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Qualitative Spatial-Relation Reasoning for Design

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Studying Visual and Spatial Reasoning for Design Creativity

Abstract

Qualitative spatial relations are symbol abstractions of geometric representations, which allow computational analyses independent of, but consistent with, graphical depictions. This paper compiles some of the most commonly used sets of qualitative spatial relations and their logical inference mechanisms. The abstract representation of the relations’ interconnectedness in the form of their conceptual neighborhood graphs offers intriguing insight about the regularity of such complete sets of qualitative relations.

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References

  1. Egenhofer M, Franzosa R (1991) Point-set topological spatial relations. Int J Geogr Inf Syst 5(2):161–174

    Article  Google Scholar 

  2. Egenhofer M, Al-Taha K (1992) Reasoning about gradual changes of topological relationships. In: Frank A, Campari I, Formentini U (eds) Theories and methods of spatio-temporal reasoning in geographic space, lecture notes in computer science. Springer, Vol 639, pp 196–219

    Google Scholar 

  3. Randell D, Cui Z, Cohn A (1992) A spatial logic based on regions and connection. In: Nebel B, Rich C, Swartout W (eds) 3rd international conference on principles of knowledge representation and reasoning. Morgan Kaufmann, pp 165–176

    Google Scholar 

  4. Randell D, Cohn A, Cui Z (1992) Computing transitivity tables: a challenge for automated theoremprovers. 11th international conference on automated deduction, pp 786–790

    Google Scholar 

  5. Egenhofer M (1994) Deriving the composition of binary topological relations. J Vis Lang Comput 5(2):133–149

    Article  Google Scholar 

  6. Allen J (1983) Maintaining knowledge about temporal intervals. Commun ACM 26(11);361–372

    Article  Google Scholar 

  7. Freksa C (1992) Temporal reasoning based on semi-intervals. Artif Intell 54(1–2):199–227

    Article  MathSciNet  Google Scholar 

  8. Cohn A, Renz J (2008) Qualitative spatial representation and reasoning. In: van Hermelen F, Lifschitz V, Porter B (eds) Handbook of knowledge representation. Elsevier, pp 551–596

    Google Scholar 

  9. Galton A (2009) Spatial and temporal knowledge representation. Earth Sci Inf 2(3):169–187

    Article  Google Scholar 

  10. Freeman J (1975) The modeling of spatial relations. Computer Gr Imag Process 4(2):156–171

    Article  Google Scholar 

  11. Retz-Schmidt G (1988) Various views on spatial prepositions. AI Magazine 9(2):95–105

    Google Scholar 

  12. Egenhofer M, Herring J (1990) A mathematical framework for the definition of topological relationships. In: Brassel K, Kishimoto H (eds) Fourth international symposium on spatial data handling. pp 803–813

    Google Scholar 

  13. Egenhofer M, Herring J (1990) Categorizing binary topological relations between regions, lines, and points in geographic databases. Technical report. Department of Surveying Engineering University of Maine. http://www.spatial.maine.edu/~max/ 9intReport.pdf

  14. Egenhofer M, Franzosa R (1995) On the equivalence of topological relations. Int J Geogr Inf Syst 9(2):133–152

    Article  Google Scholar 

  15. Galton A (1998) Modes of overlap. J Vis Lang Computing 9(1):61–79

    Article  Google Scholar 

  16. Egenhofer M (1993) A model for detailed binary topological relationships. Geomatica 47(3–4):261–273

    Google Scholar 

  17. Guesgen H (1989) Spatial reasoning based on AllenĘĽs temporal logic, technical report. International Computer Science Institute, Berkeley

    Google Scholar 

  18. Nabil M, Shepherd J, Ngu A (1995) 2D projection interval relationships: a symbolic representation of spatial relationships. In: Egenhofer M, Herring J (eds) Advances in spatial databases, 4th international symposium, lecture notes in computer science, vol 951. Springer, pp 292–306

    Google Scholar 

  19. Sistla AP, Wu C, Haddad R (1994) Reasoning about spatial relationships in picture retrieval systems. In: Bocca J, Jarke M, Zaniolo M (eds) 20th international conference on very large data bases. Morgan Kaufmann, pp 570–581

    Google Scholar 

  20. Sistla AP, Yu C (2000) Reasoning about qualitative spatial relationships. J Automated Reason 25(4):291–328

    Article  MATH  MathSciNet  Google Scholar 

  21. Chang SK, Shi Q, Yan C (1987) Iconic indexing by 2-D strings. IEEE Transact Pattern Anal Mach Intell 9(3):413–428

    Article  Google Scholar 

  22. Talmy L (1983) How language structures space. In: Pick H, Acredolo L (eds) Spatial orientation: theory, research, and applications. Plenum Press, pp 225–282

    Google Scholar 

  23. Herskovits A (1986) Language and spatial cognition—an interdisciplinary study of prepositions in english. Cambridge University Press

    Google Scholar 

  24. Mark D, Egenhofer M (1994) Modeling spatial relations between lines and regions: combining formal mathematical models and human subjects testing. Cartogr Geogr Inf Syst 21(3):195–212

    Google Scholar 

  25. Mark D, Egenhofer M (1994), Calibrating the meanings of spatial predicates from natural language: line-region relations. Sixth international symposium on spatial data handling, pp 538–555

    Google Scholar 

  26. Ragni M, Tseden B, Knauff M (2007) Cross-cultural similarities in topological reasoning. In: Winter S, Duckham M, Kulik L, Kuipers B (eds) Spatial information theory–8th international conference, lecture notes in computer science, vol 4736. Springer, pp 32–46

    Google Scholar 

  27. Schwering A (2007) Evaluation of a semantic similarity measure for natural language spatial relations. In: Winter S, Duckham M, Kulik L, Kuipers B (eds) Spatial information theory–8th international conference, lecture notes in computer science, vol 4736. Springer, pp 116–132

    Google Scholar 

  28. Bruns HT, Egenhofer M (1996) Similarity of spatial scenes. In: Kraak MJ, Molenaar M (eds) Seventh international symposium on spatial data handling. pp 4A 31–42

    Google Scholar 

  29. Egenhofer M, Mark D (1995) Naive Geography. In: Frank A, Kuhn W (eds) Third European conference on spatial information theory, lecture notes in computer science, vol 998. Springer, pp 1–12

    Google Scholar 

  30. Egenhofer M (2010) The family of conceptual neighborhood graphs for region-region relations. In: Fabrikant S, Reichenbacher T, van Kreveld M, Schlieder C (eds) GIScience 2010, lecture notes in computer science, vol 6292. Springer, pp 42–55

    Google Scholar 

  31. Egenhofer M, Sharma J (1993) Topological relations between regions in R2 and Z2. In: Abel D, Ooi BC (eds) Third international symposium on advances in spatial databases, lecture notes in computer science, vol 692. Springer, pp 316–336

    Google Scholar 

  32. Egenhofer M (1994) Pre-processing queries with spatial constraints. Photogrammetric Eng Remote Sens 60(6):783–790

    Google Scholar 

  33. Tarski A (1941) On the calculus of relations. J Symbolic Log 6(3):73–89

    Article  MathSciNet  Google Scholar 

  34. Li S, Ying M (2002) Extensionality of the RCC8 composition table. Fundamenta Informaticae 55(3–4):363–385

    MathSciNet  Google Scholar 

  35. Jonsson P, Drakengren T (1997) A complete classification of tractability in RCC-5. J Artif Intell Res 6:211–221

    MATH  MathSciNet  Google Scholar 

  36. Grigni M, Papadias D, Papadimitriou C (1995) Topological inference. 14th international joint conference on artificial intelligence, pp 901–906

    Google Scholar 

  37. Egenhofer M, Shariff R (1998) Metric details for natural-language spatial relations. ACM Transactions Inf Syst 16(4):295–321

    Article  Google Scholar 

  38. Egenhofer M, Dube M (2009) Topological relations from metric refinements. In: Wolfson O, Agrawal D, Lu CT (eds) 17th ACM SIGSPATIAL international symposium on advances in geographic information systems, pp 158–167

    Google Scholar 

  39. Hornsby K, Egenhofer M, Hayes P (1999) Modeling cyclic change. In: Chen PPS, Embley D, Louloumdjian J, Liddle S, Roddick J (eds) Advances in conceptual modeling: ER ʼ99 workshops, lecture notes in computer science, vol 1727. Springer, pp 98–109

    Google Scholar 

  40. Egenhofer M (2005) Spherical topological relations. J Data Semant III:25–49

    Google Scholar 

  41. Zlatanova S (2000) On 3D topological relationships. In: 11th international workshop on database and expert systems applications, London, UK, pp 913–924

    Google Scholar 

  42. Shariff R, Egenhofer M, Mark D (1998) Natural-language spatial relations between linear and areal objects: the topology and metric of english-language terms. Int J Geogr Inf Syst 12(3):215–245

    Google Scholar 

  43. Egenhofer M, Vasardani M (2007) Spatial reasoning with a hole. In: Winter S, Duckham M, Kulik L, Kuipers B (eds) Spatial information theory–8th international conference, lecture notes in computer science, vol 4736. Springer, pp 303–320

    Google Scholar 

  44. Egenhofer M (2009) A reference system for topological relations between compound spatial objects. In: Heuser C, Pernul G (eds) Advances in conceptual modeling—challenging perspectives, ER 2009 workshops, lecture notes in computer science, vol 5833. Springer, pp 307–316

    Google Scholar 

  45. Frank A (1992) Qualitative spatial reasoning about distances and directions in geographic space. J Vis Lang Computing 3(4):343–371

    Article  Google Scholar 

  46. Goyal R, Egenhofer M (2000) Consistent queries over cardinal directions across different levels of detail. In: 11th international workshop on database and expert systems applications, pp 876–880

    Google Scholar 

  47. Goyal R, Egenhofer M (2001) Similarity of cardinal directions. In: Jensen C, Schneider M, Seeger B, and Tstotras V (eds) 7th international symposium on advances in spatial and temporal databases, lectures notes in computer science, vol 2121. Springer, pp 36–58

    Google Scholar 

  48. Liu Y, Wang X, Jin X, Wu L (2005) On internal cardinal directions. In: Cohn A, Mark D (eds) Spatial information theory, international conference COSIT, lecture notes in computer science, vol 3693. Springer, pp 283–299

    Google Scholar 

  49. Skiadopoulos S, Sarkas N, Sellis T, Koubararkis M (2007) A family of directional relation models for extended objects. IEEE Transactions Knowl Data Eng 19(8):1116–1130

    Article  Google Scholar 

  50. Mandelbrot B (1982) The fractal geometry of nature. W. H. Freeman and Co, New York

    MATH  Google Scholar 

  51. Nökel K (1989) Convex relations between time intervals. Proceedings 5. Österreichische Artificial-Intelligence-Tagung. Springer, Berlin, pp 298–302

    Google Scholar 

  52. Nedas K, Egenhofer M (2008) Spatial-scene similarity queries. Transact in GIS 12(6):661–681

    Article  Google Scholar 

  53. Egenhofer M (1997) Query processing in spatial-query-by-sketch. J Vis Lang Computing 8(4):403–424

    Article  Google Scholar 

  54. Li B, Fonseca F (2006) TDD—a comprehensive model for qualitative spatial similarity assessment. Sp Cognit Computation 6(1):31–62

    Article  Google Scholar 

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Acknowledgments

Max Egenhofer’s research is partially supported by the National Science Foundation under NSF grant IIS–1016740.

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Correspondence to Max J. Egenhofer .

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Egenhofer, M. (2015). Qualitative Spatial-Relation Reasoning for Design. In: Gero, J. (eds) Studying Visual and Spatial Reasoning for Design Creativity. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9297-4_9

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  • DOI: https://doi.org/10.1007/978-94-017-9297-4_9

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  • Online ISBN: 978-94-017-9297-4

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