Degree of truth
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2008-04-21T16:33:07Z
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{{POV|date=December 2007}}
The '''degree of truth''' denotes the extent to which a [[proposition]] is true.
For example, in standard [[mathematics]], the proposition ''zero belongs to the set { 0 }'' has a degree of truth of 1 (true), while proposition ''one belongs to the set { 0 }'' has a degree of truth of 0 (false). In [[fuzzy logic]], the degree of truth of a proposition may be any [[real number]] between 0 and 1, inclusive. It is possible to build a fuzzy set F so that the proposition ''zero belongs to F'' has a degree of truth of 1/2.
Degree of truth should not be confused with a [[probability]]; it is not correct to say that zero has a 50% chance of being in F and a 50% chance of not being in F. Flipping a coin has a 50% chance of being heads and a 50% chance of being tails, but one side definitively appears; therefore a coin flip's result has a degree of truth 1 even though it is a random event. Neither should a degree of truth be confused with an unknown or varying truth value. Consider the sentence ''July 4, 1897 was a sunny day in New York City.'' Even if its truth value is not 1 (a completely cloudless day) or 0 (a completely cloudy day) it is still a definite value; the sunniness does not change with repeated observations of the day.
== Applications ==
Degrees of truth are often significant in [[artificial intelligence]] models where an [[Intelligent agent|agent]] deals with fuzzy concepts. An artificial weather reporter asked "Is it sunny out?" may piece together fuzzy data such as cloud cover, time of day (even a little sun at midnight may be considered sunny), location, season, and so on, to come up with a final yes or no answer.
Similar mathematical techniques can also be used to model uncertainty in non-fuzzy data (such as the aforementioned coin flip); this is usually called a ''degree of belief'' rather than of truth.
==See also==
* [[Bivalence]]
* [[Contextualism]]
* [[Half truths]]
* [[Multi-valued logic]]
* [[False dilemma]]
* [[Relativism]]
* [[Vagueness]]
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[[Category:Fuzzy logic]]
[[Category:Logic]]
[[ru:Степень истины]]