The basic fuzzy logic BL is extended by two unary connectives L, U
(lower, upper) whose standard semantics is, given a continuous t-norm, the function assigning to each x € [0,1] the biggest idempotent < x (least idempotent > x). An axiom system is presented and shown complete with respect to the corresponding class of algebras. But the set of tautologies for a fixed continuous t-norm may have an arbitrarily high degree of insolvability.