Purpose – The purpose of this paper is to provide an introduction to alysidal algebra. Deontical impure systems are systems whose object set is formed by an s‐impure set, whose elements are perceptuales significances (relative beings) of material and/or energetic objects (absolute beings) and whose relational set is freeways of relations, formed by sheaves of relations going in two‐way directions. Objects and freeways form chains.Design/methodology/approach – The paper looks at the mathematical and logical development of human society structure.Findings – Existence of relations with positive imperative modality (obligation) would constitute the skeleton of the system. Negative imperative modality (prohibition) would be the immunological system of protection of the system. Modality permission the muscular system, that gives the necessary flexibility to the system, in as much to the modality faculty its neurocerebral system, because it allows him to make decisions. Transactions of energy, money, merchandise...