ora-0042
2.4 The ORACLE–UOCL enrichment square
The distinction between modeling and acting can be expressed as
\[ \begin{aligned} \text{interaction}& \longrightarrow \text{categorical prediction} \longrightarrow \text{categorical realization}\\ & \longrightarrow \text{online categorical learning} \longrightarrow \text{universal online decision}. \end{aligned} \]
ORACLE governs the semantic identification problem. UOCL supplies effective or explicitly realized hypothesis selection, active probing, and repair. From UOCL there are two independent enrichments. Tangent UOCL learns admissible infinitesimal variation. UODL adds information, action, consequence, and consistency maps to which left- and right-Kan constructions can be applied. Their intersection is tangent UODL:
UOCL realizes ORACLE; neither enrichment is implied by the other. DIAL-ready learning requires both, together with observers that can distinguish the infinitesimal defects on which repair depends. OCO, bandits, decentralized teams, safety, tangent repair, and lifelong transport are therefore target classes and query fragments on which ORACLE can be constrained sufficiently to support decision.