Neutrosophic logics on Non-Archimedean Structures
نویسنده
چکیده
We present a general way that allows to construct systematically analytic calculi for a large family of non-Archimedean many-valued logics: hyperrational-valued, hyperreal-valued, and p-adic valued logics characterized by a special format of semantics with an appropriate rejection of Archimedes’ axiom. These logics are built as different extensions of standard many-valued logics (namely, Lukasiewicz’s, Gödel’s, Product, and Post’s logics). The informal sense of Archimedes’ axiom is that anything can be measured by a ruler. Also logical multiple-validity without Archimedes’ axiom consists in that the set of truth values is infinite and it is not well-founded and well-ordered. We consider two cases of nonArchimedean multi-valued logics: the first with many-validity in the interval [0, 1] of hypernumbers and the second with many-validity in the ring Zp of p-adic integers. On the base of non-Archimedean valued logics, we construct non-Archimedean valued interval neutrosophic logics by which we can describe neutrality phenomena. Belarusian State University, Minsk, Belarus e-mail: [email protected]
منابع مشابه
Interval Neutrosophic Logics: Theory and Applications
In this paper, we present the interval neutrosophic logics which generalizes the fuzzy logic, paraconsistent logic, intuitionistic fuzzy logic and many other non-classical and non-standard logics. We will give the formal definition of interval neutrosophic propositional calculus and interval neutrosophic predicate calculus. Then we give one application of interval neutrosophic logics to do appr...
متن کاملNeutrosophic Computational Models
Neutrosophic approaches in logics and computing have been proposed by Smarandache and interesting developments were obtained by many researchers around the world. Not only algebraic structures, topology, statistics, and logics already benefited by the new interpretation, but also many fields of computer science: image analysis, neutrosophic databases, neutrosophic cognitive maps etc. This paper...
متن کاملDSm models and Non-Archimedean Reasoning
The Dezert-Smarandache theory of plausible and paradoxical reasoning is based on the premise that some elements θi of a frame Θ have a non-empty intersection. These elements are called exhaustive. In number theory, this property is observed only in non-Archimedean number systems, for example, in the ring Zp of p-adic integers, in the field Q of hyperrational numbers, in the field R of hyperreal...
متن کاملFlorentin Smarandache a Unifying Field in Logics: Neutrosophic
In this paper one defines the non-standard real unit interval 0, 1 as a support for neutrosophy, neutrosophic logic, neutrosophic set, neutrosophic probability and statistics encountered in the next papers.
متن کاملFlorentin Smarandache a Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability and Statistics
In this paper one defines the non-standard real unit interval 0, 1 (a simpler notation is also used: ]-0, 1+[ ) as a support for neutrosophy, neutrosophic logic, neutrosophic set, neutrosophic probability and statistics encountered in the next papers.
متن کامل