A Motion Closed World Asumption

Abstract

Yaman et. al. [Yaman et al., 2004] introduce “go theories” to reason about moving objects. In this paper, we show that this logic often does not allow us to infer that an object is not present at a given place or region, even though common sense would dictate that this is a reasonable inference to make. We define a class of models of go-theories called coherent models. We use this concept to define a motion closed world assumption (MCWA) and develop a notion of MCWA-entailment. We show that checking if a go-theory has a coherent model is NP-complete. An in atom checks if a given object is present in a given region sometime in a given time interval. We provide sound and complete algorithms to check if a ground in literal (positive or negative in atom) can be inferred from a gotheory using the MCWA. In our experiments our algorithms answer such queries in less than 1 second when there are up to 1,000 go-atoms per object.