Graph-based Knowledge Representation: Computational Foundations of Conceptual Graphs

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Overview

This book addresses the question of how far it is possible to go in knowledge representation and reasoning by representing knowledge with graphs (in the graph theory sense) and reasoning with graph operations.

The authors have carefully structured the book with the first part covering basic conceptual graphs, the second developing the computational aspects, and the final section pooling the kernel extensions. An appendix summarizes the basic ...

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More About This Book

Overview

This book addresses the question of how far it is possible to go in knowledge representation and reasoning by representing knowledge with graphs (in the graph theory sense) and reasoning with graph operations.

The authors have carefully structured the book with the first part covering basic conceptual graphs, the second developing the computational aspects, and the final section pooling the kernel extensions. An appendix summarizes the basic mathematical notions.

This is the first book to provide a comprehensive view on the computational facets of conceptual graphs. The mathematical prerequisites are minimal and the material presented can be used in artificial intelligence courses at graduate level upwards.

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Editorial Reviews

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"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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Product Details

  • ISBN-13: 9781849967693
  • Publisher: Springer London
  • Publication date: 12/10/2010
  • Series: Advanced Information and Knowledge Processing Series
  • Edition description: Softcover reprint of hardcover 1st ed. 2009
  • Edition number: 1
  • Pages: 428
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.90 (d)

Table of Contents

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

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