On Some Tractable Cases of Logical Filtering

Filtering denotes any method whereby an agent updates its belief state—its knowledge of the state of the world—from a sequence of actions and observations. In logical filtering, the belief state is a logical formula describing the possible world states. Efficient algorithms for logical filtering bear important implications on reasoning tasks such as planning and diagnosis. In this paper, we will identify classes of transition constraints that are amenable to compact and indefinite filtering—presenting efficient algorithms wherever necessary. We will first show that connected row-convex (CRC) constraints are amenable to efficient filtering when path-consistency is enforced in appropriate steps. We will then extend this theory to provide a filtering algorithm based on repeatedly enforcing path-consistency and embedding the domain values of the related variables in tree structures to guarantee global consistency. Finally, we will identify and comment on the problem of multi-agent localization as a potential application of the theory developed in the paper (under some reasonable assumptions).