Graph-based Knowledge Representation: Computational Foundations of Conceptual Graphs

Introduction (Knowledge Representation and Reasoning, Conceptual Graphs, A Graph-Based Approach to KR).-Basic Conceptual Graphs (Homomorphism, Subsumption Preorder, Irredundant BGs, Generalization and Specialization Operations, Normal BGs, Computational Complexity of Basic Problems).-Simple Conceptual Graphs (Generalization and Specialization Operations, Standard and Normal SGs, Coref-Homomorphism, Antinormal Form).- Formal Semantics of SGs (Model and FOL semantics, Soundness and Completeness of (coref) Homomorphism, Positive Conjunctive and Existential Fragment of FOL, Description Logics and Conceptual Graphs).- BG Homomorphism and Equivalent Notions (Conceptual Hypergraphs, Graphs, Relational Structures, Conjunctive Queries, Constraint Satisfaction Problem).- Basic Algorithms for BG Homomorphism (Backtrack Algorithms, Constraint Processing, Label Comparison).- Tractable Cases (Tractability Based on the Multigraph-Acyclicity of the Source BG, Tractability Based on the Hypergraph-Acyclicity of the Source BG, the Existential Conjunctive Guarded Fragment, Generalizations of Graph-Acyclicity and Hypergraph-Acyclicity).- Other Specialization/Generalization Operations (The Least Generalization and Greatest Specialization of two BGs, Maximal Join, Compatible Partitions and Extended Join, Type Expansion and Contraction).- Nested Conceptual Graphs (Nested Graphs, Logical Semantics, Soundness and Completeness).- Rules (Graph rules, Logical Semantics, Forward Chaining, Backward Chaining, Soundness and Completeness, Computational Complexity).- The BG Family (Deduction problems with Facts, Rules and Constraints, Computational Complexity).- Conceptual Graphs with Negation (Full Conceptual Graphs, Logical Semantics, Calculus, Atomic Negation, Coreference and Difference, Computational Complexity).- An Application of Nested Typed Graphs: Semantic Anotation Bases.- Mathematical Background.- References.- Index