Coherence and Compatibility of Markov Logic Networks

Markov logic is a robust approach for probabilistic relational knowledge representation that uses a log-linear model of weighted first-order formulas for probabilistic reasoning. This log-linear model always exists but may not represent the knowledge engineer's intentions adequately. In this paper, we develop a general framework for measuring this coherence of Markov logic networks by comparing the resulting probabilities in the model with the weights given to the formulas. Our measure takes the interdependence of different formulas into account and analyzes the degree of impact they have on the probabilities of other formulas. This approach can be used by the knowledge engineer in constructing a well-formed Markov logic network if data for learning is not available. We also apply our approach to the problem of assessing the compatibility of multiple Markov Logic networks, i. e., to measure to what extent the merging of these networks results in a change of probabilities.