Probabilistic Reasoning in the Description Logic ALCP with the Principle of Maximum Entropy (Full Version)

TL;DR

This paper introduces ALCP, a probabilistic description logic that models uncertain, context-dependent knowledge using maximum entropy, along with reasoning algorithms that ensure desirable probabilistic inference properties.

Contribution

It presents a novel probabilistic description logic ALCP for uncertain, context-dependent knowledge and develops reasoning algorithms based on maximum entropy.

Findings

ALCP effectively models uncertain, context-dependent knowledge.

Reasoning algorithms satisfy key probabilistic logic properties.

The approach enables sound probabilistic inference in complex domains.

Abstract

A central question for knowledge representation is how to encode and handle uncertain knowledge adequately. We introduce the probabilistic description logic ALCP that is designed for representing context-dependent knowledge, where the actual context taking place is uncertain. ALCP allows the expression of logical dependencies on the domain and probabilistic dependencies on the possible contexts. In order to draw probabilistic conclusions, we employ the principle of maximum entropy. We provide reasoning algorithms for this logic, and show that it satisfies several desirable properties of probabilistic logics.