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首页> 外文会议>Conference of the European Society for Fuzzy Logic and Technology >Non-denoting Terms in Fuzzy Logic: An Initial Exploration
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Non-denoting Terms in Fuzzy Logic: An Initial Exploration

机译：模糊逻辑中的非表示术语：初步探索

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摘要

We introduce two variants of first-order fuzzy logic that can deal with non-denoting terms, or terms that lack existing referents, e.g., Pegasus, the current king of France, the largest number, or 0/0. Logics designed for this purpose in the classical setting are known as free logics. In this paper we discuss the features of free logics and select the options best suited for fuzzification, deciding on the so-called dual-domain semantics for positive free logic with truth-value gaps and outer quantifiers. We fuzzify the latter semantics in two levels of generality, first with a crisp and subsequently with a fuzzy predicate of existence. To accommodate truth-valueless statements about nonexistent objects, we employ a recently proposed first-order partial fuzzy logic with a single undefined truth value. Combining the dual-domain semantics with partial fuzzy logic, we define several kinds of 'inner-domain' quantifiers, relativized by the predicate of existence. Finally, we make a few observations on some of the resulting rules of free fuzzy quantification that illustrate the differences between the two proposed systems of free fuzzy logic and their well known non-free or non-fuzzy variants.
机译：我们引进一阶模糊逻辑的两个变种，可以处理非表示，还是缺乏现有的参照物而言，例如，飞马，法国的现任国王，数量最多，或0/0。为此目的设计的经典设定逻辑被称为自由逻辑。在本文中，我们讨论的自由逻辑功能，并选择最适合于模糊化的选项，决定了所谓的双域语义与真值间隔和外量词积极自由的逻辑。我们将模糊化后的语义在一般性的两个层次，第一个以明快，随后与存在的模糊谓词。为了容纳约存在的对象真没有价值的发言中，我们采用了最近提出的一阶偏模糊逻辑与一个未定义的真值。组合双领域语义与局部模糊逻辑，我们定义了几种“内域”量词，由存在的谓词相对化的。最后，我们使用的部分说明免费模糊逻辑的两个提议的系统及其众所周知的非自由或非模糊变体之间的差异免费模糊量化的产生规则提出一些看法。

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