Qualitative Spatial Representations

The eld of Qualitative Spatial Reasoning is now an active research area in its own right within AI (and also in Geographical Information Systems) having grown out of earlier work in philosophical logic and more general Qualitative Reasoning in AI. In this paper (which is a slightly updated version of Cohn, 1997]) I will survey the state of the art in Qualitative Spatial Reasoning, covering representation and reasoning issues as well as pointing to some application areas. 1 What is Qualitative Reasoning? The principal goal of Qualitative Reasoning (QR) Weld and De Kleer, 1990] is to represent not only our everyday commonsense knowledge about the physical world, but also the underlying abstractions used by engineers and scientists when they create quantitative models. Endowed with such knowledge, and appropriate reasoning methods, a computer could make predictions, diagnoses and explain the behaviour of physical systems in a qualitative manner, even when a precise quantitative description is not available 1 or is computationally intractable. The key to a qualitative representation is not simply that it is symbolic, and utilises discrete quantity spaces, but that the distinctions made in these discretisations are relevant to the behaviour being modelled { i.e. distinctions are only introduced if they are necessary to model some particular aspect of the domain with respect to the task in hand. Even very simple quantity spaces can be very useful, e.g. the quantity space consisting just 1 Note that although one use for qualitative reasoning is that it allows inferences to be made in the absence of complete knowledge, it does this not by probabilistic or fuzzy techniques (which may rely on arbitrarily assigned probabilities or membership values) but by refusing to diierentiate between quantities unless there is suucient evidence to do so; this is achieved essentially by collapsingìndistinguishable' values into an equivalence class which becomes a qualitative quantity. (The case where the indistinguishability relation is not an equivalence relation has not been much considered, except by Kaufman, 1991; Hobbs, 1985].) of f?; 0; +g, representing the two semi-open intervals of the real number line, and their dividing point, is widely used in the literature, e.g. Weld and De Kleer, 1990]. Given such a quantity space, one then wants to be able to compute with it. There is normally a natural ordering (either partial or total) associated with a quantity space, and one form of simple but eeective inference is to exploit …