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| Function |
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| x ↦f (x) |
| History of the function concept |
| Types bydomain andcodomain |
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| List of specific functions |
ABoolean-valued function (sometimes called apredicate or aproposition) is afunction of the type f : X →B, where X is an arbitraryset and whereB is aBoolean domain, i.e. a generic two-element set, (for exampleB = {0, 1}), whose elements are interpreted aslogical values, for example, 0 =false and 1 =true, i.e., a singlebit ofinformation.
In theformal sciences,mathematics,mathematical logic,statistics, and their applied disciplines, a Boolean-valued function may also be referred to as a characteristic function,indicator function, predicate, or proposition. In all of these uses, it is understood that the various terms refer to a mathematical object and not the correspondingsemiotic sign or syntactic expression.
Informal semantic theories oftruth, atruth predicate is a predicate on thesentences of aformal language, interpreted for logic, that formalizes the intuitive concept that is normally expressed by saying that a sentence is true. A truth predicate may have additional domains beyond the formal language domain, if that is what is required to determine a finaltruth value.
