Intermediate quantifiers; Fuzzy natural logic; Evaluative linguistic expressions; Generalized peterson square; Graded cube of opposition

In our previous papers, we formally analyzed the generalized Aristotle’s square of opposition using tools of higher-order fuzzy logic. Namely, we introduced general definitions of selected intermediate quantifiers, constructed a generalized square of opposition consisting of them and syntactically analyzed the emerged properties. The main objective of this paper is to extend the graded Peterson’s square of opposition into the graded cube of opposition with intermediate quantifiers.