1.3 Explanation-based learning as a precedent

Explanation-based learning (EBL) provides a direct historical precedent for theory-guided sketch acquisition. Rather than estimate a concept from surface correlations across many examples, EBL constructs an explanation of why a particular example satisfies a goal concept under a domain theory. It then generalizes the proof while retaining the dependencies required by the explanation [ Mitchell et al. , 1986 ] .

The classical cup example begins with a functional specification. A cup is an open vessel that is stable and liftable. Domain knowledge connects these functions to observable structure: a suitable cavity can hold liquid, a flat base can support stability, and a graspable part together with manageable weight can support lifting. From one explained example, the learner can derive a recognition rule that ignores features unused by the proof [ Mitchell et al. , 1986 , Mooney and Bennett , 1986 ] .

In sketch language, let \(\mathbb S_{\mathrm{cup}}\) contain types such as

and arrows representing containment, filling, lifting, and support. A particular object \(c\) is admitted as a cup when its observed structure factors through the functional declaration:

The explanatory map \(e_c\) records why the example realizes the concept. Color and logo need not appear in the factorization. They can therefore vary without invalidating the explanation.

. One-example generalization is not induction from a sample of size one. Its force comes from a supplied domain theory and an explanation that identifies which properties are proof-relevant. If the theory is wrong, the generalized concept may be wrong in a systematic and highly confident way.

This is both the strength of EBL and the point at which infinitesimal creativity extends it. Classical EBL primarily operationalizes consequences of a supplied theory. DIAL also permits the theory to become an object of diagnosis and revision. A declaration that every cup must possess a handle, for example, fails on handleless drinking vessels. The repair may replace the specific morphological condition with a more general grasping, holding, or drinking affordance. The counterexample changes not merely a parameter but the explanatory vocabulary.