# Definition:Predicate Symbol

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## Definition

Let $\LL$ be a formal language (for example, the language of predicate logic $\LL_1$).

A **predicate symbol** is a letter of $\LL$ used to describe a predicate or a relation.

The name **predicate symbol** is a gesture to the reader to make clear what such a symbol should (intuitively) represent in the formal language $\LL$.

## Also known as

A **predicate symbol** is also often called a **relation symbol**.

Some sources refer to it as a **predicate letter**.

## Also see

- Definition:Symbol
- Definition:Constant Symbol
- Definition:Function Symbol
- Definition:Signature for Predicate Logic

## Sources

- 1980: D.J. O'Connor and Betty Powell:
*Elementary Logic*... (previous) ... (next): $\S \text{III}$: The Logic of Predicates $(1): \ 2$: Predicate expressions - 2009: Kenneth Kunen:
*The Foundations of Mathematics*... (previous) ... (next): $\mathrm{II}.5$ First-Order Logic Syntax: Definition $\mathrm{II.5.2}$

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- 1964: Donald Kalish and Richard Montague:
*Logic: Techniques of Formal Reasoning*... (previous) ... (next): $\text{III}$: 'ALL' and 'SOME': $\S 1$ - 1996: H. Jerome Keisler and Joel Robbin:
*Mathematical Logic and Computability*: $\S 2.1$