Qualitative Spatial Reasoning about Relative Position: The Tradeoff between Strong Formal Properties and Successful Reasoning about Route Graphs

Qualitative knowledge about relative orientation can be expressed in form of ternary point relations. In this paper we present a calculus based on ternary relations. It utilises finer distinctions than previously published calculi. It permits differentiations which are useful in realistic application scenarios that cannot directly be dealt with in coarser calculi. There is a price to pay for the advanced options: useful mathematical results for coarser calculi do not hold for the new calculus. This tradeoff is demonstrated by a direct comparison of the new calculus with the flip-flop calculus.

[1]  J. Renegar,et al.  On the Computational Complexity and Geometry of the First-Order Theory of the Reals, Part I , 1989 .

[2]  S. Levinson.  Frames of reference and Molyneux's question: Cross-linguistic evidence , 1996 .

[3]  Murray Shanahan,et al.  Noise and the Common Sense Informatic Situation for a Mobile Robot , 1996, AAAI/IAAI, Vol. 2.

[4]  Wilfried Brauer,et al.  Spatial Cognition II , 2000, Lecture Notes in Computer Science.

[5]  Klaus Stein,et al.  Qualitative and Quantitative Representations of Locomotion and their Application in Robot Navigation , 1999, IJCAI.

[6]  Andrew U. Frank,et al.  Qualitative Spatial Reasoning with Cardinal Directions , 1991, ÖGAI.

[7]  Reinhard Moratz,et al.  Qualitative Spatial Reasoning about Line Segments , 2000, ECAI.

[8]  S. Levinson,et al.  LANGUAGE AND SPACE , 1996 .

[9]  Christian Freksa,et al.  Using Orientation Information for Qualitative Spatial Reasoning , 1992, Spatio-Temporal Reasoning.

[10]  Anthony G. Cohn,et al.  A new approach to cyclic ordering of 2D orientations using ternary relation algebras , 2000, Artif. Intell..

[11]  James Renegar,et al.  On the Computational Complexity and Geometry of the First-Order Theory of the Reals, Part I: Introduction. Preliminaries. The Geometry of Semi-Algebraic Sets. The Decision Problem for the Existential Theory of the Reals , 1992, J. Symb. Comput..

[12]  Anthony G. Cohn,et al.  Qualitative Spatial Representation and Reasoning Techniques , 1997, KI.

[13]  Gérard Ligozat,et al.  Reasoning about Cardinal Directions , 1998, J. Vis. Lang. Comput..

[14]  Bernd Krieg-Brückner,et al.  Modelling Navigational Knowledge by Route Graphs , 2000, Spatial Cognition.

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

[16]  Eliseo Clementini,et al.  Qualitative Representation of Positional Information , 1997, Artif. Intell..

[17]  Bernhard Nebel,et al.  KI-97: Advances in Artificial Intelligence , 1997, Lecture Notes in Computer Science.

[18]  Kerstin Fischer,et al.  Spatial Knowledge Representation for Human-Robot Interaction , 2003, Spatial Cognition.

[19]  Bernhard Nebel,et al.  Double-Crossing: Decidability and Computational Complexity of a Qualitative Calculus for Navigation , 2001, COSIT.

[20]  Peter B. Ladkin,et al.  On binary constraint problems , 1994, JACM.

[21]  Jean-Claude Latombe,et al.  Robot motion planning , 1970, The Kluwer international series in engineering and computer science.

[22]  Christoph Schlieder,et al.  Reasoning About Ordering , 1995, COSIT.

[23]  Hiroshi Ishiguro,et al.  Acquisition of Qualitative Spatial Representation by Visual Observation , 1999, IJCAI.

[24]  Thomas Röfer,et al.  Route Navigation Using Motion Analysis , 1999, COSIT.

[25]  Gerhard Sagerer,et al.  Projective Relations for 3D Space: Computational Model, Application, and Psychological Evaluation , 1997, AAAI/IAAI.

[26]  Ugo Montanari,et al.  Networks of constraints: Fundamental properties and applications to picture processing , 1974, Inf. Sci..

[27]  Gérard Ligozat,et al.  Qualitative Triangulation for Spatial Reasoning , 1993, COSIT.

[28]  Benjamin Kuipers,et al.  A Logical Account of Causal and Topological Maps , 2001, IJCAI.

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

[30]  Christian Freksa,et al.  Qualitative spatial reasoning using orientation, distance, and path knowledge , 2004, Applied Intelligence.

[31]  James Renegar,et al.  On the Computational Complexity and Geometry of the First-Order Theory of the Reals, Part III: Quantifier Elimination , 1992, J. Symb. Comput..

[32]  Alexander Reinefeld,et al.  Effective Solution of Qualitative Interval Constraint Problems , 1992, Artif. Intell..

[33]  Andrew U. Frank,et al.  Spatial Information Theory A Theoretical Basis for GIS , 1993, Lecture Notes in Computer Science.