Hostname: page-component-8448b6f56d-xtgtn Total loading time: 0 Render date: 2024-04-18T15:58:48.359Z Has data issue: false hasContentIssue false
  • English
  • Français

A survey of qualitative spatial representations

Published online by Cambridge University Press:  17 October 2013

Juan Chen ,
Anthony G. Cohn ,
Dayou Liu ,
Shengsheng Wang ,
Jihong Ouyang  and
Qiangyuan Yu
Juan Chen
Affiliation:
College of Computer Science and Technology, Jilin University, Changchun 130012, China; e-mail: chenjuan@jlu.edu.cn Key Laboratory of Symbolic Computing and Knowledge Engineering of Ministry of Education, Jilin University, Changchun 130012, China; e-mail: liudy@jlu.edu.cn, wss@jlu.edu.cn, ouyj@jlu.edu.cn, qiangyuan@jlu.edu.cn School of Computing, University of Leeds, Leeds LS2 9JT, UK; e-mail: a.g.cohn@leeds.ac.uk
Anthony G. Cohn
Affiliation:
School of Computing, University of Leeds, Leeds LS2 9JT, UK; e-mail: a.g.cohn@leeds.ac.uk
Dayou Liu
Affiliation:
College of Computer Science and Technology, Jilin University, Changchun 130012, China; e-mail: chenjuan@jlu.edu.cn Key Laboratory of Symbolic Computing and Knowledge Engineering of Ministry of Education, Jilin University, Changchun 130012, China; e-mail: liudy@jlu.edu.cn, wss@jlu.edu.cn, ouyj@jlu.edu.cn, qiangyuan@jlu.edu.cn
Shengsheng Wang
Affiliation:
College of Computer Science and Technology, Jilin University, Changchun 130012, China; e-mail: chenjuan@jlu.edu.cn Key Laboratory of Symbolic Computing and Knowledge Engineering of Ministry of Education, Jilin University, Changchun 130012, China; e-mail: liudy@jlu.edu.cn, wss@jlu.edu.cn, ouyj@jlu.edu.cn, qiangyuan@jlu.edu.cn
Jihong Ouyang
Affiliation:
College of Computer Science and Technology, Jilin University, Changchun 130012, China; e-mail: chenjuan@jlu.edu.cn Key Laboratory of Symbolic Computing and Knowledge Engineering of Ministry of Education, Jilin University, Changchun 130012, China; e-mail: liudy@jlu.edu.cn, wss@jlu.edu.cn, ouyj@jlu.edu.cn, qiangyuan@jlu.edu.cn
Qiangyuan Yu
Affiliation:
College of Computer Science and Technology, Jilin University, Changchun 130012, China; e-mail: chenjuan@jlu.edu.cn Key Laboratory of Symbolic Computing and Knowledge Engineering of Ministry of Education, Jilin University, Changchun 130012, China; e-mail: liudy@jlu.edu.cn, wss@jlu.edu.cn, ouyj@jlu.edu.cn, qiangyuan@jlu.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

Representation and reasoning with qualitative spatial relations is an important problem in artificial intelligence and has wide applications in the fields of geographic information system, computer vision, autonomous robot navigation, natural language understanding, spatial databases and so on. The reasons for this interest in using qualitative spatial relations include cognitive comprehensibility, efficiency and computational facility. This paper summarizes progress in qualitative spatial representation by describing key calculi representing different types of spatial relationships. The paper concludes with a discussion of current research and glimpse of future work.

Type
Articles
Information
The Knowledge Engineering Review , Volume 30 , Issue 1 , January 2015 , pp. 106 - 136
Copyright
Copyright © Cambridge University Press 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Allen, J. F. 1983. Maintaining knowledge about temporal intervals. Communications of the ACM 26(11), 832–843.CrossRefGoogle Scholar
Balbiani, P., Condotta, J.-F., del Cerro, L. F. 1998. A model for reasoning about bidemensional temporal relations. In Proceedings of the Sixth International Conference on Principles of Knowledge Representation and Reasoning (KR'98), Cohn, A. G., Schubert, L. K. & Shapiro, S. C. (eds). Trento, Italy, June 2–5. Morgan Kaufmann, 124–130.Google Scholar
Balbiani, P., Condotta, J.-F., del Cerro, L. F. 1999a. A new tractable subclass of the rectangle algebra. In Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence, IJCAI 99, Dean, T. (ed.). Stockholm, Sweden, July 31–August 6. Morgan Kaufmann, 442–447.Google Scholar
Balbiani, P., Condotta, J.-F., del Cerro, L. F. 1999b. A tractable subclass of the block algebra: constraint propagation and preconvex relations. In Proceedings of the Progress in Artificial Intelligence, 9th Portuguese Conference on Artificial Intelligence, EPIA ‘99, Évora, Portugal, September 21–24. Lecture Notes in Computer Science 1695, 75–89. Springer.Google Scholar
Balbiani, P., Condotta, J.-F., Ligozat, G. 2006. On the consistency problem for the $$\[--><$>{\cal I}{\cal N}{\cal D}{\cal U}<$><!--$$ calculus. Journal of Applied Logic 4(2), 119–140.Google Scholar
Bédard, Y., Merrett, T., Han, J. 2001. Fundamentals of spatial data warehousing for geographic knowledge discovery. In Research Monographs in GIS, Miller, J. M. & Han, J. (eds). chapter 3. Taylor & Francis, 45–68.Google Scholar
Bennett, B., Isli, A., Cohn, A. G. 1997. When does a composition table provide a complete and tractable proof procedure for a relational constraint language? In Proceedings of the IJCAI97 Workshop on Spatial and Temporal Reasoning, NAGOYA, Aichi, Japan, 1–18.Google Scholar
Bittner, T. 2002. Approximate qualitative temporal reasoning. Annals of Mathematics and Artificial Intelligence 36(1–2), 39–80.CrossRefGoogle Scholar
Bittner, T., Smith, B. 2001. Granular partitions and vagueness. In Proceedings of the 2nd International Conference on Formal Ontology in Information Systems(FOIS 2001), Welty, C. & Smith, B. (eds). Ogunquit, Maine, USA, October 17–19. ACM Press, 309–320.Google Scholar
Bittner, T., Stell, J. G. 2000. Rough sets in approximate spatial reasoning. In Rough Sets and Current Trends in Computing, Second International Conference, RSCTC 2000 Banff, Canada, October 16–19. Lecture Notes in Computer Science 2005, 445–453. Springer.Google Scholar
Bittner, T., Stell, J. G. 2002. Vagueness and rough location. GeoInformatica 6(2), 99–121.Google Scholar
Bogaert, P., de Weghe, N. V., Cohn, A. G., Witlox, F., Maeyer, P. D. 2006. The qualitative trajectory calculus on networks. In Spatial Cognition V: Reasoning, Action, Interaction, International Conference Spatial Cognition 2006, Bremen, Germany, September 24–28, Revised Selected Papers. Lecture Notes in Computer Science 4387, 20–38. Springer.CrossRefGoogle Scholar
Chang, S., Jungert, E., Green, R., Gray, D., Powers, E. 1996. Symbolic Projection for Image Information Retrieval and Spatial Reasoning. Elsevier.Google Scholar
Chang, S. K., Shi, Q. Y., Yan, C. W. 1987. Iconic indexing by 2-D strings. IEEE Transactions on Pattern Analysis and Machine Intelligence 9(3), 413–428.CrossRefGoogle ScholarPubMed
Chen, J., ming Li, C., lin Li, Z., Gold, C. M. 2001. A voronoi-based 9-intersection model for spatial relations. International Journal of Geographical Information Science 15(3), 201–220.CrossRefGoogle Scholar
Chen, J., Jia, H., Liu, D., Zhang, C. 2010a. Inversing cardinal direction relations. In Proceedings of 5th International Conference on Frontier of Computer Science and Technology (FCST 2010), Stojmenovic, I., Farin, G., Guo, M., Jin, H., Li, K., Hu, L., Wei, X. & Che, X. (eds). Changchun, Jilin Province, China, August 18–22. IEEE Computer Society, 276–281.Google Scholar
Chen, J., Jia, H., Liu, D., Zhang, C. 2010b. Composing cardinal direction relations based on interval algebra. International Journal of Software and Informatics 4(3), 291–303.Google Scholar
Chen, J., Jia, H., Liu, D., Zhang, C. 2010c. Integrative reasoning with topological, directional and size information based on MBR. Journal of Computer Research and Development 47(3), 426–433.Google Scholar
Cicerone, S., Felice, P. D. 2000. Cardinal relations between regions with a broad boundary. In ACM-GIS 2000, Proceedings of the Eighth ACM Symposium on Advances in Geographic Information Systems, Li, K-J., Makki, K., Pissinou, N. & Ravada, S. (eds). Washington D.C., USA, November 10–11. ACM, 15–20.Google Scholar
Cicerone, S., Felice, P. D. 2004. Cardinal directions between spatial objects: the pairwise-consistency problem. Information Sciences 164(1–4), 165–188.Google Scholar
Clementini, E. 2008. Projective relations on the sphere. In Proceedings of Advances in Conceptual Modeling – Challenges and Opportunities, ER 2008 Workshops CMLSA, ECDM, FP-UML, M2AS, RIGiM, SeCoGIS, WISM, Barcelona Spain, October 20–23. Lecture Notes in Computer Science 5232, 313–322. Springer.Google Scholar
Clementini, E., Billen, R. 2006. Modeling and computing ternary projective relations between regions. IEEE Transactions on Knowledge and Data Engineering 18(6), 799–814.Google Scholar
Clementini, E., Felice, P. D. 1997. Approximate topological relations. International Journal of Approximate Reasoning 16(2), 173–204.CrossRefGoogle Scholar
Clementini, E., Felice, P. D. 2001. A spatial model for complex objects with a broad boundary supporting queries on uncertain data. Data Knowledge Engineering 37(3), 285–305.CrossRefGoogle Scholar
Clementini, E., Felice, P. D., Hernández, D. 1997. Qualitative representation of positional information. Artificial Intelligence 95(2), 317–356.Google Scholar
Clementini, E., Felice, P. D., van Oosterom, P. 1993. A small set of formal topological relationships suitable for end-user interaction. In Proceedings of the Advances in Spatial Databases, Third International Symposium, SSD'93, Singapore, June 23–25. Lecture Notes in Computer Science 692, 277–295. Springer.Google Scholar
Clementini, E., Skiadopoulos, S., Billen, R., Tarquini, F. 2010. A reasoning system of ternary projective relations. IEEE Transactions on Knowledge and Data Engineering 22(2), 161–178.CrossRefGoogle Scholar
Cohn, A. G. 1995. A hierarchical representation of qualitative shape based on connection and convexity. In Proceedings of the Spatial Information Theory: A Theoretical Basis for GIS, International Conference COSIT ‘95, Semmering, Austria, September 21–23. Leecture Notes in Computer Science 988, 311–326. Springer.Google Scholar
Cohn, A. G. 1997. Qualitative spatial representation and reasoning techniques. In Proceedings of the KI-97: Advances in Artificial Intelligence, 21st Annual German Conference on Artificial Intelligence, Freiburg, Germany, September 9–12. Lecture Notes in Computer Science 1303, 1–30. Springer.Google Scholar
Cohn, A. G., Bennett, B., Gooday, J., Gotts, N. M. 1997. Qualitative spatial representation and reasoning with the region connection calculus. GeoInformatica 1(3), 275–316.Google Scholar
Cohn, A. G., Gotts, N. M. 1996. The ‘egg-yolk’ representation of regions with indeterminate boundaries. In Proceedings GISDATA Specialist Meeting on Spatial Objects with Undetermined Boundaries, Burrough, P. & Frank, A. M. (eds). Francis & Taylor, 171–187.Google Scholar
Cohn, A. G., Hazarika, S. M. 2001. Qualitative spatial representation and reasoning: an overview. Fundamenta Informaticae 46(1–2), 1–29.Google Scholar
Cohn, A. G., Renz, J. 2007. Qualitative spatial reasoning. In Handbook of Knowledge Representation (Foundations of Artificial Intelligence), van Harmelen, F., Lifschitz, V. & Porter, B. (eds). chapter 13. Elsevier, 551–596.Google Scholar
Condotta, J.-F., Saade, M., Ligozat, G. 2006. A generic toolkit for n-ary qualitative temporal and spatial calculi. In Proceedings of the 13th International Symposium on Temporal Representation and Reasoning (TIME 2006), Budapest, Hungary, June 15–17. IEEE Computer Society, 78–86.Google Scholar
Davis, E., Gotts, N. M., Cohn, A. 1999. Constraint networks of topological relations and convexity. Constraints 4, 241–280.Google Scholar
Delafontaine, M., Cohn, A. G., de Weghe, N. V. 2011. Implementing a qualitative calculus to analyse moving point objects. Expert Systems with Applications 38(5), 5187–5196.Google Scholar
Delafontaine, M., de Weghe, N. V., Bogaert, P., Maeyer, P. D. 2008. Qualitative relations between moving objects in a network changing its topological relations. Information Science 178(8), 1997–2006.Google Scholar
de Weghe, N. V., Cohn, A. G., Maeyer, P. D. 2004. A qualitative representation of trajectory pairs. In Proceedings of the 16th Eureopean Conference on Artificial Intelligence, ECAI'2004, including Prestigious Applicants of Intelligent Systems, PAIS 2004, de Mántaras, R. L. & Saitta, L. (eds). Valencia, Spain, August 22–27. IOS Press, 1103–1104.Google Scholar
de Weghe, N. V., Cohn, A. G., Maeyer, P. D., Witlox, F. 2005a. Representing moving objects in computer-based expert systems: the overtake event example. Expert Systems with Application 29(4), 977–983.Google Scholar
de Weghe, N. V., Kuijpers, B., Bogaert, P., Maeyer, P. D. 2005b. A qualitative trajectory calculus and the composition of its relations. In Proceedings of the GeoSpatial Semantics, First International Conference, GeoS 2005, Mexico, November 29–30. Lecture Notes in Computer Science 3799, 60–76. Springer.CrossRefGoogle Scholar
Dong, Y., Liu, D., Wang, F., Wang, S., Lü, S. 2011. A MBR-based modeling method for direction relations between indeterminate regions. Acta Eelectronica Sinica 39(2), 329–335.Google Scholar
Du, S., Guo, L., Wang, Q. 2008a. A model for describing and composing direction relations between overlapping and contained regions. Information Science 178(14), 2928–2949.Google Scholar
Du, S., Qin, Q., Wang, Q., Li, B. 2005. Fuzzy description of topological relations I: a unified fuzzy 9-intersection model. In Proceedings of the Advances in Natural Computation, First International Conference, ICNC 2005, Part III, Changsha, China, August 27–29. Lecture Notes in Computer Science 3612, 1261–1273. Springer.Google Scholar
Du, S., Qin, Q., Wang, Q., Ma, H. 2006. Description of combined spatial relations between broad boundary regions based on rough set. In Proceedings of the Intelligent Data Engineering and Automated Learning – IDEAL 2006, 7th International Conference, Burgos, Spain, September 20–23. Lecture Notes in Computer Science 4224, 729–737. Springer.Google Scholar
Du, S., Qin, Q., Wang, Q., Ma, H. 2008b. Reasoning about topological relations between regions with broad boundaries. International Journal of Approximate Reasoning 47(2), 219–232.Google Scholar
Düntsch, I., Wang, H., McCloskey, S. 2001. A relation – algebraic approach to the region connection calculus. Theoretical Computer Science 255(1–2), 63–83.Google Scholar
Dylla, F., Frommberger, L., Wallgrün, J. O., Wolter, D. 2006. SparQ: a toolbox for qualitative spatial representation and reasoning. In Proceedings of the Workshop on Qualitative Constraint Calculi: Application and Integration at KI 2006, Bremen, Germany, 79–90.Google Scholar
Egenhofer, M. J. 2005. Spherical topological relations. Journal on Data Semantics 3(1), 25–49.CrossRefGoogle Scholar
Egenhofer, M. J., Clementini, E., Felice, P. D. 1994a. Topological relations between regions with holes. International Journal of Geographical Information Systems 8(2), 129–142.CrossRefGoogle Scholar
Egenhofer, M. J., Franzosa, R. D. 1991. Point set topological relations. International Journal of Geographical Information Systems 5(2), 161–174.Google Scholar
Egenhofer, M. J., Franzosa, R. D. 1995. On the equivalence of topological relations. International Journal of Geographical Information Systems 9(2), 133–152.CrossRefGoogle Scholar
Egenhofer, M. J., Herring, J. 1991. Categorizing Binary Topological Relationships between Regions, Lines and Points in Geographic Database. Technical report, University of Maine.Google Scholar
Egenhofer, M. J., Mark, D. M., Herring, J. 1994b. The 9-intersection: formalism and its use for natural-language spatial predicates. Technical report, National Center for Geographic Information and Analysis.Google Scholar
Egenhofer, M. J., Sharma, J. 1993. Topological relations between regions in $$\[--><$>{{{\Bbb R}}^{\rm{2}}} <$><!--$$ and $$\[--><$>{{{\Bbb Z}}^{\rm{2}}} <$><!--$$ . In Proceedings of the Advances in Spatial Databases, Third International Symposium, SSD'93, Singapore, June 23–25. Lecture Notes in Computer Science 692, 316–336. Springer.Google Scholar
Egenhofer, M. J., Vasardani, M. 2007. Spatial reasoning with a hole. In Proceedings of the Spatial Information Theory, 8th International Conference, COSIT 2007, Melbourne, Australia, September 19–23. Lecture Notes in Computer Science 4736, 303–320. Springer.Google Scholar
El-Geresy, B. A., Abdelmoty, A. I. 2004. SPARQS: a qualitative spatial reasoning engine. Knowledge Based System 17(2–4), 89–102.Google Scholar
Frank, A. U. 1991. Qualitative spatial reasoning with cardinal directions. In Proceedings of the 7th Austrian Conference on Artificial Intelligence, ÖGAI-91, Wien, September 24–27. Informatik-Fachberichte 287, 157–167. Springer.Google Scholar
Frank, A. U. 1996. Qualitative spatial reasoning: cardinal directions as an example. International Journal of Geographical Information Science 10(3), 269–290.Google Scholar
Franklin, N., Henkel, L. A., Zangas, T. 1995. Parsing surrounding space into regions. Memory & Cognition 23(4), 397–407.Google Scholar
Freksa, C. 1992. Using orientation information for qualitative spatial reasoning. In Proceedings of the Theories and Methods of Spatio-Temporal Reasoning in Geographic Space, International Conference GIS – From Space to Territory: Theories and Methods of Spatio-Temporal Reasoning, Pisa, Italy, September 21–23. Lecture Notes in Computer Science 639, 162–178. Springer.Google Scholar
Galton, A., Meathrel, R. C. 1999. Qualitative outline theory. In Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence, IJCAI 99, Dean, T. (ed.). Stockholm, Sweden, July 31–August 6. Morgan Kaufmann, 1061–1066.Google Scholar
Gantner, Z., Westphal, M., Wölfl, S. 2008. GQR – a fast reasoner for binary qualitative constraint calculi. In Proceedings of the AAAI'08 Workshop on Spatial and Temporal Reasoning, Chicago, Illinois, USA, July 13–14. AAAI Press, 24–29.Google Scholar
Gerevini, A., Renz, J. 2002. Combining topological and size information for spatial reasoning. Artificial Intelligence 137(1–2), 1–42.Google Scholar
Gottfried, B. 2003a. Tripartite line tracks – bipartite line tracks. In Proceedings of the KI 2003: Advances in Artificial Intelligence, 26th Annual German Conference on AI, KI 2003, Hamburg, Germany, September 15–18. Lecture Notes in Computer Science 2821, 535–549. Springer.Google Scholar
Gottfried, B. 2003b. Tripartite line tracks qualitative curvature information. In Proceedings of the Spatial Information Theory. Foundations of Geographic Information Science, International Conference, COSIT 2003, Ittingen, Switzerland, September 24–28. Lecture Notes in Computer Science 2825, 101–117. Springer.CrossRefGoogle Scholar
Gottfried, B. 2004. Reasoning about intervals in two dimensions. In Proceedings of the IEEE International Conference on Systems, Man & Cybernetics, The Hague, Netherlands, October 10–13. IEEE, 5324–5332.Google Scholar
Gottfried, B. 2006. Characterising meanders qualitatively. In Geographic Information Science, Proceedings of 4th International Conference, GIScience 2006, Münster, Germany, September 20–23. Lecture Notes in Computer Science 4197, 112–127. Springer.CrossRefGoogle Scholar
Gottfried, B. 2008. Qualitative similarity measures – the case of two-dimensional outlines. Computer Vision and Image Understanding 110(1), 117–133.Google Scholar
Gotts, N. M., Gooday, J. M., Cohn, A. G. 1996. A connection based approach to common-sense topological description and reasoning. The Monist 79(1), 51–75.Google Scholar
Goyal, R. K., Egenhofer, M. J. 2000. Consistent queries over cardinal directions across different levels of detail. In Proceedings of 11th International Workshop on Database and Expert Systems Applications (DEXA'00), Ibrahim, M. T., Küng, J. & Revell, N. (eds). 6–8 September, Greenwich, London, UK. IEEE Computer Society, 876–880.Google Scholar
Goyal, R. K., Egenhofer, M. J. 2001. Similarity of cardinal directions. In Proceedings of the Advances in Spatial and Temporal Databases, 7th International Symposium, SSTD 2001, Redondo Beach, CA, USA, July 12–15. Lecture Notes in Computer Science 2121, 36–58. Springer.Google Scholar
Grenon, P. 2003. Tucking RCC in Cyc's ontological bed. In IJCAI-03, Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence, Gottlob, G. & Walsh, T. (eds). Acapulco, Mexico, August 9–15. Morgan Kaufmann, 894–899.Google Scholar
Guo, L., Du, S. 2009. Deriving topological relations between regions from direction relations. Journal of Visual languages and Computing 2(6), 368–384.Google Scholar
Hirsch, R. 1999. A finite relation algebra with undecidable network satisfaction problem. Logic Journal of the IGPL 7(4), 547–554.Google Scholar
Hobbs, J. R. 1985. Granularity. In Proceedings of the 9th International Joint Conference on Artificial Intelligence, Joshi, A. K. (ed.). Los Angeles, CA, August. Morgan Kaufmann, 432–435.Google Scholar
Huttenlocher, J., Hedges, L. V., Duncan, S. 1991. Categories and particulars: prototype effects in estimating spatial location. Psychological Review 98(3), 352–376.CrossRefGoogle ScholarPubMed
Isli, A., Cohn, A. G. 2000. A new approach to cyclic ordering of 2D orientations using ternary relation algebras. Artificial Intelligence 122(1–2), 137–187.CrossRefGoogle Scholar
Isli, A., Haarslev, V., Möller, R. 2003. Combining cardinal direction relations and relative orientation relations in qualitative spatial reasoning. Technical report, University of Hamburg, Department of Informatics.Google Scholar
Kurata, Y. 2008. The 9+-intersection: a universal framework for modeling topological relations. In Proceedings of the Geographic Information Science, 5th International Conference, GIScience 2008, Park City, UT, USA, September 23–26. Lecture Notes in Computer Science 5266, 181–198. Springer.Google Scholar
Ladkin, P. B., Maddux, R. D. 1994. On binary constraint problems. Journal of the ACM 41(3), 435–469.Google Scholar
Langacker, R. 1987. The Foundations of Cognitive Grammar: volume I: Theoretical Prerequisites, Foundations of Cognitive Grammar. Stanford University Press.Google Scholar
Lee, S.-Y., Hsu, F.-J. 1990. 2D C-string: a new spatial knowledge representation for image database systems. Pattern Recognition 23(10), 1077–1087.CrossRefGoogle Scholar
Leyton, M. 1988. A process-grammar for shape. Artificial Intelligence 34(2), 213–247.Google Scholar
Li, S. 2006a. On topological consistency and realization. Constraints 11(1), 31–51.Google Scholar
Li, S. 2006b. A complete classification of topological relations using the 9-intersection method. International Journal of Geographical Information Science 20(6), 589–610.Google Scholar
Li, S. 2007. Combining topological and directional information for spatial reasoning. In IJCAI 2007, Proceedings of the 20th International Joint Conference on Artificial Intelligence, Veloso, M. M. (ed.). Hyderabad, India, January 6–12. Morgan Kaufmann, 435–440.Google Scholar
Li, S., Cohn, A. G. 2012. Reasoning with topological and directional spatial information. Computational Intelligence 28(4), 579–616.Google Scholar
Li, S., Liu, W. 2010. Topological relations between convex regions. In Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence, AAAI 2010, Fox, M. & Poole, D. (eds). Atlanta, Georgia, USA, July 11–15. AAAI Press, 321–326.Google Scholar
Li, S., Nebel, B. 2007. Qualitative spatial representation and reasoning: a hierarchical approach. The Computer Journal 50(4), 391–402.Google Scholar
Li, S., Wang, H. 2006. RCC8 binary constraint network can be consistently extended. Artificial Intelligence 170(1), 1–18.CrossRefGoogle Scholar
Li, S., Ying, M. 2003. Region connection calculus: its models and composition table. Artificial Intelligence 145(1–2), 121–146.Google Scholar
Li, S., Ying, M. 2004. Generalized region connection calculus. Artificial Intelligence 160(1–2), 1–34.Google Scholar
Li, S., Ying, M., Li, Y. 2005. On countable RCC models. Fundamenta Informaticae 65(4), 329–351.Google Scholar
Ligozat, G. 1993. Qualitative triangulation for spatial reasoning. In Proceedings of the Spatial Information Theory: A Theoretical Basis for GIS, International Conference COSIT ‘93, Marciana Marina, Elba Island, Italy, September 19–22. Lecture Notes in Computer Science 716, 54–68. Springer.CrossRefGoogle Scholar
Liu, D., Hu, H., Wang, S., Xie, Q. 2004. Research progress in spatio-temporal reasoning. Journal of Software 15(8), 1141–1149.Google Scholar
Liu, J. 1998. A method of spatial reasoning based on qualitative trigonometry. Artificial Intelligence 98(1–2), 137–168.CrossRefGoogle Scholar
Liu, W., Li, S., Renz, J. 2009. Combining RCC-8 with qualitative direction calculi: algorithms and complexity. In IJCAI 2009, Proceedings of the 21st International Joint Conference on Artificial Intelligence, Boutilier, C. (ed.). Pasadena, California, USA, July 11–17. AAAI Press, 854–859.Google Scholar
Liu, W., Zhang, X., Li, S., Ying, M. 2010. Reasoning about cardinal directions between extended objects. Artificial Intelligence 174(12–13), 951–983.Google Scholar
Liu, Y., Wang, X., Jin, X., Wu, L. 2005. On internal cardinal direction relations. In Proceedings of the Spatial Information Theory, International Conference, COSIT 2005, Ellicottville, NY, USA, September 14–18. Lecture Notes in Computer Science 3693, 283–299. Springer.Google Scholar
Moratz, R. 2006. Representing relative direction as a binary relation of oriented points. In Proceedings of the ECAI 2006, 17th European Conference on Artificial Intelligence, August 29–September 1, 2006, Riva del Garda, Italy, Including Prestigious Applications of Intelligent Systems (PAIS 2006), Frontiers in Artificial Intelligence and Applications. IOS Press, 407–411.Google Scholar
Moratz, R., Ragni, M. 2008. Qualitative spatial reasoning about relative point position. Journal of Visual Languages and Computing 19(1), 75–98.Google Scholar
Moratz, R., Renz, J., Wolter, D. 2000. Qualitative spatial reasoning about line segments. In ECAI 2000, Proceedings of the 14th European Conference on Artificial Intelligence, Horn, W. (ed.). Berlin, Germany, August 20–25. IOS Press, 234–238.Google Scholar
Moreira, J., Ribeiro, C., Saglio, J. 1999. Representation and manipulation of moving points:an extended data model for location estimation. Cartography and Geographic Information Systems 26(2), 109–123.Google Scholar
Mossakowski, T., Moratz, R. 2012. Qualitative reasoning about relative direction of oriented points. Artificial Intelligence 180–181, 34–45.Google Scholar
Navarrete, I., Sciavicco, G. 2006. Spatial reasoning with rectangular cardinal direction relations. In ECAI 2006, 17th European Conference on Artificial Intelligence, Workshop on Spatialand Temporal Reasoning, Riva del Garda, Italy, August 29–September 1, 1–10.Google Scholar
Ouyang, J., Fu, Q., Liu, D. 2009a. A model for representing and reasoning of spatial relations between simple concave regions. Acta Electronica Sinica 37(8), 1830–1836.Google Scholar
Ouyang, J., Fu, Q., Liu, D. 2009b. Improved method of qualitative shape representation for sameside distinction of concavities. Journal of Jilin University (Engineering and Technology Edition) 39(2), 413–418.Google Scholar
Pacheco, J., Escrig, M. T., Toledo, F. 2002. Integrating 3D orientation models. In Proceedings of the Topics in Artificial Intelligence, 5th Catalonian Conference on AI, CCIA 2002, Castellón, Spain, October 24–25. Lecture Notes in Computer Science 2504, 88–100. Springer.Google Scholar
Palshikar, G. K. 2004. Fuzzy region connection calculus in finite discrete space domains. Applied Soft Computing 4(1), 13–23.Google Scholar
Pujari, A. K., Kumari, G. V., Sattar, A. 1999. $$\[--><$>{\cal I}{\cal N}{\cal D}{\cal U}<$><!--$$ : An interval and duration network. In Proceedings of the Advanced Topics in Artificial Intelligence, 12th Australian Joint Conference on Artificial Intelligence, AI ‘99, Sydney, Australia, December 6–10. Lecture Notes in Computer Science 1747, 291–303. Springer.Google Scholar
Randell, D. A., Cohn, A. G., Cui, Z. 1992a. Computing transivity tables: a challenge for automated theorem provers. In Proceedings of the Automated Deduction – CADE-11, 11th International Conference on Automated Deduction, Saratoga Springs, NY, USA, June 15–18. Lecture Notes in Computer Science 607, 786–790. Springer.Google Scholar
Randell, D. A., Cui, Z., Cohn, A. G. 1992b. A spatial logic based on regions and connection. In Proceedings of the 3rd International Conference on Principles of Knowledge Representation and Reasoning (KR'92), Nebel, B., Rich, C. & Swartout, W. R. (eds). Cambridge, MA, October 25-29. Morgan Kaufmann, 165–176.Google Scholar
Renz, J. 2001. A spatial odyssey of the interval algebra: 1. directed intervals. In Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence, IJCAI 2001, Nebel, B. (ed.). Washington, USA, August 4–10. Morgan Kaufmann, 51–56.Google Scholar
Renz, J. 2002. Qualitative Spatial Reasoning with Topological Information, Lecture Notes in Computer Science 2293. Springer. ISBN 3-540-43346-5.CrossRefGoogle Scholar
Renz, J., Ligozat, G. 2005. Weak composition for qualitative spatial and temporal reasoning. In Proceedings of the Principles and Practice of Constraint Programming – CP 2005, 11th International Conference, CP 2005, Sitges, Spain, October 1–5, 2005, Lecture Notes in Computer Science 3709, 534–548. Springer.Google Scholar
Renz, J., Nebel, B. 1999. On the complexity of qualitative spatial reasoning: a maximal tractable fragment of the region connection calculus. Artificial Intelligence 108(1–2), 69–123.Google Scholar
Roddick, J. F., Spiliopoulou, M. 2002. A survey of temporal knowledge discovery paradigms and methods. IEEE Transactions on Knowledge and Data Engineering 14(4), 750–767.Google Scholar
Röhrig, R. 1994. A theory for qualitative spatial reasoning based on order relations. In Proceedings of the 12th National Conference on Artificial Intelligence, Hayes-Roth, B. & Korf, R. E. (eds). volume 2, Seattle, WA, USA, July 31–August 4. AAAI Press/The MIT Press, 1418–1423.Google Scholar
Röhrig, R. 1997. Representation and processing of qualitative orientation knowledge. In KI-97: Advances in Artificial Intelligence, Proceedings of 21st Annual German Conference on Artificial Intelligence, Freiburg, Germany, September 9–12. Lecture Notes in Computer Science 1303, 219–230. Springer.Google Scholar
Roy, A. J., Stell, J. G. 2001. Spatial relations between indeterminate regions. International Journal of Approximate Reasoning 27(3), 205–234.Google Scholar
Schneider, M. 2000. Finite resolution crisp and fuzzy spatial objects. In Proceedings of the 9th International Symposium on Spatial Data Handling(SDH), volume 2, Beijing, China, 3–17.Google Scholar
Schneider, M. 2003. Design and implementation of finite resolution crisp and fuzzy spatial objects. Data and Knowledge Engineering 44(1), 81–108.Google Scholar
Schneider, M., Behr, T. 2006. Topological relationships between complex spatial objects. ACM Transactions on Database System 31(1), 39–81.Google Scholar
Schneider, M., Chen, T., Viswanathan, G., Yuan, W. 2012. Cardinal directions between complex regions. ACM Transactions on Database System 37(2), 8–40.Google Scholar
Schockaert, S., Cock, M. D., Cornelis, C., Kerre, E. E. 2008. Fuzzy region connection calculus: an interpretation based on closeness. International Journal of Approximate Reasoning 48(1), 332–347.Google Scholar
Schockaert, S., Cock, M. D., Kerre, E. E. 2009. Spatial reasoning in a fuzzy region connection calculus. Artificial Intelligence 173(2), 258–298.Google Scholar
Schockaert, S., Cornelis, C., Cock, M. D., Kerre, E. 2006. Fuzzy spatial relations between vague regions. In Proceedings of the 3rd International IEEE Conference on Intelligent Systems, London UK, September 4–6. International IEEE Conference Print, 221–226.Google Scholar
Scivos, A., Nebel, B. 2004. The finest of its class: the natural point-based ternary calculus for qualitative spatial reasoning. In Spatial Cognition IV: Reasoning, Action, Interaction, International Conference Spatial Cognition 2004, Frauenchiemsee, Germany, October 11–13, Revised Selected Papers. Lecture Notes in Computer Science 3343, 283–303. Springer.Google Scholar
Sirin, E., Parsia, B. 2004. Pellet: an OWL DL reasoner. In Proceedings of the 2004 International Workshop on Description Logics (DL2004), Whistler, British Columbia, Canada, June 6–8. CEUR Workshop Proceedings 104. CEUR-WS.org.Google Scholar
Sistla, A. P., Yu, C. T. 2000. Reasoning about qualitative spatial relationships. Journal of Automated Reasoning 25(4), 291–328.Google Scholar
Skiadopoulos, S., Koubarakis, M. 2004. Composing cardinal direction relations. Artificial Intelligence 152(2), 143–171.Google Scholar
Skiadopoulos, S., Koubarakis, M. 2005. On the consistency of cardinal direction constraints. Artificial Intelligence 163(1), 91–135.Google Scholar
Skiadopoulos, S., Sarkas, N., Sellis, T. K., Koubarakis, M. 2007. A family of directional relation models for extended objects. IEEE Transactions on Knowledge and Data Engineering 19(8), 1116–1130.Google Scholar
Stell, J. G. 2003. Qualitative extents for spatio-temporal granularity. Spatial Cognition and Computation 3, 119–136.Google Scholar
Stickel, M. E., Waldinger, R. J., Chaudhri, V. K. 2000. A guide to SNARK. Technical report, AI Center, SRI International.Google Scholar
Stocker, M., Sirin, E. 2009. PelletSpatial: a hybrid RCC-8 and RDF/OWL reasoning and query engine. In Proceedings of the 5th International Workshop on OWL: Experiences and Directions (OWLED 2009), Chantilly, VA, United States, October 23–24. CEUR Workshop Proceedings 529. CEUR-WS.org.Google Scholar
Tarski, A. 1941. On the calculus of relations. Journal of Symbolic Logic 6(3), 73–89.Google Scholar
Vasardani, M., Egenhofer, M. J. 2008. Single-holed regions: their relations and inferences. In Proceedings of the Geographic Information Science, 5th International Conference, GIScience 2008, Park City, UT, USA, September 23–26. Lecture Notes in Computer Science 5266, 337–353. Springer.Google Scholar
Vasardani, M., Egenhofer, M. J. 2009. Comparing relations with a multi-holed region. In Proceedings of the Spatial Information Theory, 9th International Conference, COSIT 2009, Aber Wrac'h, France, September 21–25. Lecture Notes in Computer Science 5756, 159–176. Springer.Google Scholar
Vieu, L. 1997. Spatial Representation and Reasoning in Artificial Intelligence. Spatial and Temporal Reasoning, 5–41.Google Scholar
Vilain, M., Kautz, H., van Beek, P. 1990. Constraint propagation algorithms for temporal reasoning: a revised report. Morgan Kaufmann Publishers Inc., 373–381.Google Scholar
Waldinger, R., Jarvis, P., Dungan, J. 2003. Using deduction to choreograph multiple data sources. In Proceedings of the Semantic Web – ISWC 2003: Second International Semantic Web Conference, Sanibel Island, FL, USA, October 20–23. Lecture Notes of Computer Science 2870. Springer.Google Scholar
Wallgrün, J. O., Frommberger, L., Dylla, F., Wolter, D. 2010. Sparq user manual v0.7. Technical report, SFB/TR 8 spatial Cognition- Project R3-[Q-Shape].Google Scholar
Wallgrün, J. O., Frommberger, L., Wolter, D., Dylla, F., Freksa, C. 2006. Qualitative spatial representation and reasoning in the sparq-toolbox. In Spatial Cognition V: Reasoning, Action, Interaction, International Conference Spatial Cognition 2006, Bremen, Germany, September 24–28, Revised Selected Papers, Lecture Notes in Computer Science 4387, 39–58. Springer.Google Scholar
Wang, S., Liu, D., Hu, H., Wang, X. 2003. Approximate spatial relation algebra ASRA and application. Journal of Image and Graphics 8(8), 946–950.Google Scholar
Wang, S., Liu, D., Liu, J. 2005. A new spatial algebra for road network moving objects. International Journal of Information Technology 11(12), 47–58.Google Scholar
Wölfl, S., Westphal, M. 2009. On combinations of binary qualitative constraint calculi. In IJCAI 2009, Proceedings of the 21st International Joint Conference on Artificial Intelligence, Boutilier, C. (ed.). Pasadena, California, USA, July 11–17. AAAI Press, 967–973.Google Scholar
Wolter, D., Lee, J. H. 2010. Qualitative reasoning with directional relations. Artificial Intelligence 174(18), 1498–1507.Google Scholar
Yu, Q., Liu, D., Liu, Y. 2004. An extended egg-yolk model between indeterminate regions. Acta Eelectronica Sinica 32(4), 610–615.Google Scholar
Zhan, F. B. 1998. Approximate analysis of binary topological relations between geographic regions with indeterminate boundaries. Soft Computing 2(2), 28–34.Google Scholar
Zhan, F. B., Lin, H. 2003. Overlay of two simple polygons with indeterminate boundaries. Transactions in GIS 7(1), 67–81.Google Scholar
Zimmermann, K. 1993. Enhancing qualitative spatial reasoning – combining orientation and distance. In Proceedings of the Spatial Information Theory: A Theoretical Basis for GIS, International Conference COSIT ‘93, Marciana Marina, Elba Island, Italy, September 19–22. Lecture Notes in Computer Science 716, 69–76. Springer.Google Scholar
Zimmermann, K., Freksa, C. 1996. Qualitative spatial reasoning using orientation, distance, and path knowledge. Applied Intelligence 6(1), 49–58.Google Scholar
Zlatanova, S. 2000. 3D GIS for Urban Development. PhD thesis, The International Institute for Aerospace Survey and Earth Sciences.Google Scholar