I'm new here. I wish to ask a question regarding predicate logic:
I was given three predicates:
parent(p,q): p is the parent of q.
female(p): p is a female.
p = q: p and q are the same person.
Now, I was tasked with translating this sentence: Alice has a daughter.
My answer was: There exists a q such that parent(Alice,female(q)).
The answer given is: There exists a q such that female(q) AND parent(Alice,q).
Is it correct to have a predicate (in this case, female) within another predicate (in this case, parent)?
Much appreciated.
Intuitively, a predicate in a predicate doesn't make sense; predicates only take terms as arguments. Using the normal convention of abbreviating predicates and terms by letters ($P(p,q)$ for parent, $F(q)$ for female, $a$ for Alice), your example is $$\exists q\ P(a,F(q))$$ which is interpreted as "Alice is the parent of true" – absurd, since children aren't truth values. In other words, your attempt does not produce a well-formed formula.
The given answer translates as $$\exists q\ F(q)\land P(a,q)$$ which is well-formed.