direction concepts, behavioral studies, qualitative spatial reasoning


Experiments in this article test the hypothesis that formal direction models used in artificial intelligence correspond to intuitive direction concepts of humans. Cognitively adequate formal models of spatial relations are important for information retrieval tasks, cognitive robotics, and multiple spatial reasoning applications. We detail two experiments using two objects (airplanes) systematically located in relation to each other. Participants performed a grouping task to make their intuitive direction concepts explicit. The results reveal an important, so far insufficiently discussed aspect of cognitive direction concepts: Intuitive (natural) direction concepts do not follow a one-size-fits-all strategy. The behavioral data only forms a clear picture after participants' competing strategies are identified and separated into categories (groups) themselves. The results are important for researchers and designers of spatial formalisms as they demonstrate that modeling cognitive direction concepts formally requires a flexible approach to capture group differences.

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Abdelmoty, A. I., Smart, P.D., El-Geresy, B.A. & Jones, C.B. 2009. ‘Supporting frameworks for the geospatial semantic web’. In ‘Proceedings of the 11th International Symposium on Advances in Spatial and Temporal Databases’, 355–372.

Allen, J. F. 1983. ‘Maintaining knowledge about temporal intervals’. Communications of the ACM 26, no. 11: 832–843.

Belussi, A., Migliorini, S., Negri, M. & Pelagatti, G. 2012. ‘Robustness of spatial relation evaluation in data exchange’. In ‘Proceedings of the 20th International Conference on Advances in Geographic Information Systems’, SIGSPATIAL ’12, 446–449. New York, NY, USA: ACM.

Brunet, R. 1987. La carte, mode d’emploi. Paris: Fayard-Reclus.

Bryant, D. J. 1998. ‘Human spatial concepts reflect regularities of the physical world and human body’. In Patrick Olivier & Klaus-Peter Gapp (eds.) ‘Representation and processing of spatial expressions’, 215–230. Mahwah and N.J. and London: Lawrence Erlbaum.

Buchin, K., Kusters, V., Speckmann, B., Staals, F. & Vasilescu, B. 2011. ‘A splitting line model for directional relations’. In ‘Proceedings of the 19th ACM SIGSPATIAL Interna- tional Conference on Advances in Geographic Information Systems’, GIS ’11, 142–151. New York, NY, USA: ACM. http://doi.acm.org/10.1145/2093973.2093994.

Byrne, R. W. 1979. ‘Memory for urban geography’. Quarterly Journal of Experimental Psychology 31: 147–154.

Chen, Jenny J., Menezes, Natalo J. & Bradley, Adam D. 2011. ‘Opportunities for crowd- sourcing research on amazon mechanical turk’.

Cicerone, S. & Di Felice, P. 2000. ‘Cardinal relations between regions with a broad boundary’. In ‘Proceedings of the 8th ACM international symposium on Advances in geographic information systems’, GIS ’00, 15–20. New York, NY, USA: ACM.

Claramunt, C., Thériault, M. & Parent, C. 1997. ‘A qualitative representation of evolving spatial entities in two-dimensional spaces’. Innovations inGIS V,Carver, S.Ed. 119–129.

Clatworthy, J., Buick, D., Hankins, M., Weinman, J. & Horne, R. 2005. ‘The use and reporting of cluster analysis in health psychology: A review’. British Journal of Health Psychology 10: 329–358.

Clementini, E. 2013. ‘Directional relations and frames of reference’. GeoInformatica 17, no. 2: 235–255. Cohn, A. G. & Renz, Jochen. 2008. ‘Qualitative spatial representation and reasoning’. In Frank van Harmelen, Vladimir Lifschitz & Bruce Porter (eds.) ‘Handbook of knowledge representation’, Foundations of artificial intelligence, 551–596. Amsterdam: Elsevier.

Corcoran, P., Mooney, P. & Bertolotto, M. 2012. ‘Spatial Relations Using High Level Con- cepts’. ISPRS International Journal of Geo-Information 1, no. 3: 333–350.

Coventry, K. R. 1999. ‘Function, geometry and spatial prepositions: Three experiments.’ Spatial Cognition and Computation 1: 145–154.

Coventry, K. R. & Garrod, S.C. 2004. Saying, Seeing, and Acting: The Psychological Semantics of Spatial Prepositions. Hove: Psychology Press.

Duckham, M., Jeong, M-H., Li, S. & Renz, J. 2010. ‘Decentralized querying of topological relations between regions without using localization’. In ‘Proc. 18th ACM SIGSPATIAL GIS’, 414–417.

Frank, A. U. 1992. ‘Qualitative spatial reasoning about distances and directions in geographic space’. Journal of Visual Languages & Computing 3, no. 4: 343–371.

Frank, A. U. 1996. ‘Qualitative spatial reasoning: Cardinal directions as an example’. International Journal of Geographical Information Systems 10, no. 3: 269–290.

Franklin, N., Henkel, L.A. & Zangas, T. 1995. ‘Parsing surrounding space into regions’. Memory and Cognition 23: 397–407.

Freksa, C. 1992. ‘Using orientation information for qualitative spatial reasoning’. In ‘Theories and methods of spatio-temporal reasoning in geographic space’, 162–178. Springer Berlin Heidelberg.

Gahegan, M. 1995. ‘Proximity operators for qualitative spatial reasoning’. In A. U. Frank & W. Kuhn (eds.) ‘Spatial Information Theory’, 31–44. Berlin: Springer.

Galton, A. 2000. Qualitative spatial change. Spatial information systems. Oxford: Oxford Univ. Press.

Golledge, R. G., Marsh, M. & Battersby, S. 2008. ‘A conceptual framework for facilitating geospatial thinking’. Annals of the Association of American Geographers 98, no. 2: 285– 308.

Goyal, R.K. 2000. Similarity assessment for cardinal directions between extended spatial objects. Ph.D. thesis, The University of Maine.

Goyal, R.K. & Egenhofer, M.J. 1997. ‘The direction-relation matrix: A representation of direction relations for extended spatial objects’. In ‘UCGIS Annual Assembly and Summer Retreat’, Bar Harbor, ME.

Hobbs, J. R. 1985. ‘Granularity’. In A. K. Joshi (ed.) ‘Proceedings of the 9th International Joint Conference on Artificial Intelligence. Los Angeles, CA, August 1985’, 432–435. San Francisco and CA: Morgan Kaufmann.

Holmes, K. J. & Wolff, P. 2013. ‘When is language a window into the mind? Looking beyond words to infer conceptual categories’. In Markus Knauff, M. Pauen, N. Sebanz & I. Wachsmuth (eds.) ‘Proceedings of the 35th Annual Conference of the Cognitive Science Society’, Austin and TX: Cognitive Science Society.

Jiang, J. & Worboys, M. 2008. ‘Detecting basic topological changes in sensor networks by local aggregation’. In ‘Proc. 16th ACM International Conference on Advances in Geographic Information Systems’, 1–10.

Khan, A. & Schneider, M. 2010. ‘Topological Reasoning Between Complex Regions in Databases with Frequent Updates’. In ‘18th ACM SIGSPATIAL Int. Conf. on Advances in Geographic Information Systems (ACM SIGSPATIAL GIS)’, 380–389.

Klippel, A. 2012. ‘Spatial information theory meets spatial thinking - Is topology the Rosetta Stone of spatio-temporal cognition?’ Annals of the Association of American Geographers 102, no. 6: 1310–1328.

Klippel, A., Worboys, M. & Duckham, M. 2008. ‘Identifying factors of geographic event conceptualisation’. International Journal of Geographical Information Science 22, no. 2: 183–204.

Klippel, A., Wallgrün, J. O., Yang, J., Mason, J. S., Kim, E-K. & Mark, D. M. 2013. ‘Fundamental Cognitive Concepts of Space (and Time): Using Cross-Linguistic, Crowd- sourced Data to Cognitively Calibrate Modes of Overlap’. In T. Tenbrink, J. G. Stell, A. Galton & Z. Wood (eds.) ‘COSIT, vol. 8116 of Lecture Notes in Computer Science’, 377–396. Springer.

Landau, B. & Jackendoff, R. 1993. ‘"What" and "where" in spatial language and cognition’. Behavioral and Brain Sciences 16: 217–265.

Ligozat, G. 1993. ‘Qualitative Triangulation for Spatial Reasoning’. In Andrew U. Frank & Irene Campari (eds.) ‘Spatial Information Theory: A Theoretical Basis for GIS, (COSIT’93), Marciana Marina, Elba Island, Italy’, Lecture Notes in Computer Science, vol. 716, 54–68. Springer.

Ligozat, G. 1998. ‘Reasoning about Cardinal Directions’. J. Vis. Lang. Comput. 9, no. 1: 23–44.

Ligozat, G. 2012. Qualitative spatial and temporal reasoning. London: ISTE.

Medin, Douglas L., Wattenmaker, William D. & Hampson, Sarah E. 1987. ‘Family resem- blance, conceptual cohesiveness, and category construction’. Cognitive Psychology 19, no. 2: 242–279.

Moar, I. & Bower, G.H. 1983. ‘Inconsistency in spatial knowledge’. Memory and Cognition 11, no. 2: 107–113.

Montello, D. R. & Frank, A. U. 1996. ‘Modeling directional knowledge and reasoning in environmental space: Testing qualitative metrics.’ In Juval Portugali (ed.) ‘The construction of cognitive maps’, 321–344. Dodrecht: Kluwer.

Moratz, R. & Fischer, K. 2000. ‘Cognitively Adequate Modelling of Spatial Reference in Human-Robot Interaction’. In‘In IEEEInternational Conference on Toolswith Artificial Intelligence (ICTAI-2000)’, 222–228.

Moratz, R., Renz, J. & Wolter, D. 2000. ‘Qualitative Spatial Reasoning about Line Segments’. In ‘Proceedings of the 14th European Conference on Artificial Intelligence (ECAI’00)’, 234–238.

Moratz, R., Dylla, F. & Frommberger, L. 2005. ‘A Relative Orientation Algebra with Adjustable Granularity’. In ‘Proceedings of the Workshop on Agents in Real-Time and Dynamic Environments (IJCAI-05)’, Edinburgh.

Nystuen, J. D. 1968. ‘Identification of some fundamental spatial concepts’. In Berry, Brian J. L. & D. F. Marble (eds.) ‘Spatial Analysis’, 35–41. Englewood Cliffs and NJ: Prentice Hall.

Paolacci, G., Chandler, J. & Ipeirotis, P. G. 2010. ‘Running experiments on amazon mechanical turk’. Judgement and Decision Making 5, no. 5: 411–419.

Papadias, D., Egenhofer, M. J. & Sharma, J. 1996. ‘Hierarchical reasoning about direction relations’. In ‘Proceedings of the 4th ACM international workshop on Advances in geographic information systems’, GIS ’96, 105–112. New York, NY, USA: ACM.

Pothos, E. M., Perlman, A., Bailey, T. M., Kurtz, K., Edwards, D. J., Hines, P. & McDonnell, J. V. 2011. ‘Measuring category intuitiveness in unconstrained categorization tasks’. Cognition 121, no. 1: 83–100.

Pozzani, G. & Combi, C. 2011. ‘An inference system for relationships between spatial granularities’. In ‘Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems’, GIS ’11, 429–432. New York, NY, USA: ACM.

Renolen, A. 2000. ‘Modelling the Real World: Conceptual Modelling in Spatiotemporal Information System Design’. Transactions in GIS 4, no. 1: 23–42.

Renz, J. & Mitra, D. 2004. ‘Qualitative Direction Calculi with Arbitrary Granularity’. In ‘PRICAI 2004: Trends in Artificial Intelligence, 8th Pacific Rim International Confer- ence on Artificial Intelligence, Proceedings’, 65–74. Springer.

Rodríguez, M. A., Brisaboa, N., Meza, J. & Luaces, M. R. 2010. ‘Measuring consis- tency with respect to topological dependency constraints’. In ‘Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems’, 182–191.

Ross, J., Irani, L., Silberman, M. S., Zaldivar, A. & Tomlinson, B. 2010. ‘Who are the crowdworkers? Shifting demographics in mechanical turk’. In ‘CHI EA 2010 Extended Abstracts on Human Factors in Computing Systems’, 2863–2872.

Roth, R. E., Finch, B. G., Blanford, J. I., Klippel, A., Robinson, A. C. & MacEachren, A. M. 2010. ‘The card sorting method for map symbol design’. In ‘Proceedings of the 2010 International Symposium on Automated Cartography (AutoCarto)’, Orlando, FL: November 18.

Sadalla, E. K. & Montello, D. R. 1989. ‘Remembering changes in direction’. Environment and Behavior 21, no. 3: 346–363.

Schultz, C., Amor, R. & Guesgen, H. W. 2011. ‘Methodologies for qualitative spatial and temporal reasoning application design’. In S. M. Hazarika (ed.) ‘Qualitative Spatiotemporal Representation and Reasoning’, Hershey and Pa.: IGI Global.

Shelton, A. L. & Gabrieli, J. D. E. 2004. ‘Neural correlates of individual differences in spatial learning strategies’. Neuropsychology 18, no. 3: 442–449.

Tenbrink, T.2011. ‘Reference frames of space and time in language’. Journal of Pragmatics 43, no. 3: 704–722. Tullis, T. & Wood, L. 2004. ‘How many users are enough for a card-sorting study?’ In ‘Proceedings of the UPA 2004 Conference, June 7-11, Minneapolis’, Minnesota.

Tversky, B. 1981. ‘Distortion in memory for maps’. Cognitive Psychology 13, no. 3: 407– 433.

van der Zee, E. & Eshuis, R. 2003. ‘Directions from shape: How spatial features determine reference axis categorization’. In E. van der Zee & J. Slack (eds.) ‘Representing Direction in Language and Space’, 209–225. Oxford: Oxford University Press.

Vorwerg, C. 2003. ‘Use of reference direcions in spatial encoding’. In C. Freksa, W. Brauer, C. Habel & K. F. Wender (eds.) ‘Spatial Cognition III: Routes and Navigation, Human Memory and Learning, Spatial Representation and Spatial Learning’, 321–347. Berlin: Springer.