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doi:10.1016/S0004-3702(97)00046-5 
Copyright © 1997 Published by Elsevier Science B.V.
Qualitative representation of positional information
Eliseo Clementinia, 
, 
, Paolino Di Felice, a and Daniel Hernández, b
Received 1 August 1996;
Abstract
A framework for the qualitative representation of positional information in a two-dimensional space is presented. Qualitative representations use discrete quantity spaces, where a particular distinction is introduced only if it is relevant to the context being modeled. This allows us to build a flexible framework that accommodates various levels of granularity and scales of reasoning. Knowledge about position in large-scale space is commonly represented by a combination of orientation and distance relations, which we express in a particular frame of reference between a primary object and a reference object. While the representation of orientation comes out to be more straightforward, the model for distances requires that qualitative distance symbols be mapped to geometric intervals in order to be compared; this is done by defining structure relations that are able to handle, among others, order of magnitude relations; the frame of reference with its three components (distance system, scale, and type) captures the inherent context dependency of qualitative distances. The principal aim of the qualitative representation is to perform spatial reasoning: as a basic inference technique, algorithms for the composition of positional relations are developed with respect to same and different frames of reference. The model presented in this paper has potential applications in areas as diverse as Geographical Information Systems (GIS), Computer Aided Design (CAD), and Document Recognition.
Author Keywords: Spatial reasoning; Qualitative representation; Distance; Orientation; Position; Frame of reference
References
[1]. D. Altman, Fuzzy set theoretic approaches for handling imprecision in spatial analysis. Internat. J. Geographical Inform. Systems 8 3 (1994), pp. 271–289. View Record in Scopus | Cited By in Scopus (65)
[2]. American Heritage Dictionary, Houghton Mifflin Company, Boston, MA (1982).
[3]. D.H. Ballard and C.M. Brown. In: Computer Vision, Prentice-Hall, Englewood Cliffs, NJ (1982).
[4]. M. Bierwisch, On the grammar of local prepositions. In: Syntax, Semantik und LexikonBierwisch, Motsch and Zimmermann, Editors, Studia Grammatica 29, Akademie-Verlag, Berlin (1988), pp. 1–65.
[5]. Special Volume on Qualitative Reasoning about Physical SystemsD.G. Bobrow, Editor, Artificial Intelligence 24 (1984).
[6]. R. Briggs, Urban cognitive distance. In: R.M. Downs and D. Stea, Editors, Image and Environment: Cognitive Mapping and Spatial Behavior, Aldine, Chicago, IL (1973), pp. 361–388.
[7]. D. Canter and S.K. Tagg, Distance estimation in cities. Environment and Behavior 7 (1975), pp. 59–80.
[8]. W.G. Chase and M.T.H. Chi, Cognitive skill: implications for spatial skill in large-scale environments. In: J.H. Harvey, Editor, Cognition, Social Behavior and the Environment, Lawrence Erlbaum Associates, Hillsdale, NJ (1981), pp. 111–136.
[9]. E. Clementini and P. Di Felice, A model for representing topological relationships between complex geometric features in spatial databases. Inform. Sci. 90 1–4 (1996), pp. 121–136. Abstract | 
PDF (731 K)
| View Record in Scopus | Cited By in Scopus (27)
[10]. A.G. Cohn, The challenge of qualitative spatial reasoning. Comput. Surveys 27 3 (1995), pp. 323–327.
[11]. A.G. Cohn, Calculi for qualitative spatial reasoning. In: Artificial Intelligence and Symbolic Mathematical ComputationJ. Calmet, J.A. Campbell and J. Pfalzgraf, Editors, Lecture Notes in Computer Science 1138, Springer, Berlin (1996), pp. 124–143.
[12]. E. Davis, The MERCATOR representation of spatial knowledge. In: Proceedings IJCAI-83Karlsruhe, Germany, , Morgan Kaufmann, San Mateo, CA (1983), pp. 295–301. View Record in Scopus | Cited By in Scopus (4)
[13]. E. Davis. In: Representing and Acquiring Geographic Knowledge, Morgan Kaufmann, San Mateo, CA (1986).
[14]. E. Davis. In: Representations of Commonsense Knowledge, Morgan Kaufmann, San Mateo, CA (1990).
[15]. R.M. Downs and D. Stea, Cognitive maps and spatial behavior: process and products. In: R.M. Downs and D. Stea, Editors, Image and Environment: Cognitive Mapping and Spatial Behavior, Aldine, Chicago, IL (1973), pp. 8–26.
[16]. R.M. Downs and D. Stea, Editors, Image and Environment: Cognitive Mapping and Spatial Behavior, Aldine, Chicago, IL (1973).
[17]. S. Dutta, Approximate spatial reasoning: integrating qualitative and quantitative constraints. Internat. J. Approximate Reasoning 5 (1991), pp. 307–331.
[18]. M.J. Egenhofer, Deriving the composition of binary topological relations. J. Visual Languages and Computing 5 1 (1994), pp. 133–149. Abstract | PDF (518 K)
| View Record in Scopus | Cited By in Scopus (41)
[19]. B. Faltings and P. Struss, Editors, Recent Advances in Qualitative Physics, MIT Press, Cambridge, MA (1992).
[20]. K.D. Forbus, P. Nielsen and B. Faltings, Qualitative spatial reasoning: the clock projecl. Artificial Intelligence 51 (1991), pp. 417–471. Abstract | PDF (3231 K)
| View Record in Scopus | Cited By in Scopus (50)
[21]. A.U. Frank, Qualitative spatial reasoning with cardinal directions. J. Visual Languages and Computing 3 (1992), pp. 343–371. Abstract | Article | PDF (1827 K)
| View Record in Scopus | Cited By in Scopus (79)
[22]. Spatial Information Theory. A Theoretical Basis for GIS, European Conference, COSIT'93A.U. Frank and I. Campari, Editors, Lecture Notes in Computer Science 716, Springer, Berlin (1993).
[23]. Spatial Information Theory. A Theoretical Basis for GIS, International Conference, COSIT'95A.U. Frank and W. Kuhn, Editors, Lecture Notes in Computer Science 988, Springer, Berlin (1995).
[24]. C. Freksa, Temporal reasoning based on semi-intervals. Artificial Intelligence 54 (1992), pp. 199–227. Abstract | PDF (1547 K)
| View Record in Scopus | Cited By in Scopus (126)
[25]. C. Freksa, Using orientation information for qualitative spatial reasoning. In: Theories and Methods of Spatio-Temporal Reasoning in Geographic Space. International Conference GIS—From Space to TerritoryA.U. Frank, I. Campari and U. Formentini, Editors, Lecture Notes in Computer Science 639, Springer, Berlin (1992), pp. 162–178.
[26]. C. Freksa and R. Röhrig, Dimensions of qualitative spatial reasoning. In: N. Piera Carreté and M.G. Singh, Editors, Proceedings III MACS International Workshop on Qualitative Reasoning and Decision Technologies—QUARDET'93Barcelona, , CIMNE (1993), pp. 483–492.
[27]. C. Freksa and K. Zimmermann, On the utilization of spatial structures for cognitively plausible and efficient reasoning. In: Proceedings 1992 IEEE International Conference on Systems, Man and Cybernetics (1992).
[28]. R.C. Golledge, R. Briggs and D. Demko, The configuration of distances in intra-urban space. In: Proc. Assoc. Amer. Geographers I (1969), pp. 60–65.
[29]. T. Hägerstrand, Migration and area. In: Migration in SwedenD. Hannerberg, T. Hägerstrand and B. Odeving, Editors, Lund Studies in Geography, Series B, Human Geography 13, C.W.K. Gleerup, Lund, Sweden (1957), pp. 27–158.
[30]. R.A. Hart and G.T. Moore, The development of spatial cognition: a review. In: R.M. Downs and D. Stea, Editors, Image and Environment: Cognitive Mapping and Spatial Behavior, Aldine, Chicago, IL (1973).
[31]. D. Hernández, Qualitative Representation of Spatial Knowledge. In: Lecture Notes in Artificial Intelligence 804, Springer, Berlin (1994).
[32]. D. Hernández, E. Clementini and P. Di Felice, Qualitative distances. In: Spatial Information Theory. A Theoretical Basis for GIS, International Conference, COSIT'95A.U. Frank and W. Kuhn, Editors, Lecture Notes in Computer Science 988, Springer, Berlin (1995), pp. 45–57.
[33]. A. Herskovits. In: Language and Spatial Cognition. An Interdisciplinary Study of the Prepositions in English, Cambridge University Press, Cambridge, MA (1986).
[34]. M. Herweg, Zur Semantik einiger lokaler Präpositionen des Deutschen. In: Tech. Rept. LILOG-Report #21, IBM Deutschland GmbH (1988).
[35]. J.R. Hobbs, Granularity. In: A. Joshi, Editor, Proceedings IJCAI-85Los Angeles, CA, , Morgan Kaufmann, San Mateo, CA (1985), pp. 432–435.
[36]. S. Högg and I. Schwarzer, Composition of spatial relations. In: Forschungsberichte Künstliche Intelligenz FKI-163-9I, Institut für Informatik, Technische Universität München (1991).
[37]. R. Jackendoff and B. Landau, Spatial language and spatial cognition. In: Languages of the Mind: Essays on Mental Representation, MIT Press, Cambridge, MA (1992), pp. 99–124 Chapter 6 .
[38]. J.-H. Jong, Qualitative reasoning about distances and directions in geographic space. In: Ph.D. Thesis, University of Maine (1994).
[39]. J.A. Jorge and D. Vaida, A fuzzy relational path algebra for distances and directions. In: Proceedings ECAI-96 Workshop on Representation and Processing of Spatial Expressions (1996).
[40]. H.-K. Kim, Qualitative kinematics of linkages. In: B. Faltings and P. Struss, Editors, Recent Advances in Qualitative Physics, MIT Press, Cambridge, MA (1992), pp. 137–151.
[41]. B.J. Kuipers, Modelling spalial knowledge. Cognitive Sci. 2 (1978), pp. 129–153. Abstract | View Record in Scopus | Cited By in Scopus (105)
[42]. B.J. Kuipers. In: Qualitative Reasoning. Modeling and Simulation with Incomplete Knowledge, MIT Press, Cambridge, MA (1994).
[43]. T.R. Lee, Perceived dislance as a function of direction in the city. Environment and Behavior 2 (1970), pp. 40–51.
[44]. T. Levitt and D. Lawton, Qualitative navigation for mobile robots. Artificial Intelligence 44 (1990), pp. 305–360. Abstract | PDF (2621 K)
| View Record in Scopus | Cited By in Scopus (88)
[45]. J.C. Lowe and S. Moryadas. In: The Geography of Movement, Houghton Mifflin, Boston, MA (1975).
[46]. K. Lynch. In: The Image of the City, MIT Press, Cambridge, MA (1960).
[47]. A.K. Mackworth, Consistency in networks of relations. Artificial Intelligence 8 (1977), pp. 99–118. Abstract | PDF (1121 K)
| View Record in Scopus | Cited By in Scopus (460)
[48]. M.L. Mavrovouniotis and G. Stephanopoulos, Formal order-of-magnitude reasoning in process engineering. Comput. Chemical Engineering 12 (1988), pp. 867–880. Abstract | PDF (1599 K)
| View Record in Scopus | Cited By in Scopus (29)
[49]. D.V. McDermott and E. Davis, Planning routes through uncertain territory. Artificial Intelligence 22 (1984), pp. 107–156. Abstract | PDF (2527 K)
| View Record in Scopus | Cited By in Scopus (14)
[50]. M. Minsky. In: The Society of Mind, Simon and Schuster, New York (1986).
[51]. D.R. Montello, The perception and cognition of environmental distance: processes and knowledge sources. , Department of Geography, University of California, Santa Barbara, CA (1995) Unpublished Manuscript .
[52]. A. Mukerjee and G. Joe, A qualitative model for space. In: Proceedings AAAI-90Boston, MA, , AAAI Press, Menlo Park (1990), pp. 721–727 CA/MIT Press, Cambridge, MA .
[53]. F.P. Preparata and M.I. Shamos. In: Computational Geometry: An Introduction, Springer, Berlin (1985).
[54]. S. Pribbenow and S. Pribbenow, Zur Verarbeitung von Lokalisierungsausdrücken in einem hybriden System. In: Ph.D. Thesis, Universität Hamburg (1991) reprinted as: ; In: IWBS Report 211 (1992).
[55]. O. Raiman, Order of magnitude reasoning. Artificial Intelligence 51 (1991), pp. 11–38. Abstract | PDF (1244 K)
| View Record in Scopus | Cited By in Scopus (27)
[56]. R. Rajagopalan, A model for integrated qualitative spatial and dynamic reasoning about physical systems. In: Proceedings AAAI-94Seattle, WA, , AAAI Press, Menlo Park (1994), pp. 1411–1417 CA/MIT Press, Cambridge, MA . View Record in Scopus | Cited By in Scopus (3)
[57]. D.A. Randell, Z. Cui and A.G. Cohn, A spatial logic based on regions and connection. In: Proceedings 3rd International Conference on Knowledge Representation and Reasoning (KR-92), Morgan Kaufmann, San Mateo, CA (1992), pp. 165–176.
[58]. G. Reiz-Schmidt, Various views on spatial prepositions. AI Mag. 9 2 (1988), pp. 95–105.
[59]. E.K. Sadalla and S.G. Magel, The perception of traversed distance. Environment and Behaviour 12 (1980), pp. 65–79. View Record in Scopus | Cited By in Scopus (38)
[60]. J. Sharma and D.M. Flewelling, Inferences from combined knowledge about topology and directions. In: 4th International Symposium on Large Spatial Databases, SSD'95J.R. Herring and M.J. Egenhofer, Editors, Lecture Notes in Computer Science, Springer, Berlin (1995).
[61]. T.R. Smith and K.K. Park, Algebraic approach to spatial reasoning. International J. Geographical Inform. Systems 6 3 (1992), pp. 177–192. View Record in Scopus | Cited By in Scopus (26)
[62]. D. Stea, The measurement of mental maps: an experimental model for studying conceptual spaces. In: K.R. Cox and R.G. Golledge, Editors, Behavioral Problems in Geography: A Symposium, Northwestern University Press, Evanston, IL (1969), pp. 228–253.
[63]. L. Talmy, How language structures space. In: H.L. Pick and L.P. Acredolo, Editors, Spatial Orientation: Theory, Research and Application, Plenum Press, New York (1983).
[64]. B. Tversky, Cognitive maps, cognitive collages and spatial mental models. In: Spatial Information Theory. A Theoretical Basis for GIS, European Conference, COSIT'93A.U. Frank and I. Campari, Editors, Lecture Notes in Computer Science 716, Springer, Berlin (1993), pp. 14–24.
[65]. J.B. Weinberg, S. Uckun, G. Biswas and S. Manganaris, Qualitative vector algebra. In: B. Faltings and P. Struss, Editors, Recent Advances in Qualitative Physics, MIT Press, Cambridge, MA (1992), pp. 193–208.
[66]. D.S. Weld and J. de Kleer, Editors, Readings in Qualitative Reasoning about Physical Systems, Morgan Kaufmann, San Mateo, CA (1990).
[67]. Special Volume on Qualitative Reasoning about Physical Systems IIB.C. Williams and J. de Kleer, Editors, Artificial Intelligence 51 (1991).
[68]. D. Wunderlich and M. Herweg, Lokale und Direktionale. In: A. von Stechow and D. Wunderlich, Editors, Handbuch der Semantik, Athenäum, Königstein (1989).
[69]. L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning. In: Memorandum ERL-M 411, University of California at Berkeley, CA (1973).
[70]. H.-J. Zimmermann. In: Fuzzy Set Theory and its Applications, Kluwer, Dordrecht (1992).
[71]. K. Zimmermann, Enhancing qualitative spatial reasoning—combining orientation and distance. In: Spatial Information Theory. A Theoretical Basis for GIS, European Conference, COSIT'93A.U. Frank and I. Campari, Editors, Lecture Notes in Computer Science 716, Springer, Berlin (1993), pp. 69–76.
[72]. K. Zimmermann, Measuring without measures: the delta-calculus. In: Spatial Information Theory. A Theoretical Basis for GIS, International Conference, COSIT'95A.U. Frank and W. Kuhn, Editors, Lecture Notes in Computer Science 988, Springer, Berlin (1995), pp. 59–67.
