  Description logics (DLs) are well-known knowledge representation formalisms
focused on the representation of terminological knowledge. Due to their
first-order semantics, these languages (in their classical form) are not
suitable for representing and handling uncertainty. A probabilistic extension
of a light-weight DL was recently proposed for dealing with certain knowledge
occurring in uncertain contexts. In this paper, we continue that line of
research by introducing the Bayesian extension \BALC of the propositionally
closed DL \ALC. We present a tableau-based procedure for deciding consistency,
and adapt it to solve other probabilistic, contextual, and general inferences
in this logic. We also show that all these problems remain \ExpTime-complete,
the same as reasoning in the underlying classical \ALC.
