Learnable Classes of Categorial GrammarsMakoto Kanazawa
This book investigates learnability of various classes of classical categorial grammars within the Gold paradigm of identification in the limit from positive data. Two types of learning, learning from structures and learning from flat strings, are considered. The class of kvalued grammars, for k = 1,2,3,…, is shown to be learnable both from structures and from strings, while the class of leastvalued grammars and the class of leastcardinality 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 functorargument structures.
Makoto Kanazawa is Associate Professor in the Department of Cognitive and Information Sciences, Chiba University.
 Preface
 1 Introduction
 2 Learnability Theory
 2.1 Basic Definitions
 2.2 Structural Conditions and (Un)learnability
 2.3 Constraints on Learning Functions
 2.4 Representative Results
 3 A Theorem on Finite Elasticity
 4 Classical Categorical Grammar
 4.1 Basic Definitions
 4.2 Basic Facts about Classical Categorial Grammars
 4.3 Substitutions and Standardizations
 5 Basic Theory of Rigid Grammar
 5.1 Rigid and kValued Grammars
 5.2 Characteristics Samples for Rigid Grammars
 5.3 The Lattice of Rigid Grammars
 5.4 The Rigid Structure Languages
 6 Learning from Structure I: Rigid, kValued, and LeastValued Grammars
 6.1 Rigid Grammas
 6.2 kValued Grammars
 6.3 LeastValued Grammars
 7 Learnign from Structures II: Subclasses of the Optimatl Grammars
 7.1 Optimal Grammars
 7.2 Least Cardinality Grammars
 7.3 Minmal Grammars
 7.4 Summary on Learning from Structures
 8 Learning from Strings
 8.1 kValued Grammars
 8.2 Other Classes
 9 Variations
 9.1 General Combinatory Grammars
 9.2 Montague Grammars
 10 Conclusion
 A Implementations in Prolog
 Bibliography
 List of Notation
 Name Index
 Subject Index
3/1/98
ISBN (Paperback): 1575860961 (9781575860961)
ISBN (Cloth): 157586097X (9781575860978)
ISBN (Electronic): 1575869969 (9781575869964)
Subject: Linguistics; Categorical Grammar; Learning Ability

Distributed by the University of Chicago Press
