How do I write the predicate logic notation for a proposition containing a plural argument?

Question

I need to translate a sentence with an indefinite plural object, as in "I eat apples" to predicate logic notation.

If I write it as EAT(i, a), how will the plurality of the argument be accounted for (if it needs to be accounted for)? On the other hand, I do not know if I should use the universal quantifier or the existential quantifier, because this plural form seems to express generality rather than a quantity such as "all" or "more than one".

I would greatly appreciate any suggestions on how to express the sentence above in predicate logic notation.

Thank you in advance!

Answer 1

The core of the formula in Davidson’s FOL notation is ∃e.∃x.∃y.eat(e,x,y)∧I(x)∧apple(y). As for the plural, one commonly adds something like Plural(y). This looks rather trivial but can have profound consequences in light of a sophisticated background (commonsense) theory. Note that the LF is a conjunction and that all the variables are existentially typed. A great book on this topic is Paul Pietroski’s “Events and semantic architecture.”