An introduction to alysidal algebra (II)

Abstract

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.

What Are Ideological Systems?

“…In the Deontical Impure Systems (DIS) (Impure sets and their mathematical properties have been previously defined in Nescolarde Selva et al [27]) approach, the superstructure of social systems has been divided in two [27][28][29][30][31][32][33][34][35][36][37][38][39][40].…”

“…The believers work together and then experts work out what is the correct behavior, the "right" values and so on; (4) Language. A language L is the logical expression of an ideology relating one substantive (Substantive beliefs [36,37] make up a system's axioms, and most of the beliefs make up their theorems) belief [27][28][29][30][31][32][33][34][35][36][37][38][39] to the others in the belief system. Language is understood from repeated patterns in the use of sets of beliefs.…”

Structure and Superstructures in Complex Social Systems

“…This Doxical Space or belief space is a normative superstructure and includes ways of thinking about the economic and legal normative structures. Two superstructures are involved in this approach to DIS [1][2][3][4][5][6][7][8][9][10]:…”

“…Let r i k be a doxical relation belonging to a k sheaf [1][2][3][4][5][6][7][8][9][10] ( ) , with Ù being the function "and". We define the systemic significance s and there will also be a denotative significance d-s which is what we know of the significance s of an object in Reality that we call an absolute being.…”

“…In previous works, the authors have defined social systems as Deontic Impure Systems (DIS) [1][2][3][4][5][6][7][8][9][10], and provided mathematical properties of their structure. These systems are considered impure because their elements are either living things or materials and what we know of them is constrained by our ways of thinking and may vary from person to person.…”