Topo-distance: Measuring the Difference between Spatial Patterns

Appeared in: M. Ojeda-Aciego, de Guzma I., Brewka G., and Moniz Pereira L. (Eds.), Logics in Artificial Intelligence (JELIA 2000), LNAI 1919, Springer, pages 73-86, 2000. A framework to deal with spatial patterns at the qualitative level of mereotopology is proposed. The main contribution is to provide formal tools for issues of model equivalence and model similarity. The framework uses a multi-modal language S4u interpreted on topological spaces (rather than Kripke semantics) to describe the spatial patterns. Model theoretic notions such as topological bisimulations and topological model comparison games are introduced to define a distance on the space of all topological models for the language S4u. In the process, a new take on mereotopology is given, prompting for a comparison with prominent systems, such as RCC.