# Definition:Signature (Logic)

Jump to navigation
Jump to search

## Definition

Let $\LL$ be a formal language.

A choice of vocabulary for $\LL$ is called a **signature** for $\LL$.

### Signature for Predicate Logic

Let $\LL_1$ be the language of predicate logic.

Then a **signature** for $\LL_1$ is an explicit choice of the alphabet of $\LL_1$.

That is to say, it amounts to choosing, for each $n \in \N$:

- A collection $\FF_n$ of $n$-ary function symbols
- A collection $\PP_n$ of $n$-ary relation symbols

It is often conceptually enlightening to explicitly address the $0$-ary function symbols separately, as constant symbols.

## Also known as

Some sources refer to a **signature** as a **lexicon**.

Others call it a **language**, particularly in the field of model theory.

However, this is easy to conflate with the generic formal language, and therefore discouraged on $\mathsf{Pr} \infty \mathsf{fWiki}$.

## Also see

There are no source works cited for this page.Source citations are highly desirable, and mandatory for all definition pages.Definition pages whose content is wholly or partly unsourced are in danger of having such content deleted. To discuss this page in more detail, feel free to use the talk page. |