Truth value
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In logic, a truth value, or truth-value, is a value indicating to what extent a statement is true.
In classical logic, the only possible truth values are true and false. However, other values are possible in other logics. A simple intuitionistic logic has truth values of true, false, and unknown; fuzzy logic and other forms of multi-valued logic also use more truth values than simply true and false.
Algebraically, the set {true,false} forms a simple Boolean algebra. Other Boolean algebras may be used as sets of truth values in multi-valued logic, while intuitionistic logic generalises Boolean algebras to Heyting algebras.
In topos theory, the subobject classifier of a topos takes the place of the set of truth values.
References
- Article on logical constants (http://plato.stanford.edu/entries/logical-constants/) at the Stanford Encyclopedia of Philosophy;
- Weblog entry "How many is two?" (http://home.andrej.com/math/2005/05/16/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.