Sound and Complete Forward and BackwardChainings of Graph

This paper presents graph operations for processing conceptual graph rules in forward chaining and backward chaining. In both cases the operations provide sound and complete procedures with respect to rst-order logic deduction. First we present our framework: simple conceptual graphs, rules as couples of lambda-abstractions, knowledge base, logical semantics. Next we focus on forward chaining. In particular, using the notion of redundancy, we exactly characterize when the application of a rule to a graph enriches or not this graph with a \new" information. The forward mechanism is complete if the knowledge base is in normal form. Basic notions (cut points, pieces, compatible partitions, uniica-tion) for backward chaining are detailed. A parallel with previous works on backward chaining is done, in particular with the work of B.C. Ghosh and V. Wuwongse, which is close to ours. The main diierence is that we do not split the goals into trivial subgraphs (a relation and its neighbours). Instead, we determine cut points, which deene arbitrary complex subgraphs, called pieces, that can be processed as a whole.