Set Theory and Logic

1309 Submissions

[2] viXra:1309.0028 [pdf] submitted on 2013-09-05 20:36:23

N-Valued Refined Neutrosophic Logic and Its Applications to Physics

Authors: Florentin Smarandache
Comments: 9 Pages.

In this paper we present a short history of logics: from particular cases of 2-symbol or numerical valued logic to the general case of n-symbol or numerical valued logic. We show generalizations of 2-valued Boolean logic to fuzzy logic, also from the Kleene’s and Lukasiewicz’ 3-symbol valued logics or Belnap’s 4-symbol valued logic to the most general n-symbol or numerical valued refined neutrosophic logic. Two classes of neutrosophic norm (n-norm) and neutrosophic conorm (n-conorm) are defined. Examples of applications of neutrosophic logic to physics are listed in the last section. Similar generalizations can be done for n-Valued Refined Neutrosophic Set, and respectively n- Valued Refined Neutrosopjhic Probability.
Category: Set Theory and Logic

[1] viXra:1309.0013 [pdf] replaced on 2015-11-30 06:58:58

General Logic-Systems that Determine Significant Collections of Consequence Operators

Authors: Robert A. Herrmann
Comments: 19 Pages.

Relative to universal logic, it is demonstrated how useful it is to utilize general logic-systems to investigate finite consequences operators (operations). Among many other examples relative to the lattice of finite consequence operators, a general characterization for the lattice-theoretic supremum for a nonempty collection of finite consequence operators is given. Further, it is shown that for any denumerable language there is a rather simple collection of finite consequence operators and for a propositional language, three simple modifications to the finitary rule of inference that demonstrate that the lattice of finite consequence operators is not meet-complete.
Category: Set Theory and Logic