Gibbs Sampling in Probabilistic Description Logics with Deterministic Dependencies

In many applications there is interest in representing both probabilistic and deterministic dependencies. This is especially the case in applications using Description Logics (DLs), where ontology engineering usually is based on strict knowledge, while there is also the need to represent uncertainty. We introduce a Markovian style of probabilistic reasoning in first-order logic known as Markov logic and investigate the opportunities for restricting this formalism to DLs. In particular, we show that Gibbs sampling with deterministic dependencies specified in an appropriate fragment remains correct, i.e., probability estimates approximate the correct probabilities. We propose a Gibbs sampling method incorporating deterministic dependencies and conclude that this incorporation can speed up Gibbs sampling significantly.