Multidimensional Mereotopology
نویسنده
چکیده
To support commonsense reasoning about space, we require a qualitative calculus of spatial entities and their relations. One requirement for such a calculus, which has not so far been satisfactorily addressed in the mereotopological literature, is that it should be able to handle regions of different dimensions. Regions of the same dimension should admit Boolean sum and product operations, but regions of different dimensions should not. In this paper we propose a topological model for regions of different dimensions, based on the idea that a region of positive codimension is a regular closed subset of the boundary of a region of the next higher dimension. To satisfy the requirements of the commonsense theory, it is required that regions of the same dimension in the model can be summed, and we show that this is always the case. We conclude with a discussion of the possible applicability of the technical results to commonsense spatial reasoning.
منابع مشابه
Multidimensional Mereotopology with Betweenness
Qualitative reasoning about commonsense space often involves entities of different dimensions. We present a weak axiomatization of multidimensional qualitative space based on ‘relative dimension’ and dimension-independent ‘containment’ which suffice to define basic dimension-dependent mereotopological relations. We show the relationships to other meoreotopologies and to incidence geometry. The ...
متن کاملA Reconciliation of Logical Representations of Space: from Multidimensional Mereotopology to Geometry by
A Reconciliation of Logical Representations of Space: from Multidimensional Mereotopology to Geometry Torsten Hahmann Doctor of Philosophy Graduate Department of Computer Science University of Toronto 2013 Reasoning about spatial knowledge is an important aspect of computational intelligence. Humans easily switch between high-level and low-level spatial knowledge, while computers have tradition...
متن کاملA Theory of Multidimensional Qualitative Space: Semantic Integration of Spatial Theories that Distinguish Interior from Boundary Contact
We extend our multidimensional qualitative theory of space based on relative dimension and containment by closures under intersections and differences and by a new primitive relation of boundary containment, a special kind of incidence. We provide a descriptions of the intended structures which ensure that boundary and interior are always clearly distinguishable. The resulting theory can define...
متن کاملModel-Theoretic Analysis of Asher And Vieu's Mereotopology
Model-Theoretic Analysis of Asher And Vieu's Mereotopology
متن کاملDynamic Mereotopology: A Point-free Theory of Changing Regions. I. Stable and unstable mereotopological relations
Dimiter Vakarelov DYNAMIC MEREOTOPOLOGY
متن کامل