Towards a Qualitative Representation for Specifying Natural Language

The imprecision of natural language such as X is before Y does not provide any information about the distance between X and Y. The human's way of reasoning often uses incomplete knowledge, and any formalization of natural language should be able to produce qualitative reasoning. For that purpose, we introduce a modeling for specifying cognitive geometry. More precisely, in this paper we tackle the problem of geometric reasoning using a formal representation that is built from an appropriate spatial theory which departs from classical geometry in many points. Instead of basic spatial entities of ordinary geometry such as points, lines and surfaces, we rather consider physical three-dimensional objects used to perceive space based on pointless geometry. Based on Tarski's mereogeometry of solids, we explain how the interpretation of mereogeometry within Lesniewski's framework of mereology leads to a coherent and simplified framework in which qualitative representations (e.g., solids, balls, concentricity, equidistance, etc.) can be expressed.