Truth functions of further propositional connectives can be defined by means of the t-norm and its residuum, for instance the residual negation formula_98 In this way, the left-continuous t-norm, its residuum, and the truth functions of additional propositional connectives (see the section "Standard semantics" below) determine the truth values of complex propositional formulae in [0, 1]. Formulae that always evaluate to 1 are then called "tautologies" with respect to the given left-continuous t-norm formula_99 or "formula_100tautologies." The set of all formula_100tautologies is called the "logic" of the t-norm formula_99 since these formulae represent the laws of fuzzy logic (determined by the t-norm) which hold (to degree 1) regardless of the truth degrees of atomic formulae. Some formulae are tautologies with respect to "all" left-continuous t-norms: they represent general laws of propositional fuzzy logic which are independent of the choice of a particular left-continuous t-norm. These formulae form the logic MTL, which can thus be characterized as the "logic of left-continuous t-norms."