Commonsense Reasoning about Containers using Radically Incomplete Information
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6.1 ContainersWe are primarily concerned with containers and their contents. We distinguish four particular types of containers (figure 5). A closed container is an object or set of objects that completely envelopes an internal cavity. An open container surrounds a cavity on all sides but one, where it has a single opening. An upright open container is an open container with the opening on top. A box with lid is a pair of objects that together form a closed container for a cavity, and that have the property that, if the box is moved, the lid will remain in place. The formal theory of these relations is given in sections 7.3.2, 7.4.3, and 7.4.4. “Closed container”, “open container” and “open upright container” are defined purely in terms of the geometry of the objects involved. “Box with lid” involves both geometrical and physical characteristics, since the constraint that the lid will remain on the box depends on the physical characteristics of the two objects. 
Figure 5: Types of containers In a container made of flexible material, cavities can split and merge; they can open up to the outside world or close themselves off from the outside world.8 To characterize cavities dynamically, we use histories; that is, functions from time to regions[Hay79]. Thus the value of history H at time T is a region denoted Slice(T,H). The place occupied by an object, or by a set of objects, over time is one kind of history. We say that a history Hc is a dynamic cavity of history Hx from time Ta to time Tb if it satisfies these two conditions: At all times Tm strictly between Ta and Tb, Slice(Tm,Hc) is a cavity inside the spatial closed container Slice(Tm,Hx). Hc is weakly continuous. That is, for any time Tm there exists an interval (Tc,Td) and a region R such that throughout (Tc,Td) R is part of Hc. Intuitively, a cavity is weakly continuous if a small marble that can foresee how Hc will evolve and can move arbitrarily quickly can succeed in staying inside Hc. We distinguish three categories of dynamic cavities (figure 6): Hc is a no-exit cavity of Hx if there is no way to escape from Hc except through Hx. Hc is a no-entrance cavity of H if there is no way to get into Hc except through Hx. Hc is a persistent cavity of H if it is both a no-exit and a no-entrance cavity. 
C is a no-exit cavity from TA to TB. D is a no-entrance cavity from TA to TB. Figure 6: Dynamic cavities
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