About considering two constants when using Herbrand's universe

Question

Excuse the poor wording if the question wasn't so clear or misleading, tried to word it to the best of my abilities.If it's worded incorrectly please don't hesitate to tell me the correct question or edit it yourself if you can. Here's the purpose of my question:

I'm considering both the father and mother of a person in the universe I am building. Let's name this person John. I have it set up so that in the end it looks like the following:

∃x{~P(f) v [P(x) ^ ~R(x)] v (R(x) ^ ~ A(x)] v ~R(m)} v {A(m) v A(f)}

where:
f :- father of John
m :- mother of John

How exactly would I label anything with an x if, once again, I'm considering both the father and mother for that same argument? If my question is unclear please let me know so that I can explain further. Also, not exactly sure how to tag the question with the proper tags, any help with that would be great.

Answer 1

It's not clear to me what are you trying to translate.

I think that you must start with building the Herbrand's universe.

You have one individual constant : John , and two functions (NOT two individual constant) : "father of _" and "mother of _" :

let J the individual constant meaning John and

let f(x) meaning "the father of x" and m(x) meaning "the mother of x".

You must apply the functions to all constants, so to build up H, the herbrand universe :

H = [ J, f(J), m(J), f(f(J)), f(m(J)), m(m(J)), m(f(J)), ...]