Aleatoric Description Logic for Probailistic Reasoning (Long Version)

TL;DR

This paper introduces aleatoric description logic, a probabilistic extension of description logics that models uncertainty through subjective beliefs about dice biases, enabling reasoning under uncertainty and learning from observations.

Contribution

It presents a novel probabilistic logic framework that generalizes ALC, including algorithms for model-checking and consistency, and demonstrates how agents can learn beliefs from data.

Findings

Aleatoric description logic generalizes ALC with probabilistic reasoning.

Algorithms for model-checking and consistency are developed.

The logic supports belief updating based on observations.

Abstract

Description logics are a powerful tool for describing ontological knowledge bases. That is, they give a factual account of the world in terms of individuals, concepts and relations. In the presence of uncertainty, such factual accounts are not feasible, and a subjective or epistemic approach is required. Aleatoric description logic models uncertainty in the world as aleatoric events, by the roll of the dice, where an agent has subjective beliefs about the bias of these dice. This provides a subjective Bayesian description logic, where propositions and relations are assigned probabilities according to what a rational agent would bet, given a configuration of possible individuals and dice. Aleatoric description logic is shown to generalise the description logic ALC, and can be seen to describe a probability space of interpretations of a restriction of ALC where all roles are functions. Several computational problems are considered and model-checking and consistency checking algorithms are presented. Finally, aleatoric description logic is shown to be able to model learning, where agents are able to condition their beliefs on the bias of dice according to observations.