Signature (First-Order Logic)

first-order-logic

Definition

Signature

A signature is a tuple $(\mathcal{F},\mathcal{P})$ of two countably infinite, pairwise disjoint sets:

• $\mathcal{F}$ — function symbols, each with a fixed arity $n\ge 0$.
• $\mathcal{P}$ — predicate symbols, each with a fixed arity $n\ge 0$.

Together with a countably infinite set $\mathcal{V}$ of variables (disjoint from $\mathcal{F}\cup \mathcal{P}$), the signature defines the non-logical symbols of a first-order language.