 The works of Frege and Russell introduced a different perspective on the way to approach logic. In those works, a logic system was given by a formal language and a deductive calculus, namely a set of axioms and a set of inference rules. Let us (for this entry) call such a pair a logical deduction system, and the formulas derivable in the calculus its theorems (nowadays it is common practice in algebraic logic to refer to this type of calculi as Hilbert-style and in proof complexity theory as Frege systems). In Frege and Russell’s approach, a formal (mathematical) semantics of whatever kind (algebraic, model-theoretic, etc.) for the formal languages they used was lacking. The only semantics present was of an intuitive, informal kind.