Toward a formal representation of space in language: A commonsense reasoning approach

This paper proposes some formal tools for representing the semantic content of French expressions referring to space. These tools consist of first, a relational --or qualitative-geometry encompassing topology, distance notions and projective geometry, as well as temporal notions, thus constituting a rather complete theory of naive space-time; and second, several formalisms to deal with functional aspects of entities such as intrinsic orientation, internal structure and categorizing; more generally, it is claimed that a representation in three levels (geometric, functional and pragmatic) is required to account for spatial expressions' semantics. To analyze the semantics of some of these expressions, this work systematically looks for valid reasoning schemata involving them; this approach also enables the testing of the proposed formal system as well as the evaluation of the definitions obtained for the studied lexemes.