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5.3 Constraints on the use of information 99 5.4 Constraint on convergence 100 5.5 Constraints on the relation between conjectures 107 5.6 Strategies for function identification 115 5.7 Bibliographic notes 120 5.8 Exercises 122 6 Criteria of Learning 127 6.1 Criteria for function identification 127 6.2 Criteria of language identification 138 6.3 Bibliographic notes 144 6.4 Exercises 145 7 Inference of Approximations 151 7.1 Approximations 151 7.2 Some background 152 7.3 Approximate explanatory identification 154 7.4 Uniform approximate explanatory identification 158 7.5 Bibliographic notes 163 7.6 Exercises 163 8 Environments 167 8.1 Inaccurate data 168 8.2 Texts with additional structure 180 8.3 Multiple texts 184 8.4 Bibliographic notes 189 8.5 Exercises 189 III Part III: Additional Topics 195 9 Team and Probabilistic Learning 197 9.1 Introduction 197 9.2 Motivation for identification by teams 197 9.3 Team identification of functions 199 9.4 Identification by probabilistic scientists 201 9.5 212 9.6 Team and probabilistic identification of languages 213 9.7 Bibliographic notes 219 9.8 Exercises 219 10 Learning with Additional Information 221 10.1 Introduction 221 10.2 Upper bound on the size of hypothesis 222 10.3 Approximate hypotheses as additional information 235 10.4 Bibliographic notes 244 10.5 Exercises 245