Logic for Learning: Learning Comprehensible Theories from Structured DataSpringer Science & Business Media, 2003 M08 6 - 257 pages 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. |
Contents
Introduction | 3 |
12 Setting the Scene | 7 |
13 Introduction to Learning | 12 |
14 Introduction to Logic | 18 |
Bibliographical Notes | 29 |
Logic | 33 |
22 Type Substitutions | 37 |
23 Terms | 40 |
Bibliographical Notes | 129 |
Exercises | 130 |
Predicates | 133 |
42 Standard Predicates | 141 |
43 Regular Predicates | 148 |
44 Predicate Rewrite Systems | 153 |
45 The Implication Preorder | 160 |
46 Efficient Construction of Predicates | 165 |
24 Subterms | 47 |
25 Term Substitutions | 57 |
26 AConversion | 66 |
27 Model Theory | 74 |
28 Proof Theory | 78 |
Bibliographical Notes | 81 |
Exercises | 82 |
Individuals | 85 |
32 Normal Terms | 91 |
33 An Equivalence Relation on Normal Terms | 95 |
34 A Total Order on Normal Terms | 97 |
35 Basic Terms | 99 |
36 Metrics on Basic Terms | 107 |
37 Kernels on Basic Terms | 117 |
Other editions - View all
Logic for Learning: Learning Comprehensible Theories from Structured Data John W. Lloyd Limited preview - 2013 |
Logic for Learning: Learning Comprehensible Theories from Structured Data John W. Lloyd Limited preview - 2003 |
Logic for Learning: Learning Comprehensible Theories from Structured Data John W. Lloyd No preview available - 2010 |
Common terms and phrases
a₁ Abloy abstractions algorithm ALKEMY append application arity Ax.if Ax.s Ax.t background theory basic terms BNode Null BTree computation concat constant constructor of arity data constructor declarative programming languages default data constructor default term defined definition edges Example exists final predicate follows free variable free with relative function grounding type substitution Hence higher-order logic hypothesis language idempotent induction hypothesis inductive logic programming initial predicate kernel knowledge representation List Int logic programming machine learning Medium metric Molecule multiset normal terms nullary p₁ parameters Pi,j predicate derivation predicate rewrite system proj Width projLength projNumProngs Proof Proposition redex regular predicate regularisation relative type s₁ satisfies Conditions signature standard predicate subderivation subterm Suppose switchable t₁ term of type term substitution tn then sn top top top total order transformations tree type List unifiable Vertex Atom Bond Xx.if