Reasoning About Probabilistic Actions at Multiple Levels of Granularity

Models of physical actions are abstractions of the physical world and can never represent reality precisely. There are two fundamental choices anyone modeling physical action must face: The choice of what granularity to represent actions at and the choice of how to represent the state description. These two choices are closely coupled and form a basic tradeoff. Finer grain actions require more detail in the state description in order to discern possible interactions between the actions. This extra detail can result in large and complex models that are hard to acquire and tedious to use. Coarser grain actions alleviate the need to discern interactions and thus enable a more abstract state description to be used just as effectively; however, by modeling only coarse grain actions, the models are less flexible and less general. To reap the benefits of coarse-grain actions without sacrificing the flexibility of fine-grain actions, we advocate the use of models at multiple levels of granularity. Few (if any) existing frameworks support action models at multiple levels of granularity in a coherent fashion. We demonstrate this fact for the case of standard probabilistic models, and then introduce an approach that can handle multiple granularities and use it to demonstrate the fundamental tradeoff between abstraction and granularity.