Tractable subsets of first-order logic are a central topic in AI research. Several of these formalisms have been used as the basis for first-order probabilistic languages. However, these are intractable, losing the original motivation. Here we propose the first non-trivially tractable first-order probabilistic language. It is a subset of Markov logic, and uses probabilistic class and part hierarchies to control complexity. We call it TML (Tractable Markov Logic). We show that TML knowledge bases allow for efficient inference even when the corresponding graphical models have very high treewidth. We also show how probabilistic inheritance, default reasoning, and other inference patterns can be carried out in TML. TML opens up the prospect of efficient large-scale first-order probabilistic inference.

We present an algorithm for learning high-treewidth Markov networks where inference is still tractable. This is made possible by exploiting context specific independence and determinism in the domain. The class of models our algorithm can learn has the same desirable properties as thin junction trees: polynomial inference, closed form weight learning, etc., but is much broader. Our algorithm searches for a feature that divides the state space into subspaces where the remaining variables decompose into independent subsets (conditioned on the feature or its negation) and recurses on each subspace/subset of variables until no useful new features can be found. We provide probabilistic performance guarantees for our algorithm under the assumption that the maximum feature length is k (the treewidth can be much larger) and dependences are of bounded strength. We also propose a greedy version of the algorithm that, while forgoing these guarantees, is much more efficient.Experiments on a variety of domains show that our approach compares favorably with thin junction trees and other Markov network structure learners.