PDT Logic for Stream Reasoning in Multi-agent Systems

We present Probabilistic Doxastic Temporal (PDT) Logic for streams, a formalism to reason about probabilistic beliefs and their infinite temporal evolution in multi-agent systems. Extending previous work on PDT Logic, this formalism builds on a Markov chain model to represent infinite streams of possible worlds. Within these streams, it enables the quantification of beliefs through probability intervals as well as the representation of temporal relations and epistemic actions. We show how agents can update their beliefs with respect to their observations, provide a model for infinite streams of possible worlds and show how we can map clippings of these streams to finite time windows. Based on these time windows, we introduce an adoption of the semantics of PDT Logic for finite time frames, and show how this provides a means to overcome the limitation of finite time domains.