Fuzzy natural logic; Intermediate quantifiers; Intermediate syllogisms; Graded cube of opposition; Evaluative linguistic expressions.

This paper focuses on the use of fuzzy natural logic for analyzing scientific data and describing it in linguistic expression. The outcome consists of IF-THEN rules that utilize evaluative linguistic expressions, enabling the characterization of quantitative data using vague terms such as ``very small'', ``large'', ``medium'', and so on. Therefore, we demonstrate that the theory of intermediate quantifiers (a component of fuzzy natural logic) can be applied to these outputs automatically, allowing for more natural linguistic summaries. In addition, we introduce the idea of using generalized Peterson's logical syllogisms which relate to graded Peterson's cube of opposition for more detailed data analysis.

This paper focuses on the use of fuzzy natural logic for analyzing scientific data and describing it in linguistic expression. The outcome consists of IF-THEN rules that utilize evaluative linguistic expressions, enabling the characterization of quantitative data using vague terms such as ``very small'', ``large'', ``medium'', and so on. Therefore, we demonstrate that the theory of intermediate quantifiers (a component of fuzzy natural logic) can be applied to these outputs automatically, allowing for more natural linguistic summaries. In addition, we introduce the idea of using generalized Peterson's logical syllogisms which relate to graded Peterson's cube of opposition for more detailed data analysis.