Graph-based Knowledge Representation

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

From the reviews: "This well-written book is a wonderful text for researchers working on theoretical artificial intelligence (AI). Fundamentally, AI represents knowledge with mathematical objects and then designs computational rules to manipulate these objects. ... In summary, this is a theoretical book for a graph-based approach to knowledge representation. ... A number of detailed algorithms presented in the book may serve as good references for designing a variety of AI systems, such as database mining and logic reasoning." (Hsun-Hsien Chang, ACM Computing Reviews, April, 2009)

From the reviews:



"This well-written book is a wonderful text for researchers working on theoretical artificial intelligence (AI). Fundamentally, AI represents knowledge with mathematical objects and then designs computational rules to manipulate these objects. ... In summary, this is a theoretical book for a graph-based approach to knowledge representation. ... A number of detailed algorithms presented in the book may serve as good references for designing a variety of AI systems, such as database mining and logic reasoning." (Hsun-Hsien Chang, ACM Computing Reviews, April, 2009)