Neutrosophic and Modal Components of Relations in Complex Systems

Semiotic components in the relations of complex systems depend on the Subject. There are two main semiotic components: Neutrosophic and Modal. Modal components are alethical and deontical. In this paper the authors applied the theory of Neutrosophy and Modal Logic to Deontical Impure Systems

Mythical systems: mathematic and logical theory

The process of elaboration of the symbolic universe leads to exciting insights regarding the search for human emotional security. The symbols end up as explanatory axes of universal reality and on them are constructed myths that form a superstructure for belief systems. Human society is a multi-level system with a material structure (society), an ideological superstructure (belief systems, values, etc.) and a super superstructure with two parts: mythical (origin and justification) and utopic (final goal). All mythical belief systems have a numinous-religious nature

Ideological systems and its validation: a neutrosophic approach

Ideologies face two critical problems in the reality, the problem of commitment and the problem of validation. Commitment and validation are two separate phenomena, in spite of the near universal myth that the human is committed because his beliefs are valid. Ideologies not only seem external and valid but also worth whatever discomforts believing entails. In this paper the authors develop a theory of social commitment and social validation using concepts of validation of neutrosophic logic

Fuzzy Structure of Complex Belief Systems: Fuzzy Relations and Fuzzy Belief Sets

In previous work, Nescolarde-Selva and Usó-Doménech (2014a Nescolarde-Selva, J. and J. L. Usó-Doménech. “Semiotic Vision of Ideologies.” Found Sci 19 (2014a): 263–282.[CrossRef], [Web of Science ®], b) discussed the theory that complex belief systems have a topological structure. In this article it is suggested that this structure is also fuzzy. We introduce the concepts of fuzzy sets in the context of beliefs (substantive and derived), and between derived beliefs themselves. Also introduced are the concepts of fuzzy covering and fuzzy invariance and the relationships between them

Textual Theory and Complex Belief Systems: Topological Theory

In order to establish patterns of materialization of the beliefs we are going to consider that these have defined mathematical structures. It will allow us to understand better processes of the textual, architectonic, normative, educative, etc., materialization of an ideology. The materialization is the conversion by means of certain mathematical correspondences, of an abstract set whose elements are beliefs or ideas, in an impure set whose elements are material or energetic. Text is a materialization of ideology and it is any representation of the Reality represented by symbolic means. In all text T we can observe diverse topological structures: Metric Textual Space, Textual Topology and a Textual Lattice

Topological structures of complex belief systems (II): Textual materialization

Mythical and religious belief systems in a social context can be regarded as a conglomeration of sacrosanct rites, which revolve around substantive values that involve an element of faith. Moreover, we can conclude that ideologies, myths and beliefs can all be analyzed in terms of systems within a cultural context. The significance of being able to define ideologies, myths and beliefs as systems is that they can figure in cultural explanations. This, in turn, means that such systems can figure in logic-mathematical analyses

What Are Ideological Systems?

Ideology is a systemic property of cognition central to the transmission and actualization of beliefs. Ideologies take many forms including religious, philosophical, popular and scientific. They play a central role in both personal identity and in the way society holds itself together. Therefore, it is important to understand how to model identities. The article introduces ideologies as a function of cognition that have been described by political scientists and critical theorists. There follows a typology of ideologies that shows their increasing complexity as societies develop. These considerations lead to the identification of key elements and variables in an ideology that can be expressed mathematically together with some of their systemic relations. These variables may be used to estimate the validation of ideologies

Myth, Language, and Complex Ideologies

Ideologies use for their conservation and propagation persuasive methods of communication: rhetoric. Rhetoric is analyzed from the semiotic and logical-mathematical points of view. The following hypotheses are established: (1) language L is a self-explanatory system, mediated by a successive series of systems of cultural conventions, (2) connotative significances of an ideological advertising rhetoric must be known, and (3) the notion of ideological information is a neutral notion that does not imply the valuation of ideology or its conditions of veracity or falsification. Rhetorical figures like metonymy, metaphor, parable analogy, and allegory are defined as relations. Metaphor and parable are order relations. Operations of metonymic and metaphoric substitution are defined and several theorems derived from these operations have been deduced

Reality, Systems and Impure Systems

Impure systems contain Objects and Subjects: Subjects are human beings. We can distinguish a person as an observer (subjectively outside the system) and that by definition is the Subject himself, and part of the system. In this case he acquires the category of object. Objects (relative beings) are significances, which are the consequence of perceptual beliefs on the part of the Subject about material or energetic objects (absolute beings) with certain characteristics.The IS (Impure System) approach is as follows: Objects are perceptual significances (relative beings) of material or energetic objects (absolute beings). The set of these objects will form an impure set of the first order. The existing relations between these relative objects will be of two classes: transactions of matter and/or energy and inferential relations. Transactions can have alethic modality: necessity, possibility, impossibility and contingency. Ontic existence of possibility entails that inferential relations have Deontic modality: obligation, permission, prohibition, faculty and analogy. We distinguished between theorems (natural laws) and norms (ethical, legislative and customary rules of conduct)

Linguistic Knowledge of Reality: A Metaphysical Impossibility?

Reality contains information (significant) that becomes significances in the mind of the observer. Language is the human instrument to understand reality. But is it possible to attain this reality? Is there an absolute reality, as certain philosophical schools tell us? The reality that we perceive, is it just a fragmented reality of which we are part? The work that the authors present is an attempt to address this question from an epistemological, linguistic and logical-mathematical point of view