Elementary Logic
Elementary Logic
Elementary Logic
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Natural Deduction (cont.)<br />
Γ, A ⊢ B (→I )<br />
Γ ⊢ A → B<br />
Γ ⊢ A → B<br />
Γ ⊢ B<br />
Γ ⊢ A (→E)<br />
Γ, A ⊢ B ∧ ¬B (¬I )<br />
Γ ⊢ ¬A<br />
Γ ⊢ A Γ ⊢ ¬A (¬E)<br />
Γ ⊢ B<br />
Γ ⊢ A (¬¬I )<br />
Γ ⊢ ¬¬A<br />
Γ ⊢ ¬¬A (¬¬E)<br />
Γ ⊢ A<br />
These inference rules collectively are called System ND (the<br />
propositional part).<br />
Yih-Kuen Tsay (SVVRL @ IM.NTU) <strong>Elementary</strong> <strong>Logic</strong> FLOLAC 2011 29 / 64
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