neutrosophic logic

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neutrosophic 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".

["Neutrosophy / Neutrosophic probability, set, and logic", F. Smarandache, American Research Press, 1998].
References in periodicals archive ?
14] Florentin Smarandache, Degree of Dependence and Independence of the (Sub) Components of Fuzzy Set and Neutrosophic Set, Neutrosophic Sets and Systems, vol.
Neutrosophy / Neutrosophic Probability, Set, and Logic", Florentin Smarandache, American Research Press, 1998].
Said Broumi (1), Assia Bakali (2), Mohamed Talea (3), Florentin Smarandache (4)
Florentin Smarandache, currently associate professor of mathematics at the University of New Mexico University, is a Romanian exile who has spent years in Turkish refugee camps and who lost many of the manuscripts that he had tried to get out of the country during the Ceausescu era.
1] Ion Patrscu and Florentin Smarandache, A Theorem about Simultaneous Orthological and Homological Triangles, in arXiv.
Zadeh, founder of the fuzzy logic (FL) idea, which he established in 1965 [7], and Professor Florentin Smarandache, founder of the neutrosophic logic (NL) idea, which he established in 1995 [1].
1] Florentin Smarandache, Neutrosophic Overset, Neutrosophic Underset, and Neutrosophic Offset.
Florentin Smarandache (born on December 10, 1954)--polymath, professor of mathematics, scientist, poet and writer (originally writting in Romanian, French, and English).
The study of Smarandache Algebraic Structures was initiated in the year 1998 by Raul Padilla following a paper written by Florentin Smarandache called "Special Algebraic Structures".
Vasantha Kandasamy (Indian Instute of Technology, Madras, Chennai) and Florentin Smarandache (U.
7] Florentin Smarandache, Neturosophic logic--Generalization of Intuitionistic Fuzzy Logic, presented at the special session on Intuitionistic Fuzzy Sets and Related Concepts, of International EUSFLAT Conference, Zittau, Germany, 10-2 September 2003.