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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.

The paper looks at the mathematical and logical development of human society structure.

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, 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.

The concepts of alysidal set are introduced, whose elements are chains and coupling function between alysidal sets. Environment is formed as well by different DIS. That is to say, by an alysidal set whose elements are simultaneously systems. Specific interchanges (stimulus‐response) leave certain nodes and act on certain nodes of the alysidal sets (stimulus environment‐DIS‐response environment). The paper defines a special coupling function, denominated gnorpsic function, that can be used for algebraic operations between alysidal sets.

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.

The approach used was mathematical and logical development of human society structure.

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.

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.

The purpose of this paper is to demonstrate mathematically the impossibility of achieving a utopian society. Demonstrate that any attempt to correct deviations from a hypothetical trajectory whose ultimate goal is the utopia, increasingly demands more work, including measures that lead to terror, which may even be absolute, leading to the horrible paradox that in seeking paradise hell is constructed.

Scientific tools that the authors have used are: the theory of the system linkage, alysidal algebra, kinematic theory and vector analysis.

Myths are the substrate of some complex systems of beliefs and utopia is its ultimate goal. The use of the combination of the theory of trajectories, belonging to the alysidal algebra, the theorem of unintended effects and kinematics theory provides an approximation to deviations suffering utopian ideological currents and their corrections.

This paper is a continuation of other previous papers developing the theory of complex societies.

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 and at least one of its relations has deontical properties such as permission, prohibition, obligation and faculty.

The paper looks at the mathematical and logical development of human society structure.

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, population, etc. would be the equivalent one to the sanguineous system. These economic transactions and inferential relations, depend, as well, of the existence of a legislative body with their obligations, prohibitions and permissions that regulate them. A Social System Σ may be considered like an alysidal set with an only alysidal element. The authors consider two theories: Enlarged theory and Reduced theory.

This paper is a continuation of two previous papers – Part I published in Kybernetes, Vol. 41 No. 1/2 and Part II published in Vol. 41 No. 5/6 – and develops the theory of deontical impure systems.

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 and at least one of its relations has deontical properties such as permission, prohibition, obligation and faculty. The paper aims to discuss these issues.

Mathematical and logical development of human society ethical and normative structure.

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. Four theorems have been formulated based on Gödel's theorem demonstrating the inconsistency or incompleteness of DISs. For each constructed systemic conception can happen to it one of the two following things: either some allowed responses are not produced or else some forbidden responses are produced. Responses prohibited by the system are defined as nonwished effects.

This paper is a continuation of the four previous papers and is developed the theory of deontical impure systems.

In this paper, we discussed relations between drivers' cognition and the dynamics of traffic conditions. When we take into account drivers' cognition, many types of psychological impedance to behavioral change could be accounted for, including cognitive conservatism and habitual decision making. Based on psychological theories with respect to these impedance to behavioral change, we elucidated the process of changes in traffic conditions that might be induced by changes in road-network structure. As a result of the discussion, we concluded that traffic conditions are unlikely change as much as predicted by theories that assume a simple, and sometimes unique, relation between a traffic condition and a road-network structure, e.g., theories that assume user equilibrium.