Natural deduction  

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Kunstformen der Natur (1904) by Ernst Haeckel
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Kunstformen der Natur (1904) by Ernst Haeckel

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.

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