Exploiting constraints, sequential structure, and knowledge in Markov logic networks

Thesis (Ph. D.)--University of Rochester. Dept. of Computer Science, 2014.
In this dissertation we propose extensions to Markov logic networks that can improve inference and learning by exploiting deterministic constraints, expert knowledge or se- quential/temporal structure. The dissertation consists of the description of four different approaches. First, we discuss how we can speed up inference and hence learning in Markov logic networks when deterministic constraints are present, using constraint programming techniques. Second, we propose a new probabilistic model (slice normal- ized dynamic Markov logic networks) for reasoning in sequential (temporal) domains, which is more suitable for particle filtering than dynamic conditional random fields. In the third part of the dissertation, we propose a framework for parameter learning in Markov logic networks that can combine the possibly inconsistent knowledge of a domain expert with the information obtained from training data according to Bayesian statistics. Finally, we propose two possible ways of extending propositional Markov logic with modal operators to get a framework that allows reasoning about beliefs and knowledge of agents. Most of our results are general enough to hold also for random fields, and exponential families of probability distributions, due to their close relationship to Markov logic networks.