Spatial Reasoning Using Symbolic Arrays

In this paper we have proposed the use of multi-level knowledge representation techniques for Geographic Information Systems. We believe that adopting different levels of representations can significantly improve the functionality and efficiency of a system. Although we have presented symbolic arrays as a medium for organising spatial knowledge, this is by no means the only way for structuring hierarchical knowledge. Some of the questions we are currently working on include: 1] Problems of implementation. This involves the separation of the abstract notion of the symbolic array from the actual implementation. We are currently working on formal methods for representing spatial relationships among physical spatial concepts in symbolic arrays (similar work can be found in [5]) and we are developing algorithms for the creation and update of symbolic arrays in order to have an optimal size without the loss of useful information. 2] Query Optimisation. This area involves the study of the relations and the combinations of relations that can be encoded in a symbolic array in order to facilitate query optimisation for some classes of queries. 3] Learning. One interesting subject is learning knowledge rules from relational databases. Learning techniques (such as the ones described in [4]) incorporate knowledge encoded in concept hierarchies in order to extract rules from large amounts of data. We believe that symbolic arrays not only provide a means for representing concept hierarchies, but also a means for representing extracted rules. 4] Deduction and Induction. Symbolic arrays provide the capability for inference (deduction and induction). Logic interfaces can be used not only to extract propositional information from symbolic arrays, but also to modify symbolic arrays with respect to propositional information. 8 Information embodied in a symbolic array can be represented in different ways, for instance, using binary relations or sets of propositions. Although information in the symbolic representation can be expressed as a set of propositions, the representations are not computationally equivalent; that is, the efficiency of the inference mechanisms is not the same [10]. The spatial structure of symbolic arrays possesses properties which help avoid the combinatorial explosion of correct but trivial inferences that must be explicitly represented in a propositional system. Lindsay argues that spatial representations (symbolic arrays in our case) support non-deductive inference by a constraint satisfaction mechanism built into the processes that construct and access them [11]. Consider for example the spatial representation of the map of Europe. To retrieve the information …