# 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