Towards an Ontology of Space for GFO

Space and time are basic categories of any top-level ontology. They account for fundamental assumptions of the modes of existence of those individuals that are said to be in space and time. The present paper is devoted to GFO-Space, the ontology of space in the General Formal Ontology (GFO). This ontology is introduced by a set of axioms formalized in first-order logic and further elucidated by consequences of the axiomatization. The theory is based on four primitives: the category of space regions, the relations of being a spatial part and being a spatial boundary, as well as the relation of spatial coincidence. The presence of boundaries and the notion of coincidence witness an inspiration of the ontology by well-motivated ideas of Franz Brentano on space, time and the continuum. Taking up a line of prior investigations of his approach, the present work contributes a further step in establishing a corresponding ontology of space, employing rigorous logical methods.