ifc-0312

20.1 The argument in one view

The book’s argument can be compressed into the following chain:

\[ \begin{aligned} \text{acquire }\mathfrak R\supset \mathbb S& \longrightarrow \text{realize }D \longrightarrow \text{probe }(A,B) \\ & \longrightarrow \text{localize }\Omega \longrightarrow \text{test }\gamma \\ & \longrightarrow \text{test less-disruptive controls} \\ & \longrightarrow \text{propose }\Upsilon :\mathfrak R\to \mathfrak R^{+} \\ & \longrightarrow \text{transport and test independently} \\ & \longrightarrow \text{admit and persist, or reject and retract.} \end{aligned} \]

The initial representational package \(\mathfrak R\), including its theory \(\mathbb S\), realization semantics, observers, doctrine, proposal language, and admission interface, may be supplied explicitly, learned from demonstration, or acquired through an apprenticeship in which a teacher corrects the learner’s interpretation. A model \(D\) realizes that theory in a particular domain. Assimilative probes \(A\) improve behavior while preserving the current declaration; proto-accommodative probes \(B\) test how the declaration might have to change. Their mixed interaction produces a diagnostic class, schematically

\[ \Omega (a,b) = [\rho _A(a),\rho _B(b)] \pmod{\operatorname {im}\rho _A+\operatorname {im}\rho _B}. \]

A nonzero bracket is not automatically creative. The relevant signal is a persistent quotient obstruction: an interaction that cannot be explained by the already admitted directions and survives the chosen Weil probes, uncertainty model, and negative controls. An integration observer must then test whether the candidate local repair composes into a coherent finite realization. Before a package change is submitted, registered no-change, parameter, stronger in-language, measurement, observer, and domain-specific alternatives must be tested where applicable. Only after those gates does the system submit a comparison \(\Upsilon :\mathfrak R\to \mathfrak R^+\). If the theory presentation changes, \(J:\mathbb S\to \mathbb S^+\) is one component of \(\Upsilon \), not the whole delta. The proposal must preserve what remains valid, support new models or actions, and pass an independent admission test before it is persisted; otherwise it is retracted while its counter-witnesses remain in the audit record.

. Creativity is not identified with surprise. In DIAL, a creative transition is a typed and auditable extension of a maintained representational language, prompted by a persistent compositional obstruction, supported by a coherent finite realization or a counter-witness to one inside the old theory, and retained because the extension is conservative, productive, and reusable.

This view changes the unit of learning. A conventional learner usually returns parameters, predictions, actions, or samples. A DIAL system may return those things, but its distinctive artifact is a change in the language that makes them possible: a latent causal alternative, a new skill constructor, a new state abstraction, a new experiment, or a new visual operation. The extension matters only if subsequent reasoning can use it.

Not every admitted package comparison is therefore a creative theory extension. A change of parameters, observer, inference routine, or enforcement policy may be operationally important while leaving the declared language fixed. ARTISTIC repairs chiefly occupy this category. The stronger representational-language claim requires a registered enlargement of the presentation or generative operations, together with evidence that the added structure is irreducible, productive, transportable, and reusable. DILATE is designed to test that still-open step.