Quantitative Method Based on Cotangent Similarity Degree in Three‐Valued Łukasiewicz Logic

Abstract

The main purpose of this paper is to establish a type of quantitative model by using the contangent similarity function in the three-valued Ł ukasiewicz propositional logic system \begin{document}$\text{Ł}_{3}$\end{document} . We introduce the concepts of the cotangent similarity degree, cotangent pseudo-distance and cotangent truth degree of the propositions, together with their basic properties in \begin{document}$\text{Ł}_{3}$\end{document} . We investigate the relationship between the cotangent truth degree and contangent pseudo-distance, and prove the continuity of the logical connectives \begin{document}$\neg, \vee$\end{document} and \begin{document}$\rightarrow$\end{document} in the \begin{document}$\text{Ł}_{3}$\end{document} logical metric space. We propose a graded reduction method and three types of graded reasoning frameworks on the propositions set F(S), and provide several examples and basic properties of it.