Abstract. One shortcoming of classic Descriptions Logics, DLs, is their inability to encode probabilistic knowledge and reason over it. This is, however, a strong demand of some modern applications, e.g. in biology and healthcare. Therefore, probabilistic extensions of DLs are attracting attention nowadays. We introduce the probabilistic DL SHIQP which extends a known probabilistic DL. We in-vestigate two reasoning problems for TBoxes: deciding consistency and com-puting tight probability bounds. It turns out that both problems are not harder than reasoning in the classic counterpart SHIQ. We gain insight into complex-ity sources.
