Vocabulary (Predicate Logic)

A vocabulary (signature) $\sigma$ is a collection of:

• a non-empty set $\{c_1,...,c_n\}$ of constants (symbols).
• a possible empty set $\{f_1,...,f_n\}$ of functions (symbols), each of them associated with an integer $\text{arity}(f_i)=a_i\ge 1$.
• a possibly empty set $\{P_1,...,P_n\}$ of predicates (or relations), each of them associated with an integer $\text{arity}(P_i)=a_i\ge 0$.