Definition:Predicate Symbol

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: $\S 2.1$