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

Abstract

We present a probabilistic extension of the description logic $\mathcal{A}\mathcal{LC}$ 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 $\mathcal{A}\mathcal{LC}$.

16 pages. Extended version of "Towards Statistical Reasoning in Description Logics over Finite Domains" published at the 11th International Conference on Scalable Uncertainty Management (SUM 2017)