An important component of spatial data quality is the imprecision resulting from the resolution at which data are represented. Current research on topics such as spatial data integration and generalization needs to be well-founded on a theory of multi-resolution. This paper provides a formal framework for treating the notion of resolution and multi-resolution in geographic spaces. It goes further to develop an approach to reasoning with imprecision about spatial entities and relationships resulting from finite resolution representations. The approach is similar to aspects of rough and fuzzy set theories. The paper concludes by providing the beginnings of a geometry of vague spatial entities and relationships.