Complexity Analysis and Variational Inference for Interpretation-based Probabilistic Description Logic

TL;DR

This paper analyzes the computational complexity of probabilistic description logics with rich features and introduces variational inference methods that leverage logical inference to improve efficiency.

Contribution

It provides a detailed complexity analysis and proposes variational inference techniques tailored for expressive probabilistic description logics.

Findings

Inference is PEXP-complete for these logics.

Variational methods can exploit logical inference to enhance efficiency.

The approach bridges logical reasoning and probabilistic inference.

Abstract

This paper presents complexity analysis and variational methods for inference in probabilistic description logics featuring Boolean operators, quantification, qualified number restrictions, nominals, inverse roles and role hierarchies. Inference is shown to be PEXP-complete, and variational methods are designed so as to exploit logical inference whenever possible.