Point-free Foundation of Geometry and Multivalued Logic
Cristina Coppola, Giangiacomo Gerla, Annamaria Miranda · Notre Dame Journal of Formal Logic · 2010
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.