Set Theory and Logic

1108 Submissions

[2] viXra:1108.0025 [pdf] submitted on 19 Aug 2011

Logical Ramblings

Authors: Thomas Evans
Comments: 11 pages

I present extensions to logic theory whose utilitarian application contains itself in the form of a developmental, logical framework determinant of all being, and then derive several applications thereof to areas of general quantum theory and pure mathematics, providing solutions to 2 longstanding relevant problems: P vs NP and the Riemann Hypothesis.
Category: Set Theory and Logic

[1] viXra:1108.0011 [pdf] submitted on 4 Aug 2011

Neutrosophic Logics on Non-Archimedean Structures

Authors: Andrew Schumann
Comments: 23 pages

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.
Category: Set Theory and Logic