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.
Probabilistic action domains, especially in terms of probabilistic effects of actions, can be formalized as Markov Decision Process (MDP). The language proposed in @cite_5 aims at facilitating elaboration tolerant representations of MDPs. The syntax is similar to @math . The semantics is more complex as it allows preconditions of actions and imposes less semantical assumption. The concept of unknown variables associated with probability distributions is similar to pf constants in our setting. There is, as far as we know, no implementation of the language. There is no discussion about probabilistic diagnosis in the context of the language. PPDDL @cite_6 is a probabilistic extension of the planning definition language PDDL. Like @math , the nondeterminism that PPDDL considers is only the probabilistic effect of actions. The semantics of PDDL is defined in terms of MDP. There are also probabilistic extensions of the Event Calculus such as @cite_13 and @cite_10 .
@cite_5 @cite_13 @cite_6 @cite_10
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In this paper we present a language to reason about actions in a probabilistic setting and compare our work with earlier work by Pearl.The main feature of our language is its use of static and dynamic causal laws, and use of unknown (or background) variables - whose values are determined by factors beyond our model - in incorporating probabilities. We use two kind of unknown variables: inertial and non-inertial. Inertial unknown variables are helpful in assimilating observations and modeling counterfactuals and causality; while non-inertial unknown variables help characterize stochastic behavior, such as the outcome of tossing a coin, that are not impacted by observations. Finally, we give a glimpse of incorporating probabilities into reasoning with narratives. We present PEC, an Event Calculus (EC) style action language for reasoning about probabilistic causal and narrative information. It has an action language style syntax similar to that of the EC variant Modular-E. Its semantics is given in terms of possible worlds which constitute possible evolutions of the domain, and builds on that of EFEC, an epistemic extension of EC. We also describe an ASP implementation of PEC and show the sense in which this is sound and complete. In this paper, we address the issue of uncertainty in event recognition by extending the Event Calculus with probabilistic reasoning. Markov Logic Networks are a natural candidate for our logic-based formalism. However, the temporal semantics of Event Calculus introduce a number of challenges for the proposed model. We show how and under what assumptions we can overcome these problems. Additionally, we demonstrate the advantages of the probabilistic Event Calculus through examples and experiments in the domain of activity recognition, using a publicly available dataset of video surveillance.