Learnability of Type-logical Grammars

Abstract

This paper extends previous research on learning procedures for classical categorial grammars and learnability of classes of such grammars. The grammatical framework here is updated to multimodal type-logical grammar, and a previously described learning procedure for these grammars is reviewed. The procedure acts on input samples of strings labeled by their semantic composition terms in the lambda calculus, and is able to learn lexical assignments of sets of categories to the vocabulary items using a broad range of permitted type logics. It is then shown that linguistically valuable subsets of the range of the algorithm are identifiable in the limit from term-labeled string data. The entire range of the algorithm is shown to be not a learnable class. It is informally argued that, given the right type logic, the learnable classes of grammars include members which generate natural languages, and thus that natural languages are learnable in this way.