Fuzzifying Spatial Relations

Abstract

Reasoning about space plays an essential role in many cultures. Not only is space, like time, one of the most fundamental categories of human cognition, but also does it structure all our activities and relationships with the external world. Space serves as the basis for many metaphors, including temporal metaphors. It is inherently more complex than time, because it is multidimensional and epistemologically multiple.

The way humans often deal with space in everyday situations is on a qualitative basis, allowing for imprecision in spatial descriptions when interacting with each other. Instead of using an absolute space (i.e., space viewed as a “container”, which exists independently of the objects that are located in it), it seems that they prefer a relative space, which is a construct induced by spatial relations over non-purely spatial entities.

In artificial intelligence, a variety of formalisms have been developed that deal with space on the basis of relations between objects. Although most approaches provide some algorithms to reason about such relations, they usually do not make any attempt to address questions like how to handle imprecision in spatial relations or how to combine qualitative spatial relations with quantitative information. Although these questions seem to be unrelated to each other, we show in this chapter that fuzzy logic can provide an answer to both of them.

Partly supported by the University of Auckland Research Committee through various grants (most recently through grant number XXX/9343/3414100).