Mathematical Aspects of Logic Programming Semantics

• Main Authors: Hitzler, Pascal, Seda, Anthony
• Format: eBook Book
• Language: English
• Published: United States CRC Press 2010; Taylor & Francis; Taylor & Francis Group
• Edition: 1
• Series: Chapman & Hall/CRC Studies in Informatics Series
• Subjects: Computer programming, programs, data; Computers; COMPUTERS / Information Theory bisacsh; COMPUTERS / Machine Theory bisacsh; COMPUTERS / Software Development & Engineering / Systems Analysis & Design bisacsh; Games; Information Theory; Logic; Logic programming; Machine Theory; Mathematical Programming; Mathematics; Mathematics and Science; Programming; Programming languages (Electronic computers); Programming languages (Electronic computers) > Semantics; Semantics; logic programming semantics; supported model semantics; Banach Theorem; Binary Threshold Units; Cauchy Sequence; Multivalued Mappings; Fixed Point Theory; Ultra-metric Space; artificial intelligence; fixed-point theory; Spherically Complete; Banach Contraction Mapping Theorem; generalized metric spaces; Convergence Class; Denotational Semantics; Predicate Symbol; Fixed Point; Basic Open Sets; Bottom Element; symbolic representations; Scott topology; Logic Programming; mathematical analysis; Ultrametric Space; Fixed Point Theorem; Complete Lattice; Complete Partial Order; Cellular Automata; artificial neural networks; perfect model semantics; transfinite induction; Totally Bounded; Web Ontology Language Owl; Hasse Diagram; Ontology Language; Cantor topology
• ISBN: 1439829624; 9781439829622; 1138114227; 1439829616; 9781439829615; 9781138114227
• DOI: 10.1201/b10397

Covering the authors' own state-of-the-art research results, this book presents a rigorous, modern account of the mathematical methods and tools required for the semantic analysis of logic programs. It significantly extends the tools and methods from traditional order theory to include nonconve...

Table of Contents:

• Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- List of Figures -- List of Tables -- Preface -- Introduction -- About the Authors -- 1 Order and Logic -- 1.1 Ordered Sets and Fixed-Point Theorems -- 1.2 First-Order Predicate Logic -- 1.3 Ordered Spaces of Valuations -- 2 The Semantics of Logic Programs -- 2.1 Logic Programs and Their Models -- 2.2 Supported Models -- 2.3 Stable Models -- 2.4 Fitting Models -- 2.5 Perfect Models -- 2.6 Well-Founded Models -- 3 Topology and Logic Programming -- 3.1 Convergence Spaces and Convergence Classes -- 3.2 The Scott Topology on Spaces of Valuations -- 3.3 The Cantor Topology on Spaces of Valuations -- 3.4 Operators on Spaces of Valuations Revisited -- 4 Fixed-Point Theory for Generalized Metric Spaces -- 4.1 Distance Functionsin General -- 4.2 Metricsand Their Generalizations -- 4.3 Generalized Ultrametrics -- 4.4 Dislocated Metrics -- 4.5 Dislocated Generalized Ultrametrics -- 4.6 Quasimetrics -- 4.7 A Hierarchy of Fixed-Point Theorems -- 4.8 Relationships Between the Various Spaces -- 4.9 Fixed-Point Theory for Multivalued Mappings -- 4.10 Partial Orders and Multivalued Mappings -- 4.11 Metrics and Multivalued Mappings -- 4.12 Generalized Ultrametrics and Multivalued Mappings -- 4.13 Quasimetrics and Multivalued Mappings -- 4.14 An Alternative to Multivalued Mappings -- 5 Supported Model Semantics -- 5.1 Two-Valued Supported Models -- 5.2 Three-Valued Supported Models -- 5.3 A Hierarchy of Logic Programs -- 5.4 Consequence Operators and Fitting-Style Operators -- 5.5 Measurability Considerations -- 6 Stable and Perfect Model Semantics -- 6.1 The Fixpoint Completion -- 6.2 Stable Model Semantics -- 6.3 Perfect Model Semantics -- 7 Logic Programming and Artificial Neural Networks -- 7.1 Introduction -- 7.2 Basics of Artificial Neural Networks
• 7.3 The Core Method as a General Approach to Integration -- 7.4 Propositional Programs -- 7.5 First-Order Programs -- 7.6 Some Extensions - The Propositional Case -- 7.7 Some Extensions - The First-Order Case -- 8 Final Thoughts -- 8.1 Foundations of Programming Semantics -- 8.2 Quantitative Domain Theory -- 8.3 Fixed-Point Theorems for Generalized Metric Spaces -- 8.4 The Foundations of Knowledge Representation and Reasoning -- 8.5 Clarifying Logic Programming Semantics -- 8.6 Symbolic and Subsymbolic Representations -- 8.7 Neural-Symbolic Integration -- 8.8 Topology, Programming, and Artificial Intelligence -- Appendix: Transfinite Induction and General Topology -- A.1 The Principle of Transfinite Induction -- A.2 Basic Concepts from General Topology -- A.3 Convergence -- A.4 Separation Properties and Compactness -- A.5 Subspaces and Products -- A.6 The Scott Topology -- Bibliography -- Index