Towards Statistical Reasoning in Description Logics over Finite Domains (Full Version)

We present a probabilistic extension of the description logic \(\mathcal {ALC}\) for reasoning about statistical knowledge. We consider conditional statements over proportions of the domain and are interested in the probabilistic-logical consequences of these proportions. After introducing some general reasoning problems and analyzing their properties, we present first algorithms and complexity results for reasoning in some fragments of Statistical \(\mathcal {ALC}\).