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否定后件.
在经典逻辑中,否定后件(拉丁语:modus tollens)有如下论证形式:
- 如果P,则Q。
- 非Q。
- 所以,非P。
它也可也被认为是否定结论,是一种有效的认证形式。
否定后件有时会与归谬法 (Proof by contradiction)(假设命题的否定成立,证明这会导致矛盾)或者反证法 (Proof by contrapositive)(证明如果P则Q,通过证明如果非Q则非P的方法实现)相混淆。
证明
步骤
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命题
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推论
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1 |
![{\displaystyle P\rightarrow Q}](https://wikimedia.org/api/rest_v1/media/math/render/svg/86439ea857adc8eaec93c4d14270b8ba6bd2a6a9) |
已知
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2 |
![{\displaystyle \neg Q}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fad34798abb0bbbc063c906e459f103a09b1660e) |
已知
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3 |
![{\displaystyle \neg P\lor Q}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ac1671e840e1ccd6af46246ab7439802c090daab) |
实质条件 (1)
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4 |
![{\displaystyle \neg P}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5eb0d6c8752f8c7256d69c62e77dfe4c466dbe58) |
选言三段论 (3,2)
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