Is there a definition of a translation from propositional logic to first order logic?

Question

I want to know if there is a universally applicable definition of a translation from propositional logic to first-order logic. I'm able to translate almost any propositional formula to a first-order logic by defining first-order functions with quantifiers, variables and constant, but i did not found any definition of a translation in my books..

So is there such a definition of a translation? Thank you...

Answer 1

Hold on ....

Many (most?) standard versions of FOL have either (i) a separate class of propositional letters as well as predicate letters, or (ii) allow zero-adic predicates, i.e. predicates that take zero terms to form a wff, and so are in effect acting as propositional letters.

Either way, a PL wff can then just be rendered directly into a corresponding FOL wff (with some change of alphabet perhaps) without using any quantifiers variables or individual constants.

If you are using a textbook which as it happens doesn't build in propositional letters/zero-adic predicates to its version of the language of FOL, then adding them is a trivial variation of no real significance.