Design and Comparison of Lattices of Topological Relations Based on Galois Lattice Theory

This paper presents an approach to spatial representation and reasoning with lattices of topological relations. This approach is based on the Galois lattice theory that is used to create concepts, by associating sets of objects to sets of attributes. The objects considered here are the base relations of the region connection calculus RCC8 and the attributes are computational conditions that are used in geographic information systems for modeling topological relations. Three lattices, named TgE, TgL, and TgM, involving three sets of computational conditions, are introduced. The design and the properties of these lattices are detailed and then compared on the basis of the underlying computational conditions. Finally the three lattices are compared to each others, and to a fourth lattice, Tp, that is based on the set of all disjunctions of RCC8 relations, with respect to qualitative spatial reasoning capabilities.

[1]  Anthony G. Cohn,et al.  Representing and Reasoning with Qualitative Spatial Relations About Regions , 1997 .

[2]  Rokia Missaoui,et al.  An Incremental Concept Formation Approach for Learning from Databases , 1994, Theor. Comput. Sci..

[3]  Gérard Ligozat.  Simple Models for Simple Calculi , 1999, COSIT.

[4]  Bernhard Nebel,et al.  On the Complexity of Qualitative Spatial Reasoning: A Maximal Tractable Fragment of the Region Connection Calculus , 1999, Artif. Intell..

[5]  Volker Haarslev,et al.  Foundations of Spatioterminological Reasoning with Description Logics , 1998, KR.

[6]  L. Beran,et al.  [Formal concept analysis]. , 1996, Casopis lekaru ceskych.

[7]  Alain Guénoche,et al.  Galois approach to the induction of concepts , 1993 .

[8]  Anthony G. Cohn,et al.  A System Handling RCC-8 Queries on 2D Regions Representable in the Closure algebra of Half-Planes , 1998, IEA/AIE.

[9]  Brian A. Davey,et al.  An Introduction to Lattices and Order , 1989 .

[10]  Ludmila Mangelinck,et al.  Représentation de relations et classification de structures spatiales , 1999 .

[11]  Volker Haarslev,et al.  A Description Logic with Concrete Domains and a Role-forming Predicate Operator , 1999, J. Log. Comput..

[12]  Michael Wessel,et al.  Terminological Default Reasoning about Spatial Information: A First Step , 1999, COSIT.

[13]  Jochen Renz,et al.  Maximal Tractable Fragments of the Region Connection Calculus: A Complete Analysis , 1999, IJCAI.

[14]  Hans W. Guesgen,et al.  Spatial and Temporal Reasoning , 2003, AI Commun..

[15]  Max J. Egenhofer,et al.  A Formal Definition of Binary Topological Relationships , 1989, FODO.

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

[17]  Amedeo Napoli,et al.  Building Viewpoints in an Object-Based Representation System for Knowledge Discovery in Databases , 1999 .

[18]  Anthony G. Cohn,et al.  A Spatial Logic based on Regions and Connection , 1992, KR.

[19]  D. Randell,et al.  Exploiting lattices in a theory of space and time , 1992 .

[20]  Guy W. Mineau,et al.  Automatic Structuring of Knowledge Bases by Conceptual Clustering , 1995, IEEE Trans. Knowl. Data Eng..

[21]  Florence Le Ber,et al.  Design and comparison of lattices of topological relations for spatial representation and reasoning , 2003, J. Exp. Theor. Artif. Intell..

[22]  R. Wille.  Concept lattices and conceptual knowledge systems , 1992 .

[23]  Jayant Sharma,et al.  Topological Relations Between Regions in R² and Z² , 1993, SSD.