The projection problem (conceptual graph projection, homomorphism, injective morphism, θ-subsumption, OI-subsumption) is crucial to the efficiency of relational learning systems. How to manage this complexity has motivated numerous studies on learning biases, restricting the size and/or the number of hypotheses explored. The approach suggested in this paper advocates a projection operator based on the classical arc consistency algorithm used in constraint satisfaction problems. This projection method has the required properties : polynomiality, local validation, parallelization, structural interpretation. Using the arc consistency projection, we found a generalization operator between labeled graphs. Such an operator gives the structure of the classification space which is a concept lattice.