In logic and proof theory, **natural deduction** is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural" way of reasoning. This contrasts with the axiomatic systems which instead use axioms as much as possible to express the logical laws of deductive reasoning.

Read more about Natural Deduction: Motivation, Judgments and Propositions, Introduction and Elimination, Hypothetical Derivations, Consistency, Completeness, and Normal Forms, First and Higher-order Extensions, Proofs and Type-theory, Classical and Modal Logics

### Famous quotes containing the word natural:

“A book should contain pure discoveries, glimpses of terra firma, though by shipwrecked mariners, and not the art of navigation by those who have never been out of sight of land. They must not yield wheat and potatoes, but must themselves be the unconstrained and *natural* harvest of their author’s lives.”

—Henry David Thoreau (1817–1862)