Function symbol

Summary

In formal systems particularly mathematical logic, a function symbol is a non-logical symbol which represents a function 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.