---
tag: BXBNDHV1HW
kind: concept
name: Function symbol
aliases: [empty-theory, free-theory, function-letter, function-symbol-logic, function-symbols, functional-predicate, mapping-logic, uninterpreted-function, uninterpreted-term]
sources:
  - wikipedia: en:174908@r1315877491
    locator: Function symbol
    note: adopted
    mention: wikipedia://en/174908
    sections: [Summary]
same_as:
  wikidata: Q5508846
  wikipedia: Function symbol
inventory: [30Z1Q9TGRC]
---

## Summary

In formal systems particularly mathematical logic, a **function symbol** is a non-logical symbol which represents a [[function|0EPAT51DXQ]] or mapping on the domain of discourse, though, formally, does not need to represent anything at all. Function symbols are a basic component in formal languages to form terms. Specifically, if the symbol $F$ is a function symbol, then given any constant symbol $X$ representing an object in the language, $F(X)$ also represents an object in the language. Similarly, if $T$ is some term in the language, $F(T)$ is also a term. As such, the interpretation of a function symbol must be defined over the whole domain of discourse. Function symbols are a primitive notion, and are therefore not defined in terms of other, more basic concepts.