Source: Garcez, A.d'A. & Lamb, L.C. (2023). "Neurosymbolic AI: the 3rd wave." Artificial Intelligence Review, 56:12387–12406. DOI: 10.1007/s10462-023-10448-w

The "3rd wave" framing positions neurosymbolic AI as the successor to symbolic AI (1st wave) and statistical/neural AI (2nd wave). The key challenge identified: trust, safety, interpretability, and accountability. The paper focuses on principled integration of learning with reasoning — but treats neural and symbolic as two components to be integrated, not as two of potentially more mechanisms of model creation. No concept equivalent to Constitution-as-mechanism appears. No concept equivalent to Accretion appears.

Source: Marcus, G. (2020). "The Next Decade in AI: Four Steps Towards Robust Artificial Intelligence." arXiv:2002.06177.

Marcus's core argument: general-purpose learning with ever-larger training sets and compute is insufficient. The alternative: hybrid architecture centered around cognitive models with rich prior knowledge and sophisticated reasoning. The phrase "rich prior knowledge" is the closest the NeSy tradition comes to naming Constitution's input — but Marcus treats prior knowledge as something to be integrated into a learning system, not as the output of a distinct mechanism. The question "how does rich prior knowledge come into existence?" is not asked.

Source: Kautz, H. (2022). "The Third AI Summer: AAAI Robert S. Engelmore Memorial Lecture." AI Magazine, 43(1):105–125. DOI: 10.1002/aaai.12036

Six types in increasing integration depth: Type 1 (Symbolic→Neuro: symbol-to-vector conversion); Type 2 (Symbolic[Neuro]: symbolic solver with neural subroutines — e.g., AlphaGo's MCTS + neural position evaluation); Type 3 (Neuro;Symbolic: pipeline, systems refine each other iteratively); Type 4 (Neuro:Symbolic→Neuro: symbolic knowledge compiled into neural architecture); Type 5 (NeuroSymbolic: logic tensorized, neural methods perform reasoning); Type 6 (Neuro[Symbolic]: neural model internally performs symbolic reasoning — e.g., attention schemas). All six types describe how components interact within a system. None describes how the system's structural constraints come into existence. The taxonomy is about integration topology, not creation mechanism.

Source: Marra, G., Dumančić, S., Manhaeve, R., & De Raedt, L. (2024). "From Statistical Relational to Neurosymbolic Artificial Intelligence: A Survey." Artificial Intelligence, 328.

Seven dimensions: (1) approach to logical inference; (2) syntax of logical theories; (3) logical semantics and learning extensions; (4) scope of learning (parameter vs. structure); (5) symbolic vs. subsymbolic representations; (6) degree of paradigm capture; (7) classes of learning tasks. Dimension (4) — "parameter vs. structure learning" — is closest to the mechanism question, but it asks "what does the system learn?" not "how does the system's foundational structure come into existence?" Structure learning in StarAI/NeSy discovers relational patterns in data; it does not constitute what can exist.

Source: Hitzler, P. & Sarker, M.K. (eds.) (2021). Neuro-Symbolic Artificial Intelligence: The State of the Art. IOS Press (Frontiers in Artificial Intelligence and Applications, 342).

The volume categorizes NeSy work into knowledge representation approaches, logic-based methods, neural theorem proving, concept learning, and applications. The "neuro" refers to artificial neural networks prominent in machine learning; "symbolic" refers to algorithmic processing at the level of meaningful symbols prominent in knowledge representation. The organizing question throughout is how to combine these two traditions — not when does each mechanism apply or what does each mechanism uniquely produce.

Source: Gruber, T.R. (1993). "A Translation Approach to Portable Ontology Specifications." Knowledge Acquisition, 5(2):199–220. 21,000+ citations per Google Scholar.

"Explicit" means the types of concepts used and the constraints on their use are explicitly defined. "Conceptualization" refers to an abstract model of relevant concepts and relationships. The definition implies an authorial act of specification — someone decides what concepts exist and how they relate. This is exactly the mechanism the three-mechanisms taxonomy calls Constitution: deliberate structural specification that defines what can meaningfully exist. But Gruber framed this as knowledge representation, not as a mechanism co-equal with learning.

Source: Guarino, N. (1998). "Formal Ontology and Information Systems." Proceedings of FOIS-98, Trento, Italy. IOS Press.

Guarino distinguished between ontological commitments (what a language can express) and knowledge base content (what is actually asserted). An ontological commitment for a language L is defined in terms of a pair K = <C, ℑ> where L commits to C by means of K. This is the constitutive/regulative distinction: ontological commitments constitute the space of meaningful assertions; knowledge base content populates that space. The formal ontology tradition has been performing Constitution for three decades — it just calls it "ontology engineering" rather than recognizing it as a mechanism of model creation co-equal with training.

Source: Convergent analysis of F6 (Gruber 1993) and F7 (Guarino 1998)

The novelty of the three-mechanisms taxonomy is not the practice of Constitution (ontology engineering has done this for 30 years) but the recognition of it as a mechanism — a distinct mode by which models come into existence, with different temporal character, structural guarantees, and ingredient coverage than training. The NeSy field calls this "the symbolic component." The ontology field calls it "knowledge representation." Neither names it as a mechanism of model creation.

Source: Theoretical argument grounded in the properties of loss-function optimization (log-loss, cross-entropy); consistent with the established literature on uncertainty types

In a trained model, a state assigned probability 0.001 could mean "this happens very rarely" or "this is structurally impossible but the model doesn't know that." The loss landscape does not distinguish these cases. A model trained on financial data might assign low probability to both "a $10B transaction from a small nonprofit" (rare but possible in edge cases) and "a transaction with negative time duration" (structurally impossible). The model treats both as low-probability tails. This conflation is intrinsic to the training mechanism — it is not a limitation of current models but a property of what training is.

Source: Helmholtz UQ Dictionary; Hüllermeier & Waegeman (2021). "Aleatoric and Epistemic Uncertainty in Machine Learning." Machine Learning (Springer); Der Kiureghian & Ditlevsen (2009). "Aleatory or Epistemic? Does it Matter?" Structural Safety.

Epistemic uncertainty: reducible through more data (we don't know, but could). Aleatoric uncertainty: irreducible randomness in the process itself (inherent variability). The literature occasionally mentions a third category — "ontological uncertainty" (Helmholtz UQ Dictionary) — resulting from inappropriate methodology or belief systems. But this is framed as a deficiency of the modeler, not as a structural property of the domain. What the rarity/prohibition argument identifies is different: there are constraints on what can exist in a domain, and these constraints are not learnable from data because they manifest as absence, not as signal. We propose the term "constitutional uncertainty" for this third type: uncertainty about whether a low-probability observation represents rarity or prohibition. This uncertainty is resolvable — but only by specification (Constitution), not by observation (Training).

Source: Hassana Labs (2026). Why World Models Alone Can't Be AGI. Hassana Labs preprint, 19 pages. The specific mathematical theorems on log-loss and symmetry breaking were published in Chlon (2025a) arXiv:2507.11768 and Chlon (2025b) arXiv:2509.11208, engaged in S11. Chlon is the researcher behind Hassana Labs.

The argument: log-loss optimization is designed to minimize prediction error over training data. This optimization process treats symmetries (invariant properties) as degrees of freedom to be exploited for compression, not as structural properties to be preserved. This report applies the result to governance: a governance system requires certain invariances to hold always (e.g., every decision has exactly one accountable party). Training may approximate this pattern if the training data consistently shows it, but it cannot guarantee it — because the mechanism has no concept of "must hold always" as opposed to "holds in all observed cases." This is the formal version of the rarity/prohibition claim.

Source: Yuenyong, K. (2025). "The Death of Ontology Engineering: Why Machines Have Outgrown Human-Made Frameworks." Medium.

Yuenyong's argument: neural networks identify relationships, hierarchies, and structures directly from datasets without requiring manual specification; LLMs learn concepts, relationships, and constraints implicitly during training; LLMs provide scalability and automation that ontologies cannot match. The argument holds for descriptive knowledge — patterns that exist in data. It fails for constitutive knowledge — structural constraints that define what can exist, which by definition are not present in data as positive examples. An LLM trained on financial data learns that most transactions are positive — but it cannot learn that negative-value transactions are structurally prohibited by accounting rules as opposed to merely unobserved. This is exactly the rarity/prohibition conflation (F9). Yuenyong's argument is the strongest form of the counter-position, and its failure at the constitutive boundary is the strongest evidence for Constitution as a distinct mechanism.

Source: Synthesis of F1–F5 (NeSy tradition) and F6–F8 (ontology tradition)

Kautz's six types (F3) describe how neural and symbolic components interact. But they don't ask where the symbolic component comes from — how it was created, by what process, with what guarantees. Similarly, Garcez & Lamb's "3rd wave" (F1) and Marcus's "hybrid architecture" (F2) treat symbolic knowledge as a given to be integrated, not as the output of a mechanism that needs to be understood on its own terms. The mechanism question reveals three distinct modes:

Training: Episodic optimization over data. Produces pattern recognition (distinctions, temporal regularities, transition probabilities). Cannot produce structural guarantees.

Constitution: Deliberate specification of what can exist. Produces structural constraints, ontological commitments, governance rules. Cannot produce content — defines the container, doesn't fill it.

Accretion: Continuous operational accumulation. Produces domain-specific knowledge within constituted structures. Cannot produce structure — needs Constitution to define what to capture.

Source: Systematic review of F1–F5; absence of concept in Garcez & Lamb 2023, Kautz 2022, Marra et al. 2024, Hitzler & Sarker 2021

The NeSy tradition focuses on system architecture: how to build a system that combines neural and symbolic processing. Accretion is an operational mechanism — the ongoing accumulation of knowledge through the system's use. It is invisible to NeSy because that tradition focuses on system design, not on organizational knowledge lifecycle. The organizational memory literature (Walsh & Ungson 1991, Nonaka & Takeuchi 1995, Argote 2013 — engaged in S3 and S14) has studied Accretion extensively but not named it as a mechanism of model creation. The three-mechanisms taxonomy bridges NeSy (which sees Training and Constitution-as-component) with organizational science (which sees Accretion-as-memory) by recognizing all three as mechanisms in a unified framework.

Source: Synthesis of F3 (Kautz taxonomy), F6–F8 (ontology tradition), F14 (Accretion absence)

Training operates episodically: train, deploy, retrain. Constitution operates rarely: it defines the structural frame and changes only when the frame needs revision (architectural events). Accretion operates continuously: every operational interaction potentially adds to the accumulated knowledge. Kautz's Types 1–6 all describe systems operating at a single temporal scale — the scale of inference/prediction. The three-mechanisms taxonomy operates across temporal scales, which is why no single NeSy integration architecture can capture all three.

Source: Goldfeder, J., Wyder, P., LeCun, Y., & Shwartz-Ziv, R. (2026). "AI Must Embrace Specialization via Superhuman Adaptable Intelligence." arXiv:2602.23643.

SAI is defined as "intelligence that can learn to exceed humans at anything important that we can do, and that can fill in the skill gaps where humans are incapable." The paper systematically dismantles AGI, arguing that human intelligence is fundamentally specialized. The technical approach directs engineering toward self-supervised learning, modular architectures, and predictive world models. The paper's core argument — that AI systems should be composed of specialized modules — validates the claim that world models are composed, not monolithic. But the paper's focus on what to specialize and how to train leaves the coordination question unanswered: how do you govern the interactions between specialized modules? Who decides which module has authority over which domain? How do you prevent conflicting specializations from producing incoherent joint behavior?

Source: MILA World Modeling Workshop 2026; Lambda AI blog wrap-up; workshop program at world-model-mila.github.io

The workshop focused on scalable architectures, representation learning, multimodal integration, and computational foundations for world models. The aim: establish shared vocabulary, identify common challenges, surface synergies. The governance question — how to coordinate multiple world model components under authority, with accountability — was not a workshop theme. This report observes the absence: governance was not among the workshop themes, suggesting the world modeling community treats governance as downstream of architecture, not as an architectural concern.

Source: Helmholtz UQ Dictionary

Ontological uncertainty is defined as resulting from "unconscious utilization of inappropriate methodology or belief systems." This is close to but distinct from constitutional uncertainty: ontological uncertainty is about the modeler's limitations; constitutional uncertainty is about the domain's structural constraints. The distinction matters: ontological uncertainty is resolvable by improving the modeler's methodology; constitutional uncertainty is resolvable only by explicit specification of structural constraints (i.e., Constitution).