The way in which the term logic as a count noun is actually used by logicians it usually includes a semantics for the formal language Just check the many articles about particular kinds of logics on Wikipedia most have a section Semantics on the same footing as the section Syntax Statements such as that Gdel proved that firstorder logic is complete which can be found everywhere are meaningless unless the logic has a semantics Our article Soundness also presupposes that a logical system has a semantics This is not surprising a logic without a semantics is utterly useless what good does it do to anyone to learn that the uninterpretable sequence of symbols  is a theorem but  is not