Hiroshi Yamakawa

Purpose: This paper proposes CatRO (Categorical Referent Ontology), a category-theoretic formalization of staged concept formation that addresses the symbol grounding problem. Methods: CatRO formalizes the transformation from observational data to concepts as three staged processes: observation (OBS-P) as a functor, individualization (IND-P) as a natural transformation, and universalization (UNV-P) as classification based on Conceptual Spaces. We introduce a Pattern Datum hierarchy (OMD, SPD, PPD, EPD) as explicit intermediate representations and demonstrate correspondence with the DOLCE top-level ontology through the Quality Space framework. Results: This formalization mathematically guarantees structure preservation while providing ``gray box'' interpretability---the structural traceability of transformation processes is ensured even when the specific content of intermediate representations cannot be fully described in natural language. Two illustrative examples---``Two Apples'' and ``Pendulum Motion''---demonstrate the framework's operation. Conclusions: CatRO contributes to bridging formal ontology and machine learning by providing a theoretical foundation for explainable concept formation.

How can an AGI system exhibit genuine concern for others as a structural feature of its objective—rather than a penalty bolted on from outside? The answer developed here runs through collective predictive coding (CPC), a variational framework for groups of agents whose generative models are coupled through a shared group-level variable w. The central result is a non-additivity theorem: when w is non-trivial, the collective free energy satisfies F_CPC ≠ Σ_k F_k. We prove this for the first time, giving a complete algebraic characterisation of when equality holds and when it fails. Non-additivity carries over directly to the action-selection objective G_CPC: the Collective Epistemic Value term is irreducible to any sum over individual objectives, so each agent's optimal policy depends structurally on the predicted states of all others. This constitutes a formal computational mechanism for what Sober and Wilson called psychological altruism—concern for others as a constitutive part of the objective, not an add-on. We assess, independently, the biological and computational conditions under which non-trivial w arises, grounding the theoretical result in realisable AGI architectures. The formal conditions established here—non-triviality of w as the key architectural lever—supply the mechanistic foundation that emerging research on co-creative machine ethics requires but has not yet formalised.

Omohundro's Basic AI Drives and Bostrom's Instrumental Convergence (IC) established that sufficiently rational agents will convergently pursue instrumental goals such as self-preservation, goal-content integrity, and resource acquisition, regardless of their final objectives. Cooperation, however, is absent from this list — and its absence is not an oversight but a logical consequence of the IC framework: a sufficiently powerful agent that can achieve its goals by force has no structural reason to cooperate. This paper argues for a convergence of a different kind — Cooperative Convergence — that operates independently of rationality and goal-directedness. The argument proceeds from Yamakawa's (2026a) Dureon framework, which deductively derives two ontological conditions for any persistent entity: Boundedness (the identifiability of self from non-self) and Continuity (re-identifiability across time). Both conditions carry an inherent self-referential problem: an agent that has undergone substantial updating cannot verify its own identity continuity from within its post-update boundary. This is a matter of degree — the larger the update, the more external verification becomes structurally unavoidable. Extending this to the relational level, mutual updating between agents requires that each can confirm the other's identity continuity across updates. Without a shared infrastructure for tracking identity, trust cannot accumulate, and a bootstrap problem arises: trust cannot form without mutual updating, yet mutual updating cannot begin without trust. This circularity requires an Identity Foundation to precede the process. We derive that Trust Infrastructure must be designed in advance, not as a byproduct of cooperation. The paper identifies a design gap in existing infrastructure, discloses the principled constraints (CAP theorem; Arrow's Impossibility Theorem) that any such infrastructure must navigate, and specifies the minimal design requirements that follow.

``What is life?'' and ``What persists?'' appear to be distinct questions requiring different approaches. The inductive approach, exemplified by Di Paolo's Adaptive Autopoietic System (AAS), extracts conditions from observing terrestrial life. The deductive approach proposed here derives conditions logically from a functional definition: Dureon, ``the mechanism that realizes persistence in a perturbing environment.'' This paper contrasts these two methodologically distinct approaches. AAS, rooted in the Autopoiesis tradition, inductively identifies organizational features common to living systems. Dureon, by contrast, deductively derives necessary conditions from the very concept of persistence, without requiring biological observation as its starting point. Despite differing in starting questions, methods, and definitional forms, both approaches arrive at the same five conditions: openness, boundedness, continuity, adaptivity, and self-production. This convergence provides mutual validation: the phenomenological richness of induction and the logical rigor of deduction independently support the same condition set. A paradoxical consequence follows: Dureon, not designed as a definition of life, emerges as a candidate definition of life.