Euclidean and Mereological Qualitative Spaces: a Study of SCC and DCC

We determine the implicit assumptions and the structure of the Single and Double Cross Calculi within Euclidean geometry, and use these results to guide the construction of analogous calculi in mereogeometry. The systems thus obtained have strong semantic and deductive similarities with the Euclidean-based Cross Calculi although they rely on a different geometry. This fact suggests that putting too much emphasis on usual classification of qualitative spaces may hide important common-alities among spaces living in different classes.