*Article* **A Formal Analysis of Generalized Peterson's Syllogisms Related to Graded Peterson's Cube**

**Karel Fiala 1,† and Petra Murinová 2,\*,†**

	- 702 00 Ostrava, Czech Republic

**Abstract:** This publication builds on previous publications in which we constructed syntactic proofs of fuzzy Peterson's syllogisms related to the graded square of opposition. The aim of the publication is to be formally able to find syntactic proofs of fuzzy Peterson's logical syllogisms with forms of fuzzy intermediate quantifiers that design the graded Peterson's cube of opposition.

**Keywords:** fuzzy Peterson's syllogisms; fuzzy intermediate quantifiers; graded Peterson's cube of opposition

**MSC:** 03B16, 03B38, 03B50
