Analyzing Qualitative Spatio-Temporal Calculi using Algebraic Geometry |
| |
Authors: | Diedrich Wolter |
| |
Institution: | SFB/TR 8, Universit?t Bremen , Bremen , Germany |
| |
Abstract: | Abstract Qualitative spatial reasoning is based on calculi which comprise relations and operation tables that encode operations like relation composition. Designing a calculus involves determining these tables and analyzing reasoning properties—a demanding task that is susceptible to errors if performed manually. This paper is concerned with automating computation of operation tables and analysis of qualitative calculi over real-valued domains like the plane ![/></span> <sup>2</sup>. We present an approach to specify qualitative relations using polynomial equations that allows methods from algebraic geometry to be applied. This paper shows how reasoning with qualitative relations can be posed algebraically and demonstrates algebraic reasoning using Gröbner base analysis. We evaluate this approach and describe our implementation, which is freely available as part of the spatial reasoning toolbox SparQ.</td>
</tr>
<tr>
<td align=](/na101/home/literatum/publisher/tandf/journals/content/hscc20/2012/hscc20.v012.i01/13875868.2011.586079/20130531/images/medium/hscc_a_586079_o_uf0025.gif) | |
Keywords: | qualitative spatio-temporal reasoning algebraic geometry geometric theorem proving |
|
|