Definition:Predicate Symbol
Definition
Let $\mathcal L$ be a formal language (for example, the language of predicate logic $\mathcal L_1$).
A predicate symbol is a letter of $\mathcal L$ 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 $\mathcal L$.
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: $\S 2.1$