Non-classical Markov logic and network analysis

First order languages express properties of entities and their relationships in rich models of heterogeneous network phenomena. Markov logic is a set of techniques for estimating the probabilities of truth values of such properties. This article generalizes Markov logic in order to allow nonclassical sets of truth values. The new methods directly support uncertainties in both data sources and values. The concepts and methods of categorical logic give precise guidelines for selecting sets of truth values based on the form of a network model. Applications to alias detection, cargo shipping, insurgency analysis, and other problems are given. Open problems include complexity analysis and parallelization of algorithms.