Knowledge Representation and Reasonings Based on Graph Homomorphism

The main conceptual contribution in this paper is to present an approach to knowledge representation and reasonings based on labeled graphs and labeled graph homomorphism. Strengths and weaknesses of this graph-based approach are discussed. Main technical contributions are the followings. Fundamental results about the kernel of this approach, the so-called simple graphs model are synthesized. It is then shown that the basic deduction problem on simple graphs is essentially the same problem as conjunctive query containment in databases and constraint satisfaction; polynomial parcimonious transformations between these problems are exhibited. Grounded on the simple graphs model, a knowledge representation and reasoning model allowing to deal with facts, production rules, transformation rules, and constraints is presented, as an illustration of the graph-based approach.