Neutrosophic Logics On Non Archimedean Structures
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Neutrosophic logics on Non-Archimedean Structures
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.
Neutrality and Many-Valued Logics
In this book, we consider various many-valued logics: standard, linear, hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We survey also results which show the tree different proof-theoretic frameworks for many-valued logics, e.g. frameworks of the following deductive calculi: Hilbert's style, sequent, and hypersequent. Recall that hypersequents are a natural generalization of Gentzen's style sequents that was introduced independently by Avron and Pottinger. In particular, we consider Hilbert's style, sequent, and hypersequent calculi for infinite-valued logics based on the three fundamental continuous t-norms: Lukasiewicz's, Godel?s, and Product logics. 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, Godel?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 non-Archimedean multi-valued logics: the first with many-validity in the interval [0,1] of hypernumbers and the second with many-validity in the ring of p-adic integers. Notice that in the second case we set discrete infinite-valued logics. Logics investigated: 1. hyperrational valued Lukasiewicz's, Godel?s, and Product logics, 2. hyperreal valued Lukasiewicz's, Godel?s, and Product logics, 3. p-adic valued Lukasiewicz's, Godel?s, and Post's logics.
Introduction to Neutrosophic Measure, Neutrosophic Integral, and Neutrosophic Probability
In this book, we introduce for the first time the notions of neutrosophic measure and neutrosophic integral, and we develop the 1995 notion of neutrosophic probability. We present many practical examples. It is possible to define the neutrosophic measure and consequently the neutrosophic integral and neutrosophic probability in many ways, because there are various types of indeterminacies, depending on the problem we need to solve. Neutrosophics study the indeterminacy. Indeterminacy is different from randomness. It can be caused by physical space materials and type of construction, by items involved in the space, etc.