Generalized Intermediate Quantifiers, Generalized Syllogisms, Validity/Invalidity of Syllogisms

This article aims to continue the analysis of generalized Peterson's syllogisms with more premises. Namely, we use the theory of intermediate quantifiers, which provides the mathematical interpretation of natural language expressions indicating the amount or quantity of objects, such as ``Almost all'', ``Several'' etc. In the second part of this paper, we propose an algorithm for the computation of truth degrees of expressions containing such quantifiers and verify the validity/invalidity of several syllogisms.