The interpretation also defines predicate symbols as denoting a subset of the relevant Herbrand base, effectively specifying which ground atoms are true in the interpretation. This allows the symbols in a set of clauses to be interpreted in a purely syntactic way, separated from any real instantiation.
The interpretation assigns predicate symbols to correspond with a segment of the Herbrand base, thus identifying which ground atoms should be deemed true in the interpretation. This method permits the symbols in a clause set to be interpreted solely based on syntax, not involving actual instantiations.