ifc-0020

1.2 Four routes into a domain

Four acquisition routes should be distinguished. The first three supply new evidence directly; the fourth reuses a theory acquired elsewhere and therefore enters the acquisition map through \(\mathfrak R_{\mathrm{prior}}\).

Explicit instruction.: A teacher directly names objects, relations, rules, goals, or invariants. The learner receives part of the declaration in symbolic or linguistic form: a racket strikes a ball; a legal serve begins behind the baseline; quantity is preserved when liquid is poured without loss.
Imitation.: The learner observes one or more competent performances and reconstructs a task theory from their regularities. It must infer which entities play stable roles, which actions compose, and which apparent details are incidental.
Apprenticeship.: The learner acts in the task while a teacher selects examples, redirects attention, corrects actions, supplies explanations, and introduces counterexamples. The evidence is interactive and depends on the learner’s current theory.
Theory transport.: The learner imports a typed construction from an earlier domain through an analogy, ontology alignment, or explicit theory map. The imported structure is provisional: its source types, preserved relations, and unsupported target-side assumptions must remain visible.

The distinction between imitation and apprenticeship is structural, not merely terminological. Under imitation, the evidence can be represented as a fixed family of expert traces

\[ \mathcal D=\{ \tau _1^E,\ldots ,\tau _n^E\} . \]

Under apprenticeship, the teacher observes a learner trace \(\tau _t^L\) and returns a context-sensitive intervention

\[ f_t =\operatorname {Coach}(\tau _t^L,\widehat{\mathfrak R}_t), \]

which may correct an action, identify a missing precondition, contrast two cases, or amend the learner’s explanation. The next evidence therefore depends on the current learner. Apprenticeship is a closed-loop acquisition process.

Imitation reconstructs a task sketch from observed expert traces. Apprenticeship adds an adaptive teacher who diagnoses the learner’s own attempts and supplies corrections, contrasts, and explanations. The resulting sketch is an auditable starting theory for later assimilation… — Figure 1.1 Imitation reconstructs a task sketch from observed expert traces. Apprenticeship adds an adaptive teacher who diagnoses the learner’s own attempts and supplies corrections, contrasts, and explanations. The resulting sketch is an auditable starting theory for later assimilation and accommodation.

Modern literature sometimes uses apprenticeship learning for learning from demonstrations, including inverse reinforcement learning [ Abbeel and Ng , 2004 ] . This book uses the narrower distinction above because teacher feedback changes the acquisition problem. Passive traces reveal what an expert did; coaching can reveal why an action was chosen, which latent error the learner made, and what it should attend to next.