  We present a logic for reasoning with if-then formulas which involve
constants for rational truth degrees from the unit interval. We introduce
graded semantic and syntactic entailment of formulas. We prove the logic is
complete in Pavelka style and depending on the choice of structure of truth
degrees, the logic is a decidable fragment of the Rational Pavelka logic (RPL)
or the Rational Product Logic (R{\Pi}L). We also present a characterization of
the entailment based on least models and study related closure structures.
