This book investigates the learnability of various classes of classical categorial grammars within the Gold paradigm of identification in the limit from positive data. Learning from structure and learning from flat strings are considered. The class of k-valued grammars, for k = 1,2,3,., is shown to be learnable both from structures and from strings, while the class of least-valued grammars and the class of least-cardinality grammars are shown to be learnable from structures. In proving these learnable results, crucial use is made of a theorem on the concept known as finite elasticity. The learning algorithms used in this work build on Buszkowski and Penn's algorithm for finding categorial grammars from input consisting of functor-argument structures.
1. Introduction; 2. Learnability theorem; 3. A theorem of finite elasticity; 4. Classical categorial grammar; 5. Basic theory of rigid grammars; 6. Learning from structures I: rigid, k-valued, and least-valued grammar; 7. Learning from structures II: Subclasses of the optimal grammars; 8. Learning from strings; 9. Variations; 10. Conclusions; Appendix.
"The book does an excellent job of summarizing previous work and preparing the reader for the main results. The text is clean, the presentation clear and rigorous, and the comprehensive list of references will be helpful to anyone wishing to pursue some of the interesting open questions raised in this monograph." R. Roos, Computing Reviews
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