- Boolean-valued function
A

**boolean-valued function**, in some usages a predicate or a proposition, is a function of the type f : X →**B**, where X is an arbitrary set and where**B**is aboolean domain .A

**boolean domain****B**is a generic 2-element set, say,**B**= {0, 1}, whose elements are interpreted aslogical value s, for example, 0 = false and 1 = true.In the

formal science s,mathematics ,mathematical logic ,statistics , and their applied disciplines, a boolean-valued function may also be referred to as acharacteristic function ,indicator function , predicate, orproposition . 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.In formal semantic theories of

truth , a**truth predicate**is a predicate on the sentences 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 final truth value.**References*** Brown, Frank Markham (2003), "Boolean Reasoning: The Logic of Boolean Equations", 1st edition, Kluwer Academic Publishers, Norwell, MA. 2nd edition, Dover Publications, Mineola, NY, 2003.

* Kohavi, Zvi (1978), "Switching and Finite Automata Theory", 1st edition, McGraw–Hill, 1970. 2nd edition, McGraw–Hill, 1978.

* Korfhage, Robert R. (1974), "Discrete Computational Structures", Academic Press, New York, NY.

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Mathematical Society of Japan , "Encyclopedic Dictionary of Mathematics", 2nd edition, 2 vols., Kiyosi Itô (ed.), MIT Press, Cambridge, MA, 1993. Cited as EDM.* Minsky, Marvin L., and Papert, Seymour, A. (1988), "

Perceptrons , An Introduction to Computational Geometry", MIT Press, Cambridge, MA, 1969. Revised, 1972. Expanded edition, 1988.**ee also**

*Boolean algebra (logic)

*Boolean domain

*Boolean logic

*Propositional calculus

*Truth table

*Logic minimization **Equivalent concepts***

Characteristic function

*Indicator function

* Predicate, in some senses.

*Proposition , in some senses.**Related concepts***

Finitary boolean function

*Boolean function

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