Definition:Truth Function

Definition
Let $\mathbb B$ be the set of truth values, and let $k$ be a natural number.

A mapping $f: \mathbb B^k \to \mathbb B$ is called a truth function.

Truth Functions of Connectives
Currently /Connective

In treatments of symbolic logic, the following specific functional notation is sometimes used:


 * The negation connective $\neg$ gives rise to the truth function $f^\neg: \mathbb B \to \mathbb B$.
 * The conjunction connective $\land$ gives rise to the truth function $f^\land: \mathbb B^2 \to \mathbb B$.
 * The disjunction connective $\lor$ gives rise to the truth function $f^\lor: \mathbb B^2 \to \mathbb B$.

And so on.

Also known as
Some sources hyphenate: truth-function.

Others speak of a boolean function or a boolean operator, alluding to the fact that there are two possible outputs.

Also see

 * Definition:Truth Table, a common method for tabulating the definition of a truth function.