A semantic study of the first-order predicate logic with uncertainty involved |
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Authors: | Xingfang Zhang Xiang Li |
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Institution: | 1. School of Mathematical Sciences, Liaocheng University, Liaocheng, 252059, China 2. School of Economics and Management, Beijing University of Chemical Technology, Beijing, 100029, China
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Abstract: | In this paper, we provide a semantic study of the first-order predicate logic for situations involving uncertainty. We introduce the concepts of uncertain predicate proposition, uncertain predicate formula, uncertain interpretation and degree of truth in the framework of uncertainty theory. Compared with classical predicate formula taking true value in \(\{0,1\}\) , the degree of truth of uncertain predicate formula may take any value in the unit interval \(0,1]\) . We also show that the uncertain first-order predicate logic is consistent with the classical first-order predicate logic on some laws of the degree of truth. |
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