Towards a qualitative representation for specifying natural language

International audience—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. I. INTRODUCTION The qualitative representation of information assumes that knowledge about spatial information is expressed with a finite set of qualitative relations. It has a wide number of applications in the fields of computer vision [16], geographic information system [25], autonomous robot navigation [23], natural language understanding [3] and the like. When quantitative descriptions are not available or computationally intractable, qualitative representations appear as fruitful substitutes. For example, a few set of primitives forms the basis of a rich spatial calculus (see e.g., [17]). Assessing situations require to specify relationships between objects of the domain. Then, it seems natural to represent qualitative information with relations. Many approaches in qualitative representation are based on mereological theories. Mereology which is the theory of parts and wholes assumes that the part-of relation is the fundamental primitive [19]. However, mereology by itself is not a sufficient theory to take in account topological relations. For that purpose, mereotopology has been introduced as a common theory for integrating both topology and mereology [8], [24]. As underlined in [10] there are many situations in which mereotopology itself is lacking e.g., direction and orientation relations, distances and sizes or even, shapes. To cope with such deficiencies, mereogeometry which builds on the earlier work of Tarski [21], extends mereology with geometri