In particular, checking whether T{\displaystyle T} entails F{\displaystyle F} in this condition can be done using the rules of the propositional calculus.
如果宇宙正在膨胀,它在过去必定比较小(这也是蕴涵在膨胀观念中的逻辑结论)。
If the Universe is now expanding, then it must have been smaller in the past.(<- many tacit assumptions here, e.g. a continuous inflation).
The Paley- Wiener theorem immediately implies that if f is a nonzero distribution of compact support(these include functions of compact support), then its Fourier transform is never compactly supported.
Anderson and Belnap(see below) enumerate several"paradoxes of strict implication": for example, a contradiction still implies everything, and everything implies a tautology.
Multi-Genre Natural Language Inference(MultiNLI corpus) is also available: a crowd-sourced collection of 433k sentence pairs annotated with textual entailment information.
B)对于在第n+1步時,從A导出一个新的句子B的每个可能推理規則的应用,展示G蕴涵B。
(b) For each possible application of a rule of inference to A, leading to a new sentence B, show that G implies B.
This category is noteworthy for giving Walt Disney 12 of the 22 Academy Awards, including a posthumous 1968 award, and 10 of its first 12 awards in the category.
Read⊢ A→ A{\displaystyle\vdash A\to A} as"Assuming nothing, infer that A implies A", or"It is a tautology that A implies A", or"It is always true that A implies A".
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