1.5 What must be acquired from a demonstration?

A demonstration is not merely a sequence of states and actions. For sketch acquisition, it supplies evidence about several interacting layers:

1. Ontology: persistent objects, agents, tools, locations, and materials.

2. Typing: which actions accept which objects and which outcomes they produce.

3. Affordances: what an object makes possible in the current task.

4. Preconditions and effects: when an action is applicable and what changes after it is executed.

5. Composition: which actions form meaningful subroutines and in what order.

6. Invariants: what the expert preserves while other quantities vary.

7. Objectives: which terminal states or maintained conditions count as success.

8. Recovery structure: how the expert recognizes and repairs a failed attempt.

Consider learning tennis. Watching matches can reveal that players alternate striking a ball across a net, that serves begin points, that court regions matter, and that certain action sequences recur. It may not reveal the subtle mechanics of a grip, weight transfer, toss location, or recovery step. A coach can intervene directly: rotate the grip, move behind the baseline, keep the eye on the ball, recover toward an appropriate court position. Such feedback identifies latent variables and localizes errors that are weakly observable from expert performance alone.

The learner should therefore infer not only a policy \(\pi (a\mid s)\), but a compact inventory for a typed task sketch,

where \(O\) contains object types, \(A\) admissible actions, \(E\) their effects, \(R\) compositional relations and invariants, and \(Q\) observers for quality, legality, and failure. This tuple is a mnemonic for the generators and constraints of a presentation, not an alternative formal definition of a sketch. Policies are models or controllers defined relative to this theory. They are not substitutes for it.