Contents

List of Figures
xi

List of Tables
xiii

Preface
xv

Introduction
xix

About the Authors
xxix
1 Order and Logic
1

1.1 Ordered Sets and Fixed-Point Theorems . . . . . . . . . . .
1

1.2 First-Order Predicate Logic . . . . . . . . . . . . . . . . . . .
7

1.3 Ordered Spaces of Valuations . . . . . . . . . . . . . . . . . .
12

2 The Semantics of Logic Programs
23

2.1 Logic Programs and Their Models . . . . . . . . . . . . . . .
23

2.2 Supported Models . . . . . . . . . . . . . . . . . . . . . . . .
28

2.3 Stable Models . . . . . . . . . . . . . . . . . . . . . . . . . .
32

2.4 Fitting Models . . . . . . . . . . . . . . . . . . . . . . . . . .
37

2.5 Perfect Models . . . . . . . . . . . . . . . . . . . . . . . . . .
43

2.6 Well-Founded Models . . . . . . . . . . . . . . . . . . . . . .
56

3 Topology and Logic Programming
65
3.1 Convergence Spaces and Convergence Classes
. . . . . . . . .
66

3.2 The Scott Topology on Spaces of Valuations
. . . . . . . . .
69

3.3 The Cantor Topology on Spaces of Valuations
. . . . . . . .
76

3.4 Operators on Spaces of Valuations Revisited
. . . . . . . . .
83

4 Fixed-Point Theory for Generalized Metric Spaces
87

4.1 Distance Functions in General . . . . . . . . . . . . . . . . .
88

4.2 Metrics and Their Generalizations . . . . . . . . . . . . . . .
91

4.3 Generalized Ultrametrics . . . . . . . . . . . . . . . . . . . .
97

vii