Dynamic Bayesian Description Logics

It is well known that many artificial intelligence applications need to represent and reason with knowledge that is not fully certain. This has motivated the study of many knowledge representation formalisms that can effectively handle uncertainty, and in particular probabilistic description logics (DLs) [7–9]. Although these logics are encompassed under the same umbrella, they differ greatly in the way they interpret the probabilities (e.g. statistical vs. subjective), their probabilistic constructors (i.e., probabilistic axioms or probabilistic concepts and roles), their semantics, and even their probabilistic independence assumptions. A recent example of probabilistic DLs are the Bayesian DLs, which can express both logical and probabilistic dependencies between axioms [2–4]. One common feature among most of these probabilistic DLs is that they consider the uncertainty degree (i.e., the probability) of the different events to be fixed and static through time. However, this assumption is still too strong for many application scenarios. Consider for example a situation where a grid of sensors is collecting knowledge that is then fed into an ontology to reason about the situation of a large system. Since the sensors might perform an incorrect reading, this knowledge and the consequences derived from it can only be guaranteed to hold with some probability. However, the failure rate of a sensor is not static over time; as the sensor ages, its probability of failing increases. Moreover, the speed at which each sensor ages may also be influenced by other external factors like the weather at the place it is located, or the amount of use it is given. We propose to extend the formalism of Bayesian DLs to dynamic Bayesian DLs, in which the probabilities of the axioms to hold are updated over discrete time steps following the principles of dynamic Bayesian networks. Using this principle, we can not only reason about the probabilistic entailments at every point in time, but also reason about future events given some evidence at different times. This work presents the first steps towards probabilistic reasoning about complex events over time.