The two primary mathematical underpinnings of artificial intelligence have been first-order predicate logic and probability. Over the 15 or so years there has been substantial research activity on approaches that combine the two, producing various forms of probabilistic logic.  Within machine learning, this work is commonly called Statistical Relational Learning (SRL). At Wisconsin we have been investigating an approach to SRL where we learn probabilistic concepts expressed as a sequence of first-order regression trees.  In such trees, nodes are expressions in first-order logic and the leaves are numbers (hence the phrase 'regression trees,' rather than the more common 'decision trees').  I will present our learning algorithms for two SRL knowledge representations, Relational Dependency Networks (RDNs) and Markov Logic Networks (MLNs), and describe their performance on a variety of 'real world' testbeds, including comparison to alternate approaches. Time permitting, I will also present our work on using a relational database management system (RDBMS) and an optimization method called 'dual decomposition' to substantially speed up inference ('question answering') in MLNs.   Our approach allowed us to handle inference in an MLN testbed with 240 million facts (which lead to 64 billion 'factors' in the grounded Markov network).

Joint work with Bernd Gutmann, Kristian Kersting, Tushar Khot, Sriraam Natarajan, Feng Niu, Chris Re, and Ce Zhang.

Papers available at http://pages.cs.wisc.edu/~shavlik/mlrg/publications.html