Logics for approximate and strong entailments

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• 作者：Francesc Esteva^a ; ^{esteva@iiia.csic.es} ; Lluí ; s Godo^a ; ^{godo@iiia.csic.es} ; Ricardo O. Rodrí ; guez^b ; ^{ricardo@dc.uba.ar} ; Thomas Vetterlein^c ; ^{Thomas.Vetterlein@jku.at}
• 关键词：Non-classical logics ; Similarity-based reasoning ; Approximate entailment ; Strong entailment
• 刊名：Fuzzy Sets and Systems
• 出版年：2012
• 出版时间：16 June, 2012
• 年：2012
• 卷：197
• 期：Complete
• 页码：59-70
• 全文大小：227 K

文摘

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.