Mathematical Aspects of Logic Programming Semantics

Abstract

Order and Logic Ordered Sets and Fixed-Point Theorems First-Order Predicate Logic Ordered Spaces of Valuations The Semantics of Logic Programs Logic Programs and Their Models Supported Models Stable Models Fitting Models Perfect Models Well-Founded Models Topology and Logic Programming Convergence Spaces and Convergence Classes The Scott Topology on Spaces of Valuations The Cantor Topology on Spaces of Valuations Operators on Spaces of Valuations Revisited Fixed-Point Theory for Generalized Metric Spaces Distance Functions in General Metrics and Their Generalizations Generalized Ultrametrics Dislocated Metrics Dislocated Generalized Ultrametrics Quasimetrics A Hierarchy of Fixed-Point Theorems Relationships between the Various Spaces Fixed-Point Theory for Multivalued Mappings Partial Orders and Multivalued Mappings Metrics and Multivalued Mappings Generalized Ultrametrics and Multivalued Mappings Quasimetrics and Multivalued Mappings An Alternative to Multivalued Mappings Supported Model Semantics Two-Valued Supported Models Three-Valued Supported Models A Hierarchy of Logic Programs Consequence Operators and Fitting-Style Operators Measurability Considerations Stable and Perfect Model Semantics The Fixpoint Completion Stable Model Semantics Perfect Model Semantics Logic Programming and Artificial Neural Networks Introduction Basics of Artificial Neural Networks The Core Method as a General Approach to Integration Propositional Programs First-Order Programs Some Extensions - The Propositional Case Some Extensions - The First-Order Case Final Thoughts Foundations of Programming Semantics Quantitative Domain Theory Fixed-Point Theorems for Generalized Metric Spaces The Foundations of Knowledge Representation and Reasoning Clarifying Logic Programming Semantics Symbolic and Subsymbolic Representations Neural-Symbolic Integration Topology, Programming, and Artificial Intelligence Appendix: Transfinite Induction and General Topology The Principle of Transfinite Induction Basic Concepts from General Topology Convergence Separation Properties and Compactness Subspaces and Products The Scott Topology Bibliography Index