Introduction to Upside-Down Logic: Its Deep Relation to Neutrosophic Logic and Applications

In the study of uncertainty, concepts such as fuzzy sets [113], fuzzy graphs [79], and neutrosophic sets [88] have been extensively investigated. This paper focuses on a novel logical framework known as Upside-Down Logic, which systematically transforms truths into falsehoods and vice versa by altering contexts, meanings, or perspectives. The concept was first introduced by F. Smarandache in [99]. To contribute to the growing interest in this area, this paper presents a mathematical definition of Upside-Down Logic, supported by illustrative examples, including applications related to the Japanese language. Additionally, it introduces and explores Contextual Upside-Down Logic, an advanced extension that incorporates a contextual transformation function, enabling the adjustment of logical connectives in conjunction with flipping truth values based on contextual shifts. Furthermore, the paper introduces Indeterm-Upside-Down Logic and Certain Upside-Down Logic, both of which expand Upside-Down Logic to better accommodate indeterminate values. Finally, a simple algorithm leveraging Upside-Down Logic is proposed and analyzed, providing insights into its computational characteristics and potential applications.