I have in the lectures a sentence in English, which I have to translate to First Order Logic.
Someone who loves all animals loves all humans.
Textbook solution:
∀x.(is_human(x) ⇒ is_animal (x))
⇒
∀y.(is_human(y) ∧ ∀z.(is_animal(z) ⇒ loves(y, z)) ⇒ ∀z.(is_human(z) ⇒ loves(y, z))))
My solution: I would have interpreted the someone as an existential quantifier.
∀x.(is_human(x) ⇒ is_animal (x))
⇒
∃y.(is_human(y) ∧ ∀z.(is_animal(z) ⇒ loves(y, z)) ⇒ ∀z.(is_human(z) ⇒ loves(y, z))))
Why would this be wrong and why assuming that keywords like someone just comes with Existential quantifier is not always correct. Since I have learned that some word just introduce either existential or universal quantifier. But here in this example this is not the case anymore.