Relative Adjacencies in Spatial Pseudo-Partitions

Introduction Qualitative spatial reasoning is a valid support for inferring relationships in geographical spaces. In particular, qualitative inferences are cognitively more expressive than quantitative ones, and support reasoning mechanisms in the absence of complete spatial knowledge (Cohn 1997). In geographical space, reasoning on spatial entities is supported by representations that mainly involve topological (Pullar and Egenhofer 1988, Egenhofer 1991, Randell et al. 1992, Clementini et al. 1993, Cui et al.1993) and direction relationships (Freksa 1992, Frank 1996, Sharma 1996, Papadias and Egenhofer 1997, Goyal and Egenhofer, 2000). Those spatial relationships provide useful mechanisms to evaluate the mutual relationships of regions over space. An effective data structure for modelling geographical spaces is based on a partition of space, thus forming a coverage derived from thematic classification (Robinson et al. 1984, Frank et al. 1997). Topological relationships in spatial partitions are mainly based on two operators: adjacency and disjunction. But these operators do not provide many capabilities to qualify the relationships between the regions forming a spatial partition. Alternatives include spatial statistic operators that estimate the spatial variability of a property but not the way elements of this distribution are interrelated. We believe that in many situations there is an interest in analysing how two given regions are in relation one with respect to the other. This should also help to identify local and global structural patterns in a spatial partition.