# Definition:Predicate Logic

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## Definition

**Predicate logic** is a sub-branch of symbolic logic.

It is an extension of **propositional logic** in which the internal structure of simple statements is analyzed.

Thus in **predicate logic**, simple statements are no longer atomic.

The atoms of **predicate logic** are subjects and predicates of simple statements.

There are various formal systems allowing for rigid determination of the theorems of **predicate logic**:

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## Also known as

**Predicate logic** is sometimes referred to as **first-order logic** or **first-order language**, sometimes unhyphenated as **first order**.

Some sources refer to it as **predicate calculus**.

Similarly with propositional logic being referred to as **PropLog**, **predicate logic** is often abbreviated to **PredLog**.

## Also see

- Results about
**predicate logic**can be found**here**.

## Sources

- 1993: M. Ben-Ari:
*Mathematical Logic for Computer Science*... (previous) ... (next): Chapter $1$: Introduction: $\S 1.2$: Propositional and predicate calculus - 1996: H. Jerome Keisler and Joel Robbin:
*Mathematical Logic and Computability*... (previous) ... (next): Chapter $2$: Pure Predicate Logic - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**logic** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**logic**