Graded hexagon of opposition in fuzzy natural logic with new intermediate quantifiers

In this article, we will form a graded hexagon of opposition as an extension of the graded Peterson's square, incorporating new variations of intermediate quantifiers. We will start with the classical Aristotle's square of opposition and its extension to hexagon. Then we introduce the graded square of opposition that was suggested by Peterson and fully formalized by the authors. We also introduce quantifiers A few ( A little ) and Several and include them in the latter. Then we introduce new forms of quantifiers and study relations of contrary, sub-contrary, contradictory and sub-(sup-)altern among them. On the basis of the knowledge of the relations among all the intermediate quantifiers we construct the graded Peterson's hexagon of opposition. • Graded structures of opposition. • New forms of generalized intermediate quantifiers. • Formal proofs of properties forming graded structures of opposition. • Fuzzy natural logic.