In a logical calculus, a **signature** \(\Sigma\) is a triple \((V_\Sigma,F_\Sigma,P_\Sigma)\) of the following sets:

- the set of variables \(V_\Sigma\),
- the set of functions \(F_\Sigma\), and
- the set of predicates \(P_\Sigma\).

Every function \(f\in F_\Sigma\) has an arity $n\ge 0$, while for $n=0$ we call the functions constants.

Every predicate \(p\in P_\Sigma\) has an arity \(n\ge 1\).