Simple conceptual graphs revisited: Hypergraphs and conjunctive types for efficient projection algorithms

Abstract

Simple Conceptual Graphs (SGs) form the cornerstone for the "Conceptual Graphs" family of languages. In this model, the subsumption operation is called projection; it is a labelled graphs homomorphism (a NP-hard problem). Designing efficient algorithms to compute projections between two SGs is thus of uttermost importance for the community building languages on top of this basic model. This paper presents some such algorithms, inspired by those developped for Constraint Satisfaction Problems. In order to benefit from the optimization work done in this community, we have chosen to present an alternate version of SGs, differences being the definition of these graphs as hypergraphs and the use of conjunctive types.