An aleatoric description logic for probabilistic reasoning

Tim French, Thomas Smoker

Research output: Contribution to journalConference articlepeer-review

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 aleatoric description logic is shown to be able to model learning, via Bayesian conditioning.

Original languageEnglish
JournalCEUR Workshop Proceedings
Volume2954
Publication statusPublished - 2021
Event34th International Workshop on Description Logics, DL 2021 - Bratislava, Slovakia
Duration: 19 Sep 202122 Sep 2021

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