Towards Statistical Reasoning in Description Logics over Finite Domains (Full Version)
This work addresses the challenge of integrating statistical reasoning into description logics, which is incremental as it builds upon existing logical frameworks.
The paper tackles the problem of reasoning about statistical knowledge in description logics by introducing a probabilistic extension of $\mathcal{ALC}$ that handles conditional statements over domain proportions, and it presents initial algorithms and complexity results for fragments of this extension.
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 $\mathcal{ALC}$.