Then it is necessary that you have a definition in the “domain” like:
T = a comparison pair for height (Txy where x is taller than y)
?
Technically, the domain is the scope of what you are talking about. In other words, the domain is “what we are talking about.” The domain is part of the translation key. For instance, consider the simple sentence “∃xBx”. To understand it, we need a translation key. So I’ll give two different keys.
Domain: All things
Bx=X is big
So, with this key, the simple sentence translates to “There is a big thing”
Domain: Apples
Bx=X is big
So, with THIS key, the simple sentence translates to “There is a big apple”, because with the second key, we’re only talking about apples.
Now, we can say “there is a big apple” with the first key if we add “Ax=X is an apple” to the key. The simple sentence should be ∃x(Bx&Ax) and we would have “there is a big apple”
So, the translation key has the domain, and all your translations. You need them, otherwise you just have a collection of meaningless symbols. Meaningless symbols can show logical relations but they can’t translate into anything because they have no meaning. For example, A&B has the same logical structure as “tall & wide” even if A&B has no meaning given.
