An introduction to mathematical logic and type theory: to truth through proof
An introduction to mathematical logic and type theory: to truth through proof
Basic simple type theory
Learnable classes of categorial grammars
Learnable classes of categorial grammars
Formulas-as-types for a Hierarchy of Sublogics of Intuitionistic Propositional Logic
Proceedings of the International Workshop on Nonclassical Logics and Information Processing
Language Learning from Good Examples
AII '94 Proceedings of the 4th International Workshop on Analogical and Inductive Inference: Algorithmic Learning Theory
ACL '83 Proceedings of the 21st annual meeting on Association for Computational Linguistics
Semantic bootstrapping of type-logical grammar
Journal of Logic, Language and Information
A generative constituent-context model for improved grammar induction
ACL '02 Proceedings of the 40th Annual Meeting on Association for Computational Linguistics
The unsupervised learning of natural language structure
The unsupervised learning of natural language structure
Automated extraction of Tree-Adjoining Grammars from treebanks
Natural Language Engineering
Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151
Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151
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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聽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.