Structuration of phenotypes and genotypes through galois lattices and implications

The Galois Lattice of a binary relation formalizes it as a concept system, dually ordered in "extension"/"intension." All implications between conjunctions of properties holding in it are summarized by a canonical basis--all basis having the same cardinality. We report how these tools structure phenotypes/genotypes in behavior genetics. The first study on phenotypes of laterality has a unique set of features and two sets of instances (left-/right-handers) for which the corresponding sets of rules are compared, while the second study on partial trisomy 21 uses a unique instance set (patients) to explore the matching between two sets of features: phenotypes and genetic causes. Hence, both situations comprise two binary data sets that are paired through either a column or a row matching, which raises specific questions. If the data are small, as compared with databases in bioinformatics, this illustrates how these abstract tools can unfold better interpretations.