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

TL;DR

This paper introduces a probabilistic extension of description logic ALC to enable reasoning about statistical knowledge and proportions within finite domains, providing initial algorithms and complexity analysis.

Contribution

It presents the first probabilistic extension of ALC for statistical reasoning, along with initial algorithms and complexity results for certain fragments.

Findings

Algorithms for reasoning in probabilistic ALC fragments

Complexity analysis of probabilistic reasoning tasks

Foundational framework for statistical description logics

Abstract

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 $\mathcal{ALC}$.