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The theory of intermediate quantifiers in fuzzy natural logic revisited and the model of 'Many'

机译：重新审视模糊自然逻辑中的中间量词理论和“许多”模型。

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The fuzzy natural logic (FNL) is a formal theory whose goal is to provide a mathematical model of natural human reasoning whose typical feature is the use of natural language. One of its tasks is to develop a mathematical model of a special class of linguistic quantifiers called intermediate ones. In our previous papers, we introduced a general principle of how intermediate quantifiers can be formed and suggested generalized definitions of the relations of contrary, contradictory, subcontrary, and subalterns between these quantifiers. Based on these relations and following Peterson's book [62], we were able to suggest a formal model of the 5-square of opposition with intermediate quantifiers. This paper picks up the threads of this work and has the following goals: it contributes to the development of the theory of fuzzy natural logic. First, it gets back to some concepts of the theory of evaluative linguistic expressions, introduces slight modifications, and proves some not yet presented properties. Furthermore, it improves the formal theory of intermediate quantifiers; some definitions are made more precise, and some new theorems are proved. Finally, it contributes to the theory of the intermediate quantifier "Many" and the analysis of its position in the mentioned 5-square. We will show that "Many" manifests an ambiguous relation towards the other quantifiers. (C) 2020 Elsevier B.V. All rights reserved.
机译：模糊自然逻辑（FNL）是形式理论，其目标是提供人类自然推理的数学模型，其典型特征是使用自然语言。它的任务之一是开发一种称为中间量词的特殊语言量词的数学模型。在我们以前的论文中，我们介绍了如何形成中间量词的一般原理，并提出了这些量词之间相反，矛盾，子矛盾和子替换关系的广义定义。基于这些关系并遵循彼得森的书[62]，我们能够提出带有中间量词的反对派5平方的正式模型。本文采用了这项工作的思路，并具有以下目标：它为模糊自然逻辑理论的发展做出了贡献。首先，它回到了评价性语言表达理论的一些概念，进行了一些细微的修改，并证明了一些尚未呈现的特性。此外，它改进了中间量词的形式理论;一些定义变得更加精确，并且证明了一些新的定理。最后，它有助于中间量词“ Many”的理论及其在上述5平方中的位置分析。我们将证明“许多”与其他量词之间存在歧义关系。 （C）2020 Elsevier B.V.保留所有权利。

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