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We propose an IF...THEN... rule-based inference method, which is necessary to construct a natural language dialog system and an expert system. The method is used to estimate a truth qualifier, tauB', when the input proposition is "QA are F is tau" and the IF ... THEN ... rule "IF Q'A' are F' is tauA, THEN Q"A" are F" is tauB" is given and the inference result is "Q"A" is F" is tauB' " (Q, Q', Q": Fuzzy quantifiers, A, A', A": Fuzzy subjects, F, F', F": Fuzzy predicates, tau, tauA, tauB, tauB': Truth qualifiers). We propose a method, which infers a result proposition for monotone Q's and show concrete application examples of using the method. Furthermore, we compare the inference results under various implication functions used for obtaining a truth-value fuzzy set of the rule.