We propose a family of probabilistic description logics (DLs) that are derived in a principled way from Halpern's probabilistic first-order logic. The resulting probabilistic DLs have a two-dimensional semantics similar to temporal DLs and are well-suited for representing subjective probabilities. We carry out a detailed study of reasoning in the new family of logics, concentrating on probabilistic extensions of the DLs ALC and EL, and showing that the complexity ranges from PTime via ExpTime and 2ExpTime to undecidable.

We propose a new family of probabilistic description logics (DLs) that, in contrast to most existing approaches, are derived in a principled way from Halpern's probabilistic first-order logic. The resulting probabilistic DLs have a two-dimensional semantics similar to certain popular combinations of DLs with temporal logic and are well-suited for capturing subjective probabilities. Our main contribution is a detailed study of the complexity of reasoning in the new family of probabilistic DLs, showing that it ranges from PTime for weak variants based on the lightweight DL EL to undecidable for some expressive variants based on the DL ALC.