Part and Complement: Fundamental Concepts in Spatial Relations

The spatial world consists of regions and relationships between regions. Examples of such relationships are that two regions are disjoint or that one is a proper part of the other. The formal specification of spatial relations is an important part of any formal ontology used in qualitative spatial reasoning or geographical information systems. Various schemes of relationships have been proposed and basic schemes have been extended to deal with vague regions, coarse regions, regions varying over time, and so on. The principal aim of this paper is not to propose further schemes, but to provide a uniform framework within which several existing schemes can be understood, and upon which further schemes can be constructed in a principled manner. This framework is based on the fundamental concepts of part and of complement. By varying these concepts, for example, allowing a part-of relation taking values in a lattice of truth values beyond the two-valued Boolean case, we obtain a family of schemes of spatial relations. The viability of this approach to spatial relations as parameterized by the concepts of part and complement is demonstrated by showing how it encompasses the RCC5 and RCC8 schemes as well as the case of ‘egg–yolk regions’.

[1]  Bernhard Nebel,et al.  Efficient Methods for Qualitative Spatial Reasoning , 2001, J. Artif. Intell. Res..

[2]  Anthony G. Cohn,et al.  The ‘Egg-Yolk’ Representation of Regions with Indeterminate Boundaries , 2020 .

[3]  John G. Stell,et al.  Granulation for Graphs , 1999, COSIT.

[4]  John G. Stell.  The Representation of Discrete Multi-resolution Spatial Knowledge , 2000, KR.

[5]  P. Burrough,et al.  Geographic Objects with Indeterminate Boundaries , 1996 .

[6]  F. Benjamin Zhan,et al.  Approximate analysis of binary topological relations between geographic regions with indeterminate boundaries , 1998, Soft Comput..

[7]  Reinhold Rauh,et al.  Towards Cognitive Adequacy of Topological Spatial Relations , 2000, Spatial Cognition.

[8]  Eliseo Clementini,et al.  Approximate topological relations , 1997, Int. J. Approx. Reason..

[9]  Jochen Renz,et al.  Qualitative Spatial Reasoning with Topological Information , 2002, Lecture Notes in Computer Science.

[10]  Ralf Hartmut Güting,et al.  Explicit Graphs in a Functional Model for Spatial Databases , 1994, IEEE Trans. Knowl. Data Eng..

[11]  Michael F. Worboys,et al.  The Algebraic Structure of Sets of Regions , 1997, COSIT.

[12]  Brandon Bennett,et al.  Modal Logics for Qualitative Spatial Reasoning , 1996, Log. J. IGPL.

[13]  Anthony G. Cohn,et al.  Qualitative Spatial Representation and Reasoning with the Region Connection Calculus , 1997, GeoInformatica.

[14]  Christian Freksa,et al.  Spatial Information Theory. Cognitive and Computational Foundations of Geographic Information Science , 1999, Lecture Notes in Computer Science.

[15]  M. Egenhofer,et al.  Point-Set Topological Spatial Relations , 2001 .

[16]  Anthony G. Cohn,et al.  The EGG/YOLK reliability hierarchy: semantic data integration using sorts with prototypes , 1994, CIKM '94.

[17]  John G. Stell,et al.  Boolean connection algebras: A new approach to the Region-Connection Calculus , 2000, Artif. Intell..

[18]  Max J. Egenhofer,et al.  On the Equivalence of Topological Relations , 1995, Int. J. Geogr. Inf. Sci..

[19]  Antony Galton,et al.  Modes of Overlap , 1998, J. Vis. Lang. Comput..

[20]  Reinhold Rauh,et al.  A Cognitive Assessment of Topological Spatial Relations: Results from an Empirical Investigation , 1997, COSIT.

[21]  Ivo Düntsch,et al.  A relation - algebraic approach to the region connection calculus , 2001, Theor. Comput. Sci..

[22]  M. Egenhofer.  Categorizing Binary Topological Relations Between Regions, Lines, and Points in Geographic Databases , 1998 .