Explanation-based learning & analogy (breadth)

Knowledge-rich learning from *one* example

The methods so far were similarity-based — they need many examples and treat all features alike. Explanation-based learning (EBL) flips that: with strong domain knowledge, it can learn a general concept from a *single* example by *explaining why* that example is an instance, then generalizing the explanation.

EBL takes four inputs:

1. a target concept — the thing to learn (e.g. “cup”);
2. a training example — one instance (a specific red cup);
3. a domain theory — rules that prove the example is an instance (“liftable + holds-liquid → cup”, etc.);
4. an operationality criterion — the form the learned rule must take (use observable, structural features).

Worked example. EBL builds a *proof tree* showing the red cup satisfies “cup,” then generalizes the proof by replacing instance constants with variables. Crucially, the proof never used the cup’s *color*, so the generalized rule — “small, has-a-handle, concave-up bowl → cup” — correctly drops color. The domain theory tells EBL which features are causally relevant; similarity-based learning would need many examples to discover that color is irrelevant.

The catch (very examinable). EBL is speed-up learning, not new knowledge: every rule it produces was already in the *deductive closure* of the domain theory — the theory could have derived it without any example. The example just steers the prover to a useful, *operational* rule so you do not re-derive the proof each time. So EBL reformulates known knowledge for speed; it cannot discover facts the theory could not already entail.

Analogy — structure mapping (Gentner 1983)

Reasoning by analogy maps the *relational structure* of a known source onto an unfamiliar target. Structure-mapping theory says good analogies (1) drop surface attributes, (2) carry relations across, and (3) prefer higher-order relations — the systematicity principle. The atom-as-solar-system analogy is deep because it transfers a whole causal system (*more-massive → attracts → revolves-around*), not superficial likeness (“sunflowers look like the sun” transfers only a unary property).