The paper aims at contributing to the problem of translating natural (ethnic) language into the framework of formal logic in a structure-preserving way. There are several problems with encoding knowledge in logic-derived formalisms. Among the most difficult are those connected with natural language quantifiers. Even for relatively simple natural language sentences there are readings hard to encode in the classical formal logic. The solution we propose is to expand the language of the classical first-order logic with a number of new quantifier symbols (corresponding to the natural language quantifiers possibly co-occurring in a sentence) with a nonclassical semantics(interpretation) similar in a way to the Mostowski’s generalized quantifier, i.e. as a family of subsets of the Cartesian product of variable ranges. We claim that the logic-based formalism involving such nonclassical quantifier may be considered a good knowledge representation tool closer to the natural language than classical logic.