Computational complexity of t-norm based propositional fuzzy logics with rational truth constants

If a continuous t-norm on [0,1] maps pairs of rationals into rationals then the corresponding fuzzy propositional calculus can be extended by rational truth constants and “bookkeeping” axioms for them. (Łukasiewicz t-norm is the classical example.) Computational complexity of such logics is studied. Consequences for fuzzy description logic are formulated.