Boolean-Valued Function

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

A**boolean domain** **B** is a generic 2-element set, say, **B** = , whose elements are interpreted as logical values, for example, 0 = false and 1 = true.

In the formal 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 corresponding semiotic sign or syntactic expression.

In formal semantic theories of truth, a**truth predicate** is a predicate on the sentence of a formal 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

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In the formal 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 corresponding semiotic sign or syntactic expression.

In formal semantic theories of truth, a

- 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,......
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