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		CONTENTS

Series Foreword ix Preface xi I Fundamentals of Learning Theory 1 1 Introduction 3 1.1 Empirical inquiry 3 1.2 Paradigms 5 1.3 Some simple paradigms 5 1.4 Discussion of the paradigms 8 2 Formalities 15 3 Identification 27 3.1 Languages as theoretically possible realities 27 3.2 Language identification: Hypotheses, data 31 3.3 Language identification: Scientists 32 3.4 Language identification: Scientific success 35 3.5 Identification as a limiting process 38 3.6 Characterization of identifiable 40 3.7 Some alternative paradigms 44 3.8 Memory-limited scientists 45 3.9 Second paradigm: Identification of functions 48 3.10 Characterization of identifiable 51 3.11 Summary 54 3.12 Exercises 55 4 Identification by Computable Scientists 61 4.1 Preliminaries 61 4.2 Language identification by computable scientist 63 4.3 Function identification by computable scientist 69 4.4 Parameterized scientists 75 4.5 Exact identification 81 4.6 Summary 83 4.7 Exercises 84 II Fundamental Paradigms Generalized 89 5 Strategies for Learning 91 5.1 Strategies for language identification: Introduction 91 5.2 Constraints on potential conjectures 92