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Logics for approximate and strong entailments

机译：近似和强蕴涵的逻辑

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摘要

We consider two kinds of similarity-based reasoning and formalise them in a logical setting. In one case, we are led by the principle that conclusions can be drawn even if they are only approximately correct. This leads to a graded approximate entailment, which is weaker than classical entailment. In the other case, we follow the principle that conclusions must remain correct even if the assumptions are slightly changed. This leads to a notion of a graded strong entailment, which is stronger than classical entailment. We develop two logical calculi based on the notions of approximate and of strong entailment, respectively.
机译：我们考虑两种基于相似性的推理，并在逻辑上将其形式化。在一种情况下，我们的原则是即使得出的结论几乎是正确的，也可以得出结论。这导致分级的近似蕴涵，比经典蕴含弱。在另一种情况下，我们遵循以下原则：即使假设稍有变化，结论也必须保持正确。这导致了分级强蕴涵的概念，它比经典蕴涵强。我们分别基于近似和强蕴涵的概念开发了两个逻辑计算。

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