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
, mathematical logic
, 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
- 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.