Topological structures of complex belief systems
Identifieur interne : 000134 ( Main/Exploration ); précédent : 000133; suivant : 000135Topological structures of complex belief systems
Auteurs : Josué-Antonio Nescolarde-Selva [Espagne] ; José-Luis Us Oménech [Espagne]Source :
- Complexity [ 1076-2787 ] ; 2013-09.
English descriptors
- Teeft :
- Abelian group, Abstract level, Adherent term, Axiom, Base revisions, Belief, Belief base, Belief distance, Belief filter, Belief lattice, Belief poset, Belief pseudometrics, Belief revision, Belief sequence, Belief subset, Belief subspace topology, Belief system, Belief systems, Belief term, Belief topology, Belief uniformity, Binary operation, Binary priority operation, Cambridge university press, Cartesian product, Chicago press, Closure, Cognitive, Cognitive structure, Conceptual, Conceptual mapping, Conceptual maps, Connotative significance, Contrastive structures, Cybernetic feedback process, Dynamic interaction, Elementary forms, Finite belief, Finite sets, Fundamental system, General topology, Human beings, Human brain, Identity element, Infimum belief, Infinitesimal transformation, Initial hypotheses, Inverse element, Lattice, Linguistic series, Lower belief, Main term, Material culture, Material world, Materialization, Mathematical structures, Mcdonald institute monographs, Mental models, Mental representations, Mental world vision, Metric, Metric belief space, Metric space, Natural numbers, Neighborhood filter, Neurolinguistic theory, Nodes form, Open ball, Open balls, Open sets, Operation fulfils, Other words, Oxford university press, Periodical, Poset, Positional order, Positive integer, Primitive classification, Principal belief, Principal belief filter, Principal term, Priority relation, Pseudometric belief space, Referential order, Relative understanding, Religious beliefs, Religious life, Religious practices, Ritual practices, Semantic aspects, Semantic units, Social life, Social structure, Subset, Substantive, Substantive belief, Substantive beliefs, Supremum, Supremum belief, Textual materialization, Theory change, Topological, Topological belief space, Topological entities, Topological space, Topological structure, Topological structures, Topology, Truth value, Uniform structure, Visual contour, Visual field, Whole belief, Wiley periodicals, World vision.
Abstract
The concepts of substantive beliefs and derived beliefs are defined, a set of substantive beliefs S like open set and the neighborhood of an element substantive belief. A semantic operation of conjunction is defined with a structure of an Abelian group. Mathematical structures exist such as poset beliefs and join‐semilattttice beliefs. A metric space of beliefs and the distance of belief depending on the believer are defined. The concepts of closed and opened ball are defined. S′ is defined as subgroup of the metric space of beliefs Σ and S′ is a totally limited set. The term s is defined (substantive belief) in terms of closing of S′. It is deduced that Σ is paracompact due to Stone's Theorem. The pseudometric space of beliefs is defined to show how the metric of the nonbelieving subject has a topological space like a nonmaterial abstract ideal space formed in the mind of the believing subject, fulfilling the conditions of Kuratowski axioms of closure. To establish patterns of materialization of beliefs we are going to consider that these have defined mathematical structures. This will allow us to understand better cultural processes of text, architecture, norms, and education that are forms or the materialization of an ideology. This 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. © 2013 Wiley Periodicals, Inc. Complexity 19: 46–62, 2013
Url:
DOI: 10.1002/cplx.21455
Affiliations:
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Le document en format XML
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<term>Abstract level</term>
<term>Adherent term</term>
<term>Axiom</term>
<term>Base revisions</term>
<term>Belief</term>
<term>Belief base</term>
<term>Belief distance</term>
<term>Belief filter</term>
<term>Belief lattice</term>
<term>Belief poset</term>
<term>Belief pseudometrics</term>
<term>Belief revision</term>
<term>Belief sequence</term>
<term>Belief subset</term>
<term>Belief subspace topology</term>
<term>Belief system</term>
<term>Belief systems</term>
<term>Belief term</term>
<term>Belief topology</term>
<term>Belief uniformity</term>
<term>Binary operation</term>
<term>Binary priority operation</term>
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<term>Cartesian product</term>
<term>Chicago press</term>
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<term>Conceptual</term>
<term>Conceptual mapping</term>
<term>Conceptual maps</term>
<term>Connotative significance</term>
<term>Contrastive structures</term>
<term>Cybernetic feedback process</term>
<term>Dynamic interaction</term>
<term>Elementary forms</term>
<term>Finite belief</term>
<term>Finite sets</term>
<term>Fundamental system</term>
<term>General topology</term>
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<term>Human brain</term>
<term>Identity element</term>
<term>Infimum belief</term>
<term>Infinitesimal transformation</term>
<term>Initial hypotheses</term>
<term>Inverse element</term>
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<term>Positional order</term>
<term>Positive integer</term>
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<term>Principal belief filter</term>
<term>Principal term</term>
<term>Priority relation</term>
<term>Pseudometric belief space</term>
<term>Referential order</term>
<term>Relative understanding</term>
<term>Religious beliefs</term>
<term>Religious life</term>
<term>Religious practices</term>
<term>Ritual practices</term>
<term>Semantic aspects</term>
<term>Semantic units</term>
<term>Social life</term>
<term>Social structure</term>
<term>Subset</term>
<term>Substantive</term>
<term>Substantive belief</term>
<term>Substantive beliefs</term>
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<front><div type="abstract">The concepts of substantive beliefs and derived beliefs are defined, a set of substantive beliefs S like open set and the neighborhood of an element substantive belief. A semantic operation of conjunction is defined with a structure of an Abelian group. Mathematical structures exist such as poset beliefs and join‐semilattttice beliefs. A metric space of beliefs and the distance of belief depending on the believer are defined. The concepts of closed and opened ball are defined. S′ is defined as subgroup of the metric space of beliefs Σ and S′ is a totally limited set. The term s is defined (substantive belief) in terms of closing of S′. It is deduced that Σ is paracompact due to Stone's Theorem. The pseudometric space of beliefs is defined to show how the metric of the nonbelieving subject has a topological space like a nonmaterial abstract ideal space formed in the mind of the believing subject, fulfilling the conditions of Kuratowski axioms of closure. To establish patterns of materialization of beliefs we are going to consider that these have defined mathematical structures. This will allow us to understand better cultural processes of text, architecture, norms, and education that are forms or the materialization of an ideology. This 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. © 2013 Wiley Periodicals, Inc. Complexity 19: 46–62, 2013</div>
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