Abstract
Formal models of geographic space should support reasoning about its static and dynamic properties, its objects, their behaviors, and the relationships between them. Image schemas, used to embody spatiotemporal experiential abstractions, capture high-level perceptual concepts but do not have generally accepted formalizations. This paper provides a method for formally representing topological and physical image schemas using Milner’s bigraphical models. Bigraphs, capable of independently representing mobile locality and connectivity, provide formal algebraic specifications of geographic environments enhanced by intuitive visual representations. Using examples from a built environment, we define topological schemas CONTAINER and LINK as static bigraph components, dynamic schemas INTO and LINKTO as rule-based changes in static components, and more complex schemas REMOVAL_OF_RESTRAINT and BLOCKAGE with sequences of rules. Finally, we demonstrate that bigraphs can be used to describe scenes with incomplete information, and that we can adjust the granularity of scenes by using bigraph composition to provide additional context.
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References
Birkedal, L., Debois, S., Hildebrandt, T.: Sortings for reactive systems. In: Baier, C., Hermanns, H. (eds.) CONCUR 2006. LNCS, vol. 4137, pp. 248–262. Springer, Heidelberg (2006)
Bundgaard, M., Sassone, V.: Typed polyadic pi-calculus in bigraphs. In: Proceedings of the 8th ACM SIGPLAN international conference on Principles and practice of declarative programming, Venice, Italy, pp. 1–12 (2006)
Cardelli, L.: Abstractions for Mobile Computation. In: Vitek, J., Jensen, C. (eds.) Secure Internet Programming. LNCS, vol. 1603, pp. 51–94. Springer, Heidelberg (1999)
Cardelli, L., Gordon, A.: Mobile Ambients. In: Le Métayer, D. (ed.) Theoretical Computer Science, Special Issue on Coordination, vol. 240(1), pp. 177–213 (2000)
Egenhofer, M.J., RodrÃguez, A.: Relation algebras over containers and surfaces: An ontological study of a room space. Spatial Cognition and Computation 1(2), 155–180 (1999)
Frank, A.U.: Specifications for Interoperability: Formalizing Spatial Relations ’In’, ’Auf’ and ’An’ and the Corresponding Image Schemata ’Container’, ’Surface’ and ’Link’. Agile-Conference, ITC, Enschede, The Netherlands (1998)
Frank, A.U., Raubal, M.: Specifications for Interoperability: Formalizing Image Schemata for Geographic Space. In: Proceeding from the 8th International Symposium on Spatial Data Handling, pp. 331–348. IGU, Vancouver (1998)
Frank, A.U., Raubal, M.: Formal specification of image schemata – a step towards interoperability in geographic information systems. Spatial Cognition and Computation 1(1) (1999)
Freundschuh, S.M., Sharma, M.: Spatial Image Schemata, Locative Terms, and Geographic Spaces in Children’s Narrative: Fostering Spatial Skills in Children. Cartographica: The International Journal for Geographic Information and Geovisualization 32(2), 38–49 (1996)
Gibson, J., Shaw, R., Bransford, J.: The Theory of Affordances. Perceiving, Acting, and Knowing (1977)
Grohmann, D., Miculan, M.: Directed Bigraphs. Electron. Notes Theor. Comput. Sci. 173, 121–137 (2007)
Johnson, M.: The Body in the Mind: The Bodily Basis of Meaning, Imagination, and Reason. University Of Chicago Press (1987)
Kuhn, W.: Metaphors Create Theories for Users. In: Campari, I., Frank, A.U. (eds.) COSIT 1993. LNCS, vol. 716, pp. 366–376. Springer, Heidelberg (1993)
Kuhn, W.: An Image-Schematic Account of Spatial Categories. In: Spatial Information Theory, pp. 152-168 (2007)
Kuhn, W., Frank, A.U.: A Formalization of Metaphors and Image-Schemas in User Interfaces. Cognitive and Linguistic Aspects of Geographic Space (1991)
Lakoff, G., Nuñez, R.: Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being. Basic Books (2000)
Laiserin, J.: Comparing Pommes and Naranjas. The Laiserin Letter (15) (2002)
Mark, D.M.: Cognitive image-schemata for geographic information: Relations to user views and GIS interfaces. In: Proceedings, GIS/LIS 1989, Orlando, Florida, vol. 2, pp. 551–560 (1989)
Mark, D.M., Frank, A.U.: Concepts of space and spatial language. In: Proceedings, Ninth International Symposium on Computer-Assisted Cartography (Auto-Carto 9), Baltimore, Maryland, pp. 538–556 (1989)
Milner, R.: Communicating and mobile systems: the π-calculus. Cambridge University Press, Cambridge (1999)
Milner, R.: Bigraphical Reactive Systems. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 16–35. Springer, Heidelberg (2001)
Milner, R.: Bigraphs and Their Algebra. Electronic Notes in Theoretical Computer Science 209, 5–19 (2008)
Milner, R.: The Space and Motion of Communicating Agents. Cambridge University Press, Cambridge (2009)
Oakley, T.: Image Schemas. In: Geeraerts, D., Cuyckens, H. (eds.) The Oxford handbook of cognitive linguistics, pp. 214–235. Oxford University Press, Oxford (2007)
Raubal, M., Egenhofer, M.J., Pfoser, D., Tryfona, N.: Structuring space with image schemata: wayfinding in airports as a case study. In: Proceedings of the International Conference on Spatial Information Theory, vol. 1329, pp. 85–102 (1997)
Raubal, M., Worboys, M.: A Formal Model of the Process of Wayfinding in Built Environments. In: Spatial Information Theory. Cognitive and Computational Foundations of Geographic Information Science, p. 748 (1999)
RodrÃguez, A., Egenhofer, M.: Image-schemata-based spatial inferences: The container-surface algebra. In: Spatial Information Theory, A Theoretical Basis for GIS, pp. 35–52 (1997)
RodrÃguez, A., Egenhofer, M.: A Comparison of Inferences about Containers and Surfaces in Small-Scale and Large-Scale Spaces. Journal of Visual Languages and Computing 11(6), 639–662 (2000)
Weiser, M.: Some Computer Science Problems in Ubiquitous Computing. Communications of the ACM (July 1993)
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Walton, L., Worboys, M. (2009). An Algebraic Approach to Image Schemas for Geographic Space. In: Hornsby, K.S., Claramunt, C., Denis, M., Ligozat, G. (eds) Spatial Information Theory. COSIT 2009. Lecture Notes in Computer Science, vol 5756. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03832-7_22
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DOI: https://doi.org/10.1007/978-3-642-03832-7_22
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