<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". neutrosophic logicsmarandache/NeutLog.txt">http://gallup.unm.edu/neutrosophic logicsmarandache/NeutLog.txt. ["Neutrosophy / Neutrosophic probability, set, and logic", F. Smarandache, American Research Press, 1998]. (1999-10-04)

Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory.