intermediate quantifiers; fuzzy quantifiers; fuzzy natural logic

In this paper, we extend the model of intermediate quantifiers by three new ones, namely “a few, a little” and “several”. We proved some of the fundamental properties of these quantifiers and relations to the other ones. We also demonstrate that they naturally fall in the generalized square of opposition.

In our previous papers, we introduced a general principle in fuzzy natural logic in which the class of intermediate quantifiers can be introduced and proved all of 105 generalized syllogisms. We also proposed generalized Peterson's square of opposition with generalized definitions of contrary, contradictory, sub-contrary and subalterns. This approach is devoted to designing generalized Peterson's rules which will be used for verification of the validity of generalized syllogisms with intermediate quantifiers based on its position inside in generalized Peterson's square of opposition.