# neutrosophic logic

## neutrosophic logic

(logic)
(Or "Smarandache logic") A generalisation of fuzzy logic based on Neutrosophy. A proposition is t true, i indeterminate, and f false, where t, i, and f are real values from the ranges T, I, F, with no restriction on T, I, F, or the sum n=t+i+f. Neutrosophic logic thus generalises:

- intuitionistic logic, which supports incomplete theories (for 0<n<100 and i=0, 0<=t,i,f<=100);

- fuzzy logic (for n=100 and i=0, and 0<=t,i,f<=100);

- Boolean logic (for n=100 and i=0, with t,f either 0 or 100);

- multi-valued logic (for 0<=t,i,f<=100);

- paraconsistent logic (for n>100 and i=0, with both t,f<100);

- dialetheism, which says that some contradictions are true (for t=f=100 and i=0; some paradoxes can be denoted this way).

Compared with all other logics, neutrosophic logic introduces a percentage of "indeterminacy" - due to unexpected parameters hidden in some propositions. It also allows each component t,i,f to "boil over" 100 or "freeze" under 0. For example, in some tautologies t>100, called "overtrue".

http://gallup.unm.edu/~smarandache/NeutLog.txt.

["Neutrosophy / Neutrosophic probability, set, and logic", F. Smarandache, American Research Press, 1998].
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References in periodicals archive ?
Smarandache, A Unifying Field in Logics: Neutrosophic Logic.
Neutrosophic logic is a powerful tool to deal with incomplete, indeterminate, and inconsistent information, which is the main reason for widespread concerns of researchers.
Therefore, the neutrosophic logic, neutrosophic set, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus, and so forth were born in neutrosophy [15].
Unmatter as theoretically predicted in the framework of the neutrosophic logic and statistics [4-6] is considered as a combination of matter and antimatter that bound together, or a long-range mixture of matter and antimatter forming a weakly-coupled phase.
Neutrosophy is the basis of neutrosophic logic, neutrosophic probability, neutrosophic set, and neutrosophic statistics.
See the Proceedings of the First International Conference on Neutrosophic Logic, The University of New Mexico, Gallup Campus, 1-3 December 2001, at http://www.
Similarly, there are many ways to construct such connectives according to each particular problem to solve; here we present the easiest ones: One notes the Neutrosophic logic values of the propositions A1 and A2 by
Sukanto Bhattacharya's doctoral thesis entitled "Utility, Rationality and Beyond--From Behavioral Finance to Informational Finance" not only succeeded in earning him a PhD degree but also went on to arguably become recognized as the first comprehensive published work of its kind on the application of neutrosophic logic in theoretical finance.
Emphasizing advancements and applications to neutrosophics, this text introduces the interval neutrosophic set, which is an instance of the neutrosophic set, describes the interval neutrosophic logic based on neutrosophic sets, a situation which allows for modeling of fuzzy, incomplete, and inconsistent information, and gives a neutrosophic relational data model with a relational data base, and another model in the form of a soft semantic web services agent.
Smarandache [20] proposed a new theory, namely, neutrosophic logic, by adding another independent membership function named as indeterminacy-membership I(x) along with truth membership T(x) and falsity F(x) membership functions.
Neutrosophy and Neutrosophic Logic, First International Conference on Neutrosophy, Neutrosophic Logic, Set, Probability, and Statistics, University of New Mexico, Gallup, NM 87301, USA, 2002.
These types of fuzzy and especially neutrosophic implications are derived from the fuzzy or neutrosophic logic connectives.

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