In parameter learning, a partial interpretation most often contains information about only a subset of the parameters in the program. However, standard EM-based algorithms use all interpretations to learn all parameters, which significantly slows down learning. To tackle this issue, we introduce EMPLiFI, an EM-based parameter learning technique for probabilistic logic programs, that improves the efficiency of EM by exploiting the rule-based structure of logic programs. In addition, EM-PLiFI enables parameter learning of multi-head annotated disjunctions in ProbLog programs, which was not yet possible in previous methods. Theoretically, we show that EMPLiFI is correct. Empirically, we compare EMPLiFI to LFI-ProbLog and EMBLEM. The results show that in learning single-head annotated disjunctions, EMPLiFI is the most efficient. In learning multi-head annotated disjunctions, EMPLiFI is more accurate than EMBLEM, while LFI-ProbLog cannot handle this task.

Probabilistic model checking has been developed for verifying systems that have stochastic and nondeterministic behavior. Given a probabilistic system, a probabilistic model checker takes a property and checks whether or not the property holds in that system. For this reason, probabilistic model checking provide rigorous guarantees. So far, however, probabilistic model checking has focused on propositional models where a state is represented by a symbol. On the other hand, it is commonly required to make relational abstractions in planning and reinforcement learning. Various frameworks handle relational domains, for instance, STRIPS planning and relational Markov Decision Processes. Using propositional model checking in relational settings requires one to ground the model, which leads to the well known state explosion problem and intractability. We present pCTL-REBEL, a lifted model checking approach for verifying pCTL properties of relational MDPs. It extends REBEL, a relational model-based reinforcement learning technique, toward relational pCTL model checking. PCTL-REBEL is lifted, which means that rather than grounding, the model exploits symmetries to reason about a group of objects as a whole at the relational level. Theoretically, we show that pCTL model checking is decidable for relational MDPs that have a possibly infinite domain, provided that the states have a bounded size. Practically, we contribute algorithms and an implementation of lifted relational model checking, and we show that the lifted approach improves the scalability of the model checking approach.