We present a probabilistic extension of action language BC+. Just like BC+ is defined as a high-level notation of answer set programs for describing transition systems, the proposed language, which we call pBC+, is defined as a high-level notation of LPMLN programs---a probabilistic extension of answer set programs. We show how probabilistic reasoning about transition systems, such as prediction, postdiction, and planning problems, as well as probabilistic diagnosis for dynamic domains, can be modeled in pBC+ and computed using an implementation of LPMLN.
We present the language m P cal C + for probabilistic reasoning about actions, which is a generalization of the action language cal C + that allows to deal with probabilistic as well as nondeterministic effects of actions. We define a formal semantics of m P cal C + in terms of probabilistic transitions between sets of states. Using a concept of a history and its belief state, we then show how several important problems in reasoning about actions can be concisely formulated in our formalism.