Learning trees from strings: a strong learning algorithm for some context-free grammars

Standard models of language learning are concerned with weak learning: the learner, receiving as input only information about the strings in the language, must learn to generalise and to generate the correct, potentially infinite, set of strings generated by some target grammar. Here we define the corresponding notion of strong learning: the learner, again only receiving strings as input, must learn a grammar that generates the correct set of structures or parse trees. We formalise this using a modification of Gold’s identification in the limit model, requiring convergence to a grammar that is isomorphic to the target grammar. We take as our starting point a simple learning algorithm for substitutable context-free languages, based on principles of distributional learning, and modify it so that it will converge to a canonical grammar for each language. We prove a corresponding strong learning result for a subclass of context-free grammars.