Гладкий А.В. Введение в современную логику
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∀x( (x) ∨ )
∀x (x) ∨
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x
∃x¬ (x)
∀x( (x) ∨ )
∀x (x) ∨
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∀x (x) ∀y (y)
∃x (x) ∃y (y)
∀x (x)
(y)
∀
∀y (y)
∀
∀x (x) ∃x (x)
∃y∀x (x, y) ∀x∃y (x, y)
∀x( (x)& (x)) ∀x (x)&∀x (x)
∀x (x)&∀x (x) ∀x( (x)& (x))
∃x( (x) ∨ (x)) ∃x (x) ∨∃x (x)
∃x (x) ∨∃x (x) ∃x( (x) ∨ (x))
∀x (x) ∨∀x (x) ∀x( (x) ∨ (x))
∃x( (x)& (x)) ∃x (x)&∃x (x)
∀x( (x) → (x)) ∀x (x) →∀x (x)
∀x( (x) → (x)) ∃x (x) →∃x (x)
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(1)
⎧
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⎪
⎪
⎨
⎪
⎪
⎪
⎩
A : ∀x(S(x) → P (x));
I : ∃x(S(x)&P (x));
E : ∀x(S(x) →¬P (x));
O : ∃x(S(x)&¬P (x)).
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P
S P
∃yS (y)&∃zP(z)
(2)
⎧
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎩
A :(∃yS (y)&∃zP(z)) & ∀x(S(x) → P (x));
I :(∃yS (y)&∃zP(z)) & ∃x(S(x)&P (x));
E :(∃yS (y)&∃zP(z)) & ∀x(S(x) →¬P (x));
O :(∃yS (y)&∃zP(z)) & ∃x(S(x)&¬P (
x)).
∃yS (y)&∃zP(z)
O ∃zP(z)&∃x(S(x)&¬P (x))
I ∃x(S(x)&P (x))
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P (x)&S(x) S(x) →¬P (x) P (x) →¬S(x)
A
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0 <n<1 P
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MP PM MP PM
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SP SP SP SP
A, I, E, O
4
3
=64 AAA, AAI, AAE,...,OOO
64 · 4 = 256
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S P