Definition: Function, Arity and Constant

let $L$ be a logical calculus, $U$ the domain of discourse, and $I(U,L)$ the corresponding interpretation with the valuation function $[[]]_I$.

A function is a non-empty string over an alphabet $s\in L$ interpreted as a function \(U^n\to U\), taking \(n\) input arguments from the domain of discourse and mapping them to a new value from the domain of discourse.

The natural number \(n\ge 0\) of arguments of the function is called its arity. Special cases of arities are:

Examples: 1

Definitions: 1 2 3
Examples: 4

Thank you to the contributors under CC BY-SA 4.0!




  1. Hoffmann, Dirk W.: "Grenzen der Mathematik - Eine Reise durch die Kerngebiete der mathematischen Logik", Spektrum Akademischer Verlag, 2011