5.4.1 Anomalous Learning
A learner \(\mathbf{Ex}^*\)-identifies a language \(L\) if it \(\mathbf{Ex}\)-converges to an index \(e\) such that \(W_e\) differs from \(L\) on at most finitely many strings. That is, the final hypothesis may contain finitely many errors, finitely many strings incorrectly included or excluded.
Anomalous learning relaxes \(\mathbf{Ex}\) by removing the requirement of exact correctness, replacing it with correctness up to a finite set. In graph terms, this is a restricts edge from \(\textsf{\small anomalous\_ learning}\) to \(\textsf{\small ex\_ learning}\): the constraint (zero anomalies) is removed, and no new grammatical structure is introduced. The class of \(\mathbf{Ex}^*\)-identifiable families strictly contains the class of \(\mathbf{Ex}\)-identifiable families [ .