Discussion
What is an interpretation in first order logic?
Answer: C
An interpretation supplies a non-empty domain of objects and assigns each constant an object, each function symbol a mapping and each predicate a relation, and a sentence is then true or false in it. Truth value assignment is the propositional analogue and is insufficient here. Proofs and translations are different objects. Specifying meaning by fixing a domain and interpreting every symbol is what makes truth in first order logic precise. Checking the units of each quantity catches a wrong formula before the arithmetic begins.
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