# Grammar Induction by Unification of Type-logical Lexicons

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DOI: 10.1007/s10849-009-9108-7

- Cite this article as:
- Fulop, S.A. J of Log Lang and Inf (2010) 19: 353. doi:10.1007/s10849-009-9108-7

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## Abstract

A method is described for inducing a type-logical grammar from a sample of bare sentence trees which are annotated by lambda terms, called *term-labelled trees*. Any type logic from a permitted class of multimodal logics may be specified for use with the procedure, which induces the lexicon of the grammar including the grammatical categories. A first stage of *semantic bootstrapping* is performed, which induces a general form lexicon from the sample of term-labelled trees using Fulop’s (J Log Lang Inf 14(1):49–86, 2005) procedure. Next we present a two-stage procedure for performing *distributional learning* by unifying the lexical types that are initially discovered. The first *structural unification* algorithm in essence unifies the initial family of sets of types so that the resulting grammar will generate all term-labelled trees that follow the usage patterns evident from the learning sample. Further altering the lexical categories to generate a recursively extended language can be accomplished by a second unification. The combined unification algorithm is shown to yield a new type-logical lexicon that extends the learning sample to a possibly infinite (and possibly context-sensitive) language in a principled fashion. Finally, the complete learning strategy is analyzed from the perspective of algorithmic learning theory; the range of the procedure is shown to be a class of term-labelled tree languages which is *finitely learnable from good examples* (Lange et al in Algorithmic learning theory, Vol 872 of lecture notes in artificial intelligence, Springer, Berlin, pp 423–437), and so is identifiable in the limit as a corollary.