Note to semantical interpretation of non-trivial syllogisms with intermediate quantifiers

This paper is a contribution to the study of a special kind of syllogisms with intermediate quantifiers. We stem from our previous papers where a formal theory of the intermediate quantifiers was introduced. Besides other results, we syntactically proved validity of 105 basic syllogisms with them. We also demonstrated how our theory works in the semantic interpretation. In this paper, we will address some special kinds of syllogisms that are non-trivial in the sense that both premises as well as conclusion contain general intermediate quantifiers.