Editing Liar paradox (section)

===Fuzzy logic===
In [[fuzzy logic]], the truth value of a statement can be any real number between 0 and 1 both inclusive, as opposed to [[Boolean logic]], where the truth values may only be the integer values 0 or 1. In this system, the statement "This statement is false" is no longer paradoxical as it can be assigned a truth value of 0.5,<ref>{{cite journal|last1 = Hájek | first1 = P. | last2 = Paris | first2 = J. | first3 = J. | last3 = Shepherdson | title = The Liar Paradox and Fuzzy Logic | journal = The Journal of Symbolic Logic | volume = 61 | number = 1 | pages = 339–346 | date = Mar 2000 | doi=10.2307/2586541 | jstor = 2586541 | s2cid = 6865763 }}</ref><ref>{{cite journal | last1 = Kehagias | first1 = Athanasios | last2 = Vezerides | first2 = K. | title = Computation of fuzzy truth values for the liar and related self-referential systems | url = http://users.auth.gr/~kehagiat/Papers/journal/2007MVLSC.pdf | journal = Journal of Multiple-Valued Logic and Soft Computing | volume = 12 | number = 5–6 | pages = 539–559 | date = Aug 2006 | access-date = 2021-02-17 | archive-date = 2021-07-08 | archive-url = https://web.archive.org/web/20210708230916/http://users.auth.gr/~kehagiat/Papers/journal/2007MVLSC.pdf | url-status = live }}</ref> making it precisely half true and half false. A simplified explanation is shown below.

Let the truth value of the statement "This statement is false" be denoted by <math display>x</math>. The statement becomes

: <math display="block"> x = NOT(x) </math>

by generalizing the NOT operator to the equivalent [[Zadeh operator]] from [[fuzzy logic]], the statement becomes

: <math display="block"> x = 1 - x </math>

from which it follows that

: <math display="block"> x = 0.5 </math>