This article presents a new approach for structural rule extraction and knowledge discovery by means of Structural Galois Lattice and genetic algorithms. The approach synthesizes symbolic learning in feature extraction as a pre-processing and a subsymbolic learning as a post-processing for extracting rules. Structural Galois Lattice was used to represent structural patterns, perform classification tasks, and extract features. These structural patterns were described by labeled graphs. The proposed method, GAsRule, is based on genetic algorithms which were adapted to 1) allow pattern recognition--this is done by matching the rule antecedents with the rule precedent (i.e., paths/graphs); 2) preserving the syntax and semantics of the context of description; and 3) evaluate rule sets for knowledge discovery and evolve new rules sets for prediction. The goal of our experiment is to solve the fundamental issue of extracting structural rules in structural pattern recognition. Experiments were based upon the examples of arch definition, which are widely used in machine learning. We hope to extend this method to real-world data sets in future work.