7.7 Two enrichments of categorical learning

Let \(\mathbb D\) be a decision declaration specifying information objects, actions, consistency maps, consequences, and observers. There is a forgetful passage

that discards the action readout and its consequence semantics. Its essential image consists of UOCL learners whose hypotheses are decision-ready for \(\mathbb D\). The passage is not generally reversible: a predictive category may omit an action object, fail to identify distinctions on which action depends, or support no safe intervention semantics.

Active UOCL probes and UODL actions must also be distinguished. A probe is licensed for its ability to separate hypotheses. A decision is evaluated by its consequences and may endogenously change the later presentation. In special cases one event serves both roles, but then the identification value, decision value, and safety obligation remain separately typed.

Independently, there is a forgetful passage

that discards tangent structure. Neither this functor nor the decision forgetful functor factors through the other in general. Their pullback over \(\mathbf{UOCL}\) is the class of tangent decision learners: the natural home for LINCS comparisons and DIAL repair.

Part IV now specializes UOCL to decision-bearing worlds. Its later tangent sections operate on the intersection just defined. It introduces the principal-past semantics, nerves, homotopy-coherent persistence, and observer comparisons needed before the later OCO, bandit, decentralized, safety, and lifelong instances can be studied.