Truth value
161711
217011120
2008-06-04T06:08:54Z
Hans Adler
5773149
moved [[Logical value]] to [[Truth value]] over redirect: Undoing absurd page move by now banned editor (JA)
In [[logic]] and [[mathematics]], a '''logical value''', also called a '''truth value''', is a value indicating the extent to which a [[proposition]] is [[truth|true]].
{{Wiktionarypar|logical}}
In [[classical logic]], the only possible truth values are [[true]] and [[false]].
However, other values are possible in other logics:
[[fuzzy logic]] and other forms of [[multi-valued logic]] use more truth values than simply true and false.
Algebraically, the set {true, false} forms a two-element [[Boolean algebra (structure)|Boolean algebra]]. Other kinds of [[Algebra|algebras]] may be used as sets of truth values in non-classical logics: for instance, [[intuitionistic logic]] uses [[Heyting algebra]]s.
In [[topos|topos theory]], the [[subobject classifier]] of a topos takes the place of the set of truth values.
* The '''truth value''' of a [[proposition]] is shown using '''0s''' and '''1s'''.
:[[True]] = 1
:[[False]] = 0
==See also==
* [[Boolean domain]]
* [[Degrees of truth]]
* [[False dilemma]]
* [[Fuzzy logic]]
* [[Logical connective]]
* [[Multivalued logic]]
* [[Relativism]]
* [[Slingshot argument]]
* [[Negation]]
==External links==
* [http://plato.stanford.edu/entries/logical-constants/ Article on logical constants] at the [[Stanford Encyclopedia of Philosophy]]
* [http://math.andrej.com/2005/05/16/how-many-is-two/ Weblog entry "How many is two?"] by [[Andrej Bauer]] discussing the relationship between truth values in intuitionistic logic and topos theory on the one hand and classical logic on the other.
[[Category: Logic]]
[[de:Wahrheitswert]]
[[es:Valor de verdad]]
[[fr:Booléen]]
[[he:ערך אמת]]
[[it:Valore di verità]]
[[ko:진리값]]
[[mk:Вистинитосна вредност]]
[[ja:真理値]]
[[nl:Waarheidswaarde]]
[[pl:Wartość logiczna]]
[[pt:Valor de verdade]]
[[simple:Truth value]]
[[th:ค่าความจริง]]
[[zh:真值]]