lin-0264

22.3 Adaptive sites and learned covers

Localization is always relative to a cover. In SID the cover contains foundry contexts and overlaps; in LINCS-Toulmin it contains sources, argument roles, and reasoning steps; in DLINCS it may contain layers, branches, retrieval blocks, or agent subgraphs. A fixed cover can omit exactly the interaction that creates the global obstruction.

An adaptive system should therefore be able to:

  1. detect that the current cover is incomplete;

  2. propose a refinement or enlargement;

  3. transport existing local witnesses to the new cover;

  4. test whether newly visible overlaps explain the global failure; and

  5. retain an audit trail connecting the two localization regimes.

Let \(\mathcal U\preceq \mathcal U'\) denote a refinement. A local obstruction family \(o_{\mathcal U}\) should restrict or transport naturally along refinement, while new intersections in \(\mathcal U'\) can reveal higher-order incompatibilities. The comparison

\[ o_{\mathcal U} \longrightarrow \operatorname {Res}_{\mathcal U}^{\mathcal U'}(o_{\mathcal U'}) \]

tests whether the old diagnosis is recovered inside the richer one.

Design principle

Cover selection should optimize information gained about unresolved obstructions, not simply minimize the measured obstruction on the chosen cover.

The statistical problem resembles active experimental design. A proposed context or overlap has a cost, an expected diagnostic value, and a risk of selection bias. Adaptive covers therefore need uncertainty-aware stopping rules and explicit “coverage not established” outcomes.