode each agent’s beliefs over others’ reasoning levels using hierarchical Poisson-Gamma structures, realizing bounded rationality through best-response operators, and maintaining tractable recursive belief updating via conjugate closed-form updates and QMDP approximations (Zhu et al., 27 Nov 2025).

These models provide an explicit computational machinery for recursive, multi-agent “thinking about thinking,” scalable to tractable inference through statistical approximation and modularity.

6. Subjectivity, Consciousness, and Functional Metrics

Subjectivity and consciousness are treated as measurable, emergent properties of information integration, coherence, and reflexivity within internal computational systems. In Modular Consciousness Theory, each cycle produces an Integrated Informational State (IIS), a discrete packet of fused module outputs tagged with a multidimensional density vector $\boldsymbol{\rho}$ capturing logical coherence, affective salience, autobiographical anchoring, and temporal continuity (Gillon, 2 Oct 2025). The norm $\|\boldsymbol{\rho}\|$ directly quantifies the subjective intensity and is used to prioritize memory consolidation, action selection, and physiological readiness.

Consciousness is further operationalized as arising at the collective phase transition point when internal communication induces a globally coherent, reflexive self-model, measurable by information integration ($\Phi$), mutual synchrony, and topological metrics such as Betti numbers (Fitz, 30 Nov 2025). In meta-cognitive networks, the entropy of responsibility signals $H$ densely tracks the degree of conscious awareness—with lower $H$ indicating focused, high-coherence “conscious” states, and higher $H$ reflecting diffuse or absent consciousness (Kawato et al., 2021).

7. Categorical, Logical, and Quantum Extensions

Recent theoretical advances leverage categorical logic and algebraic frameworks to provide a general unifying substrate for describing mind-internal computation. The CES-IMU-HSG framework anchors computation in a minimal axiom (Cogito, ergo sum) implemented categorically via three-axis hierarchical state grids, with both human and machine cognition described as temporal compositions of “inter-universal algorithms” over categorical fibers linking neural, endocrine, genetic, and computational substrates (Itoh, 15 Oct 2025).

Quantum perspectives propose representing internal mental logic as extensive Boolean formulae (derived from EEG/MEG) evaluated by quantum circuits to overcome classical intractability, metaphorically linking massive neural parallelism to quantum superposition (Miranda, 2020). In all cases, the architectural goal is a scalable, extensible, and self-grounded internal computational logic that bridges formal ontologies, machine implementation, and subjective experience.

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Taken together, these frameworks and empirical models assert that mind-internal computational systems are best characterized as multi-layered, modular, reflexive, and meta-cognitively competent architectures. They blend automata-theoretic constraints, communication-driven integration, theory-of-mind capability, and category-theoretic extensibility, offering both a rigorous descriptive language and direct avenues for experimental instantiation and measurement in natural and artificial minds (Granger, 2020, Fitz, 30 Nov 2025, Gillon, 2 Oct 2025, Itoh, 15 Oct 2025, Kim, 22 Jul 2025, Adami, 2017, Kawato et al., 2021, Schad, 2019, Oguntola et al., 2021, Zhu et al., 27 Nov 2025).