# Definition:Logical Inference

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## Definition

**Logical inference** is the process used in natural deduction to deduce the validity of statement forms from other statement forms by use of proof rules.

Given a set of logical formulae and the proof rules, we **(logically) infer** other formulas.

## Also known as

The term **logical inference** is often used as just **inference**.

This process is sometimes called **logical derivation** or just **derivation**.

## Sources

- 1964: Donald Kalish and Richard Montague:
*Logic: Techniques of Formal Reasoning*... (previous) ... (next): $\text{I}$: 'NOT' and 'IF': $\S 3$