Improving the Forward Chaining Algorithm for Conceptual Graphs Rules

Simple Conceptual Graphs (SGs) are used to represent entities and relations between these entities: they can be translated into positive, conjunctive, existential first-order logics, without function symbols. Sound and complete reasonings w.r.t. associated logic formulas are obtained through a kind of graph homomorphism called projection. Conceptual Graphs Rules (or CG rules) are a standard extension to SGs, keeping sound and complete reasonings w.r.t. associated logic formulas (they have the same form as tuple generating dependencies in database): these graphs represent knowledge of the form "IF ... THEN". We present here an optimization of the natural forward chaining algorithm for CG rules. Generating a graph of rules dependencies makes the following sequences of rule applications far more efficient, and the structure of this graph can be used to obtain new decidability results.