Whitehead, in two basic books, considers two different approaches to point-free geometry: the inclusion-based approach, whose primitive notions are regions and inclusion relation between regions, and the connection-based approach, where the connection relation is considered instead of the inclusion. We show that the latter cannot be reduced to the first one, although this can be done in the framework of multivalued logics.
"Point-free Foundation of Geometry and Multivalued Logic." Notre Dame J. Formal Logic 51 (3) 383 - 405, 2010. https://doi.org/10.1215/00294527-2010-024