Summary of Quantifier Negation Rules
| Quantifier Negation
Rule
(QNR) |
|
| ~(x)Fx ⊃ (∃x)~Fx | |
| ~(∃x)Fx ⊃ (x)~Fx |
| Categorical Quantifier
Negation Rule (CQNR) |
|
| (x)(Sx ⊃ Px) ≡ ~(∃x)(Sx & ~Px) | |
| (x)(Sx ⊃ ~Px) ≡ ~(∃x)(Sx & Px) | |
| ~(x)(Sx ⊃ Px) ≡ (∃x)(Sx & ~Px) | |
| ~(x)(Sx ⊃ ~Px) ≡ (∃x)(Sx & Px) |
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