This chapter proposes a commonsense understanding of distance and orientation knowledge between extended objects, and presents a formal representation of spatial knowledge. The connection relation is taken as primitive. A new axiom is introduced to govern the connection relation. Notions of ‘near extension’ regions and the ‘nearer’ predicate are coined. Distance relations between extended objects are understood as degrees of the near extension from one object to the other. Orientation relations are understood as distance comparison from one object to the sides of the other object. Therefore, distance and orientation relations are internally related through the connection relation. The ‘fiat projection’ mechanism is proposed to model the mental formation of the deictic orientation reference framework. This chapter shows diagrammatically the integration of topological relations, distance relations, and orientation relations in the RCC frameworks.
TopIntroduction
When we open our eyes, we see a snapshot view of the spatial environment. In this chapter, spatial environments are those in which objects are projectively as large as, or larger than, the body but can be visually apprehended from a single place without appreciable locomotion (Montello, 1993, p. 315). They are vista spatial environments following Montello (1993), or the space surrounding the body following (Tversky, Morrison, Franklin, & Bryant, 1999; Tversky, 2005).
We subjectively decompose snapshot spatial environments into objects and spatial relations among them; recognize them, describe spatial relations, and identify whether it is the target environment which we want to enter, even detect object movements in the environment. For example, when you have the first snapshot view of your office in the morning, you will recognize objects in the room, such as a chair and a desk which are indistinguishable from yours, describe their relations, such as the chair is near and in front of the desk, identify whether it is your office, and detect object movements, such as the chair has been moved a bit to the left than its location when you left yesterday. There are several interesting issues involved in the knowledge that people have about snapshot views of spatial environments.
Firstly, from snapshot views, we only see part of objects, and other parts may be blocked. However, we can recognize them. This can be evidenced by the Gestalt Theory, e.g., (Koehler, 1929; Koffka, 1935; Wertheimer, 1958), and research in object recognition, e.g., (Biederman, 1987; Spelke, 1990; Buelthoff & Edelman, 1992; Humphreys & Khan, 1992; Tarr, 1995; Tarr & Buelthoff, 1995). We can even recognize objects in snapshot views both from the real world and from the virtual world, e.g., films, TV programs, and photos. When you open your office door in the morning, you receive the light reflection from the chair, and you recognize your office chair; when you see a photo of your office, you receive the light reflection from the photo, and you also recognize your office chair. Recognizing objects either in the real environment or in the photo owes to the light reflection and to our recognition activity—we have knowledge about objects. The knowledge of objects resides in the memory and is activated either by some external stimuli or by certain mental desires. Secondly, object recognition means categorization. Objects in the same category are considered equivalent. Rosch, Mervis, Gray, Johnson, & Boyes-Braem (1976) argued that categories of recognized objects are structured such that there is generally one level of abstraction at which we find it easiest to name objects and recognize them the fastest, namely the “basic level category”. The basic level is the first categorization made during perception of the environment. This suggests a link between our spatial knowledge and our spatial descriptions. That is, the spatial knowledge acquired through perception structures our language, i.e., Tversky & Lee (1999).