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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.