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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:
- \(n=0\): Nullary functions (or operations) are usually called constants
- \(n=1\): Unary functions (or operations)
- \(n=2\): Binary functions (or operations)
- \(n=3\): Ternary functions (or operations)
- generally \(n\)-nary functions (or operations)
Table of Contents
Definitions: 1 2 3
- Hoffmann, Dirk W.: "Grenzen der Mathematik - Eine Reise durch die Kerngebiete der mathematischen Logik", Spektrum Akademischer Verlag, 2011