Abstract
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).
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