A computer-implemented method for processing a logic rule in a graph database. The method includes obtaining a graph database comprising at least one graph, each graph of the database being represented in one or more adjacency matrices (R-Matrix), each adjacency matrix representing a group of tuples of the graph comprising a same predicate, obtaining the logic rule concluding to a head predicate, generating a virtual adjacency matrix comprising one of the one or more adjacency matrices (R-Matrix) and an entailed data matrix (E-Matrix), the virtual adjacency matrix representing the head predicate, the entailed data matrix representing a group of tuples that are computed by applying the logic rule, and receiving a query by the database using the head predicate.