Authors: Andrew Schumann
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 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 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.
Comments: 23 pages
[v1] 4 Aug 2011
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