Garvesh Raskutti has some nice slides on Probabilistic Graphical Models and Markov Logic Networks (Richardson & Domingos 2006).  Markov Logic Networks encode first order predicate logic into a Markov Random Field. The resulting networks can be quite large because statements like “for all x, y, and z, x is y’s parent and z is x’s parent imply z is y’s grandparent” require the existence of $2n^2$ nodes in the graph where $n$ is the number of people considered.  The resulting networks are frequently solved by using Gibbs Sampling.  For even more information Pedro Domingos has put an entire course online at

www.cs.washington.edu/homes/pedrod/803

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