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.
There exist various formalisms for reasoning in probabilistic action domains. @math + @cite_7 is a generalization of the action language @math + that allows for expressing probabilistic information. The syntax of @math is similar to @math +, as both the languages are extensions of @math . @math expresses probabilistic transition of states through so-called context variables , which are similar to pf constants in @math , in that they are both exogenous variables associated with predefined probability distributions. In @math , in order to achieve meaningful probability computed through @math , assumptions such as all actions have to be always executable and nondeterminism can only be caused by pf constants, have to be made. In contrast, @math does not impose such semantic restrictions, and allows for expressing qualitative and quantitative uncertainty about actions by referring to the sequence of belief'' states---possible sets of states together with probabilistic information. On the other hand, the semantics is highly complex and there is no implementation of @math as far as we know.
@cite_7
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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.