Authors had reported before two dual Boolean algebras to understand the underlying logic of the genetic code structure. In such Boolean structures, deductions have physico-chemical meaning. We summarize here that these algebraic structures can help us to describe the gene evolution process. Particularly in the experimental confrontation, it was found that most of the mutations of several proteins correspond to deductions in these algebras and they have a small Hamming distance related to their respective wild type. Two applications of the corresponding codification system in bioinformatics problems are also shown. The first one is the classification of mutations in a protein. The other one is related with the problem of detecting donors and acceptors in DNA sequences. Besides, pure mathematical models, Statistical techniques (Decision Trees) and Artificial Intelligence techniques (Bayesian Networks) were used in order to show how to accomplish them to solve these knowledge-discovery practical problems.