  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.
