Qualitative triangulation for spatial reasoning
This paper presents a systematic way of defining qualitative calculi for spatial reasoning. These calculi, which derive from the concept of qualitative triangulation, allow inference about the relative relationships of punctual objects in two-dimensional space. After introducing the general concept of qualitative triangulation, we discuss the main aspects of some important members of this family of calculi, including the so-called flipflop calculus, which subsumes the relative calculus in dimension one, and the calculus introduced by Freksa (orientation-based spatial inference). This allows us to present in a general setting the notions of coarse and fine inference, as well as the conceptual neighborhood properties of sets of spatial relations. We also show how these calculi can be used for actual inference, and how switching from a particular calculus to a refinement of it can be used to strengthen the inference.
KeywordsNeighborhood Structure Geographic Space Fine Reasoning Spatial Reasoning Spatial Entity
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- [A1183]J. F. Allen, Maintaining Knowledge about Temporal Intervals, Communications of the ACM 26, 11 (1983) 832–843.Google Scholar
- [BeLi85]H. Bestougeff and G. Ligozat, Parametrized abstract objects for linguistic information processing, in: Proceedings of the European Chapter of the Association for Computational Linguistics, Geneva, (1985), 107–115.Google Scholar
- [BeLi89]H. Bestougeff and G. Ligozat, Outils logiques pour le traitement du temps: de la linguistique à l'intelligence artificielle, Masson, Paris, 1989.Google Scholar
- [EgA192]M.J. Egenhofer, K. Al-Taha, Reasoning about Gradual Changes of Topological Relationships, in Frank, A.U., Campari, I. and Formentini, U. (Eds.) Theories and Methods of Spatio-Temporal Reasoning in Geographic Space, Proceedings of the International Conference GIS-From Space to Territory, Pisa, Italy, September 1992, 196–219.Google Scholar
- [Fre91]C. Freksa, Qualitative Spatial Reasoning, in: D.M. Mark & A.U. Frank (Eds.), Cognitive and Linguistic Aspects of Geographic Space, Kluwer, Dordrecht, 1991.Google Scholar
- [Fre92]C. Freksa, Using Orientation Information for Qualitative Spatial Reasoning, in Frank, A.U., Campari, I. and Formentini, U. (Eds.) Theories and Methods of Spatio-Temporal Reasoning in Geographic Space, Proceedings of the International Conference GIS-From Space to Territory, Pisa, Italy, September 1992, 162–178.Google Scholar
- [Gus89]H.W. Güsgen, Spatial reasoning based on Allen's temporal Logic, ICSI TR-89-049, International Computer Science Institute, Berkeley, CA, 1989.Google Scholar
- [He91]D. Hernandez, Relative Representation of Spatial Knowledge: the 2-D case, in: D.M. Mark & A.U. Frank (Eds.), Cognitive and Linguistic Aspects of Geographic Space, Kluwer, Dordrecht, 1991, 373–385.Google Scholar
- [Lig90]G. Ligozat, Weak Representations of Interval Algebras, Proc. AAAI-90, 715–720.Google Scholar
- [Lig91]G. Ligozat, Generalized Interval Calculi, Proc. AAAI-91, 1991, 234–240.Google Scholar
- [MuJo90]A. Mukerjee and G. Joe, A Qualitative Model for Space, Proc. AAAI-90, 1990, 721–727.Google Scholar
- [Ran91]D. Randell, Analysing the familiar: a logical representation of space and time, Third International Workshop on semantics of Time, Space, and Movement, Toulouse, 1991.Google Scholar