Logic for Learning: Learning Comprehensible Theories from Structured Data

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Springer Science & Business Media, Aug 6, 2003 - Computers - 256 pages
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This book is concerned with the rich and fruitful interplay between the fields of computational logic and machine learning. The intended audience is senior undergraduates, graduate students, and researchers in either of those fields. For those in computational logic, no previous knowledge of machine learning is assumed and, for those in machine learning, no previous knowledge of computational logic is assumed. The logic used throughout the book is a higher-order one. Higher-order logic is already heavily used in some parts of computer science, for example, theoretical computer science, functional programming, and hardware verifica tion, mainly because of its great expressive power. Similar motivations apply here as well: higher-order functions can have other functions as arguments and this capability can be exploited to provide abstractions for knowledge representation, methods for constructing predicates, and a foundation for logic-based computation. The book should be of interest to researchers in machine learning, espe cially those who study learning methods for structured data. Machine learn ing applications are becoming increasingly concerned with applications for which the individuals that are the subject of learning have complex struc ture. Typical applications include text learning for the World Wide Web and bioinformatics. Traditional methods for such applications usually involve the extraction of features to reduce the problem to one of attribute-value learning.
  

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Contents

Introduction
1
12 Setting the Scene
5
13 Introduction to Learning
10
14 Introduction to Logic
16
Bibliographical Notes
27
Exercises
28
Logic
31
22 Type Substitutions
35
Bibliographical Notes
127
Exercises
128
Predicates
131
42 Standard Predicates
139
43 Regular Predicates
146
44 Predicate Rewrite Systems
151
45 The Implication Preorder
158
46 Efficient Construction of Predicates
163

23 Terms
38
24 Subterms
45
25 Term Substitutions
55
26 AConversion
64
27 Model Theory
72
28 Proof Theory
76
Bibliographical Notes
79
Exercises
80
Individuals
83
32 Normal Terms
89
33 An Equivalence Relation on Normal Terms
93
34 A Total Order on Normal Terms
95
35 Basic Terms
97
36 Metrics on Basic Terms
105
37 Kernels on Basic Terms
115
Bibliographical Notes
175
Exercises
176
Computation
183
52 Definitions of Some Basic Functions
188
53 Programming with Abstractions
193
Bibliographical Notes
203
Learning
207
62 Illustrations
214
Bibliographical Notes
240
Exercises
241
A Appendix
243
References
245
Notation
251
Index
253
Copyright

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About the author (2003)

John Lloyd produced Not the Nine O'Clock New, the Blackadders, and Spitting Image.

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