 One might also consider generalized quantifiers as an expansion of classical first-order logic (see the entry on  generalized quantifiers).  These quantifiers allow from an expansion between the classical “all” and “some” , and can accommodate quantifiers like “most” , “less than half” , “usually” , etc. They are useful from both a logical and linguistic perspective. For example, Kennedy and Väänänen [2021] use generalized quantifiers to argue that “ uncountable” is a logical notion.