Degree of Dependence and Independence of Neutrosophic Logic Components Applied in Physics

Neutrosophic Logic is a general framework for unification of many existing logics, and its components T (truth), I (indeterminacy), F (falsehood) are standard or non-standard real subsets of ]$^{\mathrm{-}}$0, 1$^{\mathrm{+}}$[ with not necessarily any connection between them. For single valued neutrosophic logic, the sum of the components (T$+$I$+$F) is: 0 $\le $ T$+$I$+$F $\le $ 3 when all three components are independent; 0 $\le $ T$+$I$+$F $\le $ 2 when two components are dependent, while the third one is independent from them; 0 $\le $ T$+$I$+$F $\le $ 1 when all three components are dependent. When three or two of the components T, I, F are independent, one leaves room for incomplete information (sum \textless 1), paraconsistent and contradictory information (sum \textgreater 1), or complete information (sum $=$ 1).~ If all three components T, I, F are dependent, then similarly one leaves room for incomplete information (sum \textless 1), or complete information (sum $=$ 1).~ The dependent components are tied together. Three sources that provide information on T, I, and F respectively are independent if they do not communicate with each other and to not influence each other. The sum of two components x and y in general is: 0 $\le $ x$+$y $\le $ 2 -- d\textdegree (x, y), where d\textdegree (x, y) is the \textit{degree of dependence} between x and y. Therefore 2 -- d\textdegree (x, y) is the \textit{degree of independence} between x and y. But max\textbraceleft T$+$I$+$F\textbraceright may also get any value in [1, 3]. For example, suppose that T and F are 30{\%} dependent and 70{\%} independent (hence T$+$F $\le $ 2-0.3 $=$ 1.7), while I and F are 60{\%} dependent and 40{\%} dependent (hence I$+$F $\le $ 2-0.6 $=$ 1.4). Then max\textbraceleft T$+$I$+$F\textbraceright $=$ 2.4 and occurs for T $=$ 1, I $=$ 0.7, F $=$ 0.7. p.).