Advanced Information and Knowledge Processing

Computational Foundations of Conceptual Graphs

By: Michel Chein, Marie-Laure Mugnier

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Paperback | 22 October 2010

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Paperback
444 Pages

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23.39 x 15.6 x 2.29

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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

Industry Reviews

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)

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