The challenge of qualitative spatial reasoning

The principal goal of qualitative reasoning (QR,) is to represent not only our everyda<y 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 and diagnoses and explain the behavior of physical systems in a qualitative manner, even when a precise quantitative description is unavailable or computationally intractable. The key to a qualitative representation is not simply that it is symbolic and utilizes discrete quantity spaces, lbut that the distinctions made in these discretizations are relevant to the behavior being modeled. QR has now become a mature subfield of AI, as evidenced by its tenth annual international workshop, several books (e.g., Weld and DeKleer [1990]) and a wealth of conference and journal publications. Although the field has broadened to become more than just qualitative physics (as it was first known), the bulk of the work has dealt with reasoning about scalar quantities, whether they denote the level of a liquid in a tank, the operatirlg region of a transistor, or the amount of unemployment in a model of an economy. Space, which is multidimensional and not adequately represented by single scalar quantities, has only recently become a significant research area with the field of QR and, more generally, in the knowledge representation community. In part this may be due to the Poverty Conjecture promulgated by Forbus et al. [Weld and DeKleer, 1990]: “there is no purely qualitative, generalpurpose kinematics.” Of course, qualitative spatial reasoning (QSR) is more than just kinematics, but it is instructive to recall their third (and strongest) argwment for the conjecture—”No total order: Quantity spaces don’t work in more than one dimension, leaving little hope for concluding much about combining weak information about spatial properties.” They correctly identify transitivity of values as a key feature of a qualitative quantity space but doubt that this can be exploited much in higher dimensions and conclude: “We suspect the space of representations in higher dimensions is sparse; that for spatial reasoning almost nothing weaker than numbers will do.” Happily, over the last few years an increasing amount of research has tended to refute or at least weaken this conjecture. There is a surprisingly rich diversity of qualitative spatial representations, and these can exploit transitivity, as demonstrated by the relatively sparse transitivity tables (cf. the well known table for Allen’s interval temporal logic [Weld and DelKleer 1990]) which have been built for these representations (actually “composition tables” is a better name for these structures). Below, I briefly survey the current state of the art in QSR (see Herrkindez [1994] for a partial survey and bibliography) and attempt to indicate some directions for future research in this area. —