In this paper, we develop a probabilistic approach to formally represent and reason about the interaction between knowledge and social commitments in Multi-Agent Systems (MASs). Unlike existent approaches that address social commitments within the scope of agent to agent, our approach considers commitments among multiple agents as well. In particular, we introduce a new logic called the probabilistic logic of knowledge and commitment (PCTLkc+). The logic we introduce combines a logic of knowledge and commitment (CTLKC+) with a probabilistic branching-time logic (PCTL). We then extend the resulting logic by adding further operators for the group knowledge and group commitment so that different flavors of the interaction between the two concepts can be nicely captured and reasoned about. A major contribution of this paper is the semantics of group social commitment, which has not been considered in the literature. Target systems are modeled using a new extended version of interpreted systems, a popular formal framework that models the communication between interacting agents and accounts for the uncertainty in MASs. The advancement of the proposed logic over existing logics lies in its expressiveness power that allows one to not only express knowledge and social commitments independently, but also express combinations between them in the presence of uncertainty when the scope of interacting agents goes beyond two.
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