intermediate quantifiers and valid syllogisms on eq-algebras

Intermediate quantifiers are expressions of natural language, for example “most, almost all, many, a few” using which we quantify a number of some objects in a given universe. we have shown in [23] that all valid syllogisms with intermediate  quantifiers are a consequence of only two algebraic inequalities and one equality. the result was obtained in the formalism  of lukasiewicz fuzzy type theory whose truth values form a linearly ordered complete mv-algebra. in this paper we will  prove that the same holds if we replace mv-algebra by a much more general ieq-algebra (involutive eq-algebra).