# Logical function

An $n$-place function defined on the set of truth values (cf. Truth value) $\{\text T,\text F\}$ and taking values in this set. With every logical operation $\mathfrak A$ is associated a logical function $f_\mathfrak A$: If $V_1,\ldots,V_n$ are truth values, then $f_\mathfrak A(V_1,\ldots,V_n)$ is the truth value of the proposition $\mathfrak A(P_1,\ldots,P_n)$, where $P_1,\ldots,P_n$ are propositions such that the truth value of $P_i$ is equal to $V_i$, $i=1,\ldots,n$.

A logical function is sometimes defined as an $n$-place function defined on a set $M$ and taking values in the set $\{\text T,\text F\}$. Such functions are used in mathematical logic as an analogue of the concept of a predicate.

**How to Cite This Entry:**

Logical function.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Logical_function&oldid=31700