Natural language statements have quantifiers such as, “most”, “many”, “few”, and “only”. How could ordinary first-order predicate logic with identity (hereafter, FOPL) treat statements containing these vague quantifiers? It seems that FOPL, with only the existential and universal quantifiers at its disposal, is insufficient. I read somewhere that ‘restricted quantification’ notation can ameliorate such problems. Is this true, or are there difficulties with the restricted quantification treatment of vague quantifiers?
What are some of the inference rules for restricted quantification notation? For example, in FOPL you have the existential instantiation and universal instantiation inference rules. Are there analogue inference rules for the quantifiers, "many", “most” and “few”? Can you recommend any books or articles that outline, critique or defend restricted quantification?
I also read that there are issues with FOPL regarding symbolizing adverbs and events from natural language. Is this true...