Logical value

In logic and mathematics, a logical value, also called a truth value, is a value indicating the extent to which a proposition is true.

Look up logical in Wiktionary, the free dictionary.

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. Other kinds of algebras may be used as sets of truth values in non-classical logics: for instance, intuitionistic logic uses Heyting algebras.

In 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
• Logical connective
• Slingshot argument
• Negation

External links

• Article on logical constants at the Stanford Encyclopedia of Philosophy

• 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.de:Wahrheitswert

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