  We formulate and prove logical characterizations of crisp simulations and
crisp directed simulations between fuzzy labeled transition systems with
respect to fuzzy modal logics that use a general t-norm-based semantics. The
considered logics are fragments of the fuzzy propositional dynamic logic with
the Baaz projection operator. The logical characterizations concern
preservation of positive existential (respectively, positive) modal formulas
under crisp simulations (respectively, crisp directed simulations), as well as
the Hennessy-Milner property of such simulations.
