The Probabilistic Description Logic $\mathcal{BALC}$

TL;DR

This paper introduces a Bayesian probabilistic extension of the description logic ALC, called BALC, with a tableau-based reasoning procedure that maintains the same computational complexity as classical ALC.

Contribution

It extends ALC with Bayesian probabilistic reasoning, providing a decision procedure for consistency and inference in this new logic.

Findings

The reasoning problems in BALC are extit{ExpTime}-complete.

A tableau-based decision procedure is proposed for BALC.

The complexity of reasoning remains the same as in classical ALC.

Abstract

Description logics (DLs) are well-known knowledge representation formalisms focused on the representation of terminological knowledge. Due to their first-order semantics, these languages (in their classical form) are not suitable for representing and handling uncertainty. A probabilistic extension of a light-weight DL was recently proposed for dealing with certain knowledge occurring in uncertain contexts. In this paper, we continue that line of research by introducing the Bayesian extension \BALC of the propositionally closed DL \ALC. We present a tableau-based procedure for deciding consistency, and adapt it to solve other probabilistic, contextual, and general inferences in this logic. We also show that all these problems remain \ExpTime-complete, the same as reasoning in the underlying classical \ALC.