1.1 The initialization problem

Let a maintained representational package be

where \(\mathbb S\) is a sketch presentation, \(\mathfrak D\) states which structure its models must preserve, \(\Lambda \) contains observers, \(\mathcal G\) contains admissible generative operations, and \(\mathcal A\) contains admission procedures. The later DIAL machinery assumes that some version of this package is already available. Initial sketch acquisition asks where it came from.

Write the acquisition evidence as

with explicit instructions \(\mathcal I\), expert demonstrations \(\mathcal D\), corrective feedback \(\mathcal F\), and the learner’s own interventions \(\mathcal X\). An acquisition procedure produces

Here \(\widehat{\mathfrak R}_0\) is the provisional package, \(\Gamma _0\) records how its declarations are supported by the evidence, and \(U_0\) records unresolved alternatives and unsupported components. The term \(\widehat D_0\) is a current realization or task state interpreted under the provisional package. It may be assembled from an observed example, an expert trace, or the learner’s present environment. The squiggled arrow is deliberate. Acquisition need not be a unique functor determined by the observations; several sketches, and several realizations of each sketch, may explain the same behavior.

¹1. A useful initial sketch is not necessarily true or complete. It must be explicit enough that later evidence can say where and how it fails. ↩

Within this framework, the formulation rules out two unhelpful extremes. A theory-free learner has no declared invariants against which to recognize a structural failure. A learner supplied with a complete and correct theory has no acquisition problem at all. The scientifically interesting regime lies between them: partial instruction, finite demonstrations, incomplete observers, and a theory that is useful precisely because it remains revisable.