Point-free Foundation of Geometry and Multivalued Logic

A. N. Whitehead, in two basic books, considers two dierent 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 consid- ered instead of the inclusion. We show that the latter cannot be reduced to the rst one, although this can be done in the framework of multi- valued logics.