Locally linear time temporal logic

We study linear time temporal logics of multiple agents, where the temporal modalities are local. These modalities not only refer to local next-instants and local eventuality, but also global views of agents at any local instant, which are updated due to communication from other agents. Thus agents also reason about the future, present and past of other agents in the system. The models for these logics are simple: runs of networks of synchronizing automata. Problems like gossiping in interconnection networks am naturally described in the logics proposed here. We present solutions to the satisfiability and model checking problems for these logics. Further since formulas are insensitive to different interleavings of runs, partial order based verification methods become applicable for properties described in these logics