Graph-based Knowledge Representation: Computational Foundations of Conceptual Graphs

Introduction.- Knowledge Representation and Reasoning.- Conceptual Graphs.- Basic Conceptual Graphs.- Definition of Basic Conceptual Graphs (BGs).- BG Homomorphism.- Simple Conceptual Graphs.- Simple Conceptual Graphs (SGs).- Generalization and Specialization Operations.- Formal Semantics of SGs.- Model Semantic.- Positive, Conjunctive, and Existential Fragment of FOL.- BG Homomorphism Eqivalent Notions.- Graphs.- Relational Structures and Databases.- Basic Algorithms for BG Homomorphism.- Constraint Processing.- Label comparisons.- Tractable Cases.- Tractability Based on the Multigraph-acyclicity of the Source BG.- Other Specialization/generalization Operations.- Compatible Partitions and Extended Join.- B-specializations.- Nested Conceptual Graphs.- Nested Graphs (NGs).- Rules.- Definition and Logical Semantics of a rule.- Conceptual Graphs with Negation.- An Application of Nested Typed Graphs: Semantic Anotation Bases.- Mathematical Background.