Applications of circumscription to formalizing common-sense knowledge
Artificial Intelligence
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Inducing Features of Random Fields
IEEE Transactions on Pattern Analysis and Machine Intelligence
The description logic handbook: theory, implementation, and applications
The description logic handbook: theory, implementation, and applications
Mixtures of deterministic-probabilistic networks and their AND/OR search space
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Sound and efficient inference with probabilistic and deterministic dependencies
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
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There is a growing interest in the logical representation of both probabilistic and deterministic dependencies. While Gibbs sampling is a widely-used method for estimating probabilities, it is known to give poor results in the presence of determinism. In this paper, we consider acyclic Horn logic, a small, but significant fragment of first-order logic and show that Markov chains constructed with Gibbs sampling remain ergodic with deterministic dependencies specified in this fragment. Thus, there is a new subclass of Gibbs sampling procedures known to approximate the correct probabilities and expected to be useful for lots of applications.