An introduction to alysidal algebra (II)

J. Nescolarde-Selva, F. Vives-Maciá, J. L. Usó-Doménech, D. Berend

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


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.

Original languageEnglish
Pages (from-to)780-793
Number of pages14
Issue number5
StatePublished - 1 Jun 2012


  • Algebra
  • Alysidal set
  • Chains
  • Coupling functions
  • Cybernetics
  • Freeway of relations
  • Sheaf of relations
  • Structural functions

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Theoretical Computer Science
  • Computer Science (miscellaneous)
  • Engineering (miscellaneous)
  • Social Sciences (miscellaneous)


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