On generalization/specialization for conceptual graphs

This paper centers on generalization/specialization relation in the framework of conceptual graphs (this relation corresponds to the logical subsumption when considering the logical formulas associated with conceptual graphs). Results given here apply more generally to any model where knowledge is described by labelled graphs and reasoning is based on graph subsumption, like in semantic networks or in structural machine learning. The generalization/specialization relation, as deened by Sowa, is rst precisely analyzed, especially its links with a graph morphism, called projection. Besides Sowa's specialization relation (which is a preorder), another one is actually used in some practical applications (which is an order). Both are comparatively studied. The second topic of this paper is the design of eecient algorithms for computing these specialization relations. Since the associated problems are NP-hard, the form of the graphs is restricted in order to come to polynomial algorithms. In particular, polynomial algorithms are presented for computing a projection from a conceptual \tree" to any conceptual graph, and for counting the number of such projections. The algorithms are also described in a generic way, replacing the projection by a parametrized graph morphism, and conceptual graphs by directed labelled graphs.