An introduction to alysidal algebra (II)

• Published in: Kybernetes Vol. 41; no. 5/6; pp. 780 - 793
• Main Authors: Nescolarde-Selva, J., Vives-Maciá, F., Usó-Doménech, J.L., Berend, D.
• Format: Journal Article
• Language: English
• Published: London Emerald Group Publishing Limited 08.06.2012
• Subjects: Algebra; Economics; Equivalence; Flexibility; Freeways; Ideology; Joining; Mathematical analysis; Prohibition; Alysidal set; Structural functions; Freeway of relations; Algebra; Sheaf of relations; Chains; Coupling functions; Cybernetics
• ISSN: 0368-492X; 1758-7883
• DOI: 10.1108/03684921211247541

Purpose - 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 approach used was 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 one to make decisions. Transactions of energy, money, merchandise, population, etc. would be the equivalent one to the sanguineous system. These economic transactions and inferential relations, depend, as well, on the existence of a legislative body with their obligations, prohibitions and permissions that regulate them.Originality value - This paper is a continuation of Part I, published in Kybernetes, Volume 41, Issue 1 2, 2012, continuing the development of Alysidal Algebra, which is important for the study of deontical impure systems. They are defined coupling functions and alysidal structures. It is defined as a special coupling function denominated gnorpsic function that can be used for algebraic operations between alysidal sets.