Abstract
Human use of categories exhibits a prototype effect; concepts become more defined through a conversation. Modelling these gradual clarifications of what a word signifies is equally important in human - computer interactions, for example in interactions about geographic concepts and the information that is needed in a given situation. We address here the simplified, but essentially realistic, question of what is meant by “map” and how the concept is refined. We apply the methods Aerts, Gabora and Rosch have described and explore how they can be integrated into practical systems.
In this paper we explore the optimal selection of a map through a conversation with the client to elucidate their intentions. The example case contains effects which are similar to the “guppy effect” that is known from the literature and is a key reason to apply quantum mechanical formalism. The results are promising, and we sketch the extension to the construction of “custom made” maps from layers. This will provide users with maps that optimally reflect what map elements should be visible for use in a given context.
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References
Aerts, D., Broekaert, J., Gabora, L.: Intrinsic contextuality as the crux of consciousness. In: Yasne, K., Jibu, M., Della Senta, T. (eds.) No Matter, Never Mind: Proceedings of Toward a Science of Consciousness: Fundamental Approaches, pp. 173–182. John Benjamins Publishing Company, Philadelphia (1999)
Aerts, D., Broekaert, J., Smets, S.: A quantum structure description of the liar paradox. Int. J. Theor. Phys. 38, 3231–3239 (1999)
Aerts, D., Gabora, L.: A theory of concepts and their combinations I: the structure of the sets of contexts and properties. Kybernetes 34, 167–191 (2005)
Aerts, D., Gabora, L.: A theory of concepts and their combinations II: a Hilbert space representation. Kybernetes 34, 192–221 (2005)
Aerts, D.: General Quantum Modeling of Combining Concepts: A Quantum Field Model in Fock Space. arXiv, preprint arXiv:0705.1740. 51 (2007)
Aerts, D., Sozzo, S., Tapia, J.: A quantum model for the ellsberg and machina paradoxes. In: Busemeyer, J.R., Dubois, F., Lambert-Mogiliansky, A., Melucci, M. (eds.) QI 2012. LNCS, vol. 7620, pp. 48–59. Springer, Heidelberg (2012)
Aerts, D., Broekaert, J., Gabora, L., Veloz, T.: The Guppy effect as interference. In: Busemeyer, J.R., Dubois, F., Lambert-Mogiliansky, A., Melucci, M. (eds.) QI 2012. LNCS, vol. 7620, pp. 36–47. Springer, Heidelberg (2012)
Berendt, B., Barkowsky, T., Freksa, C., Kelter, S.: Spatial representation with aspect maps. In: Freksa, C., Habel, C., Wender, K.F. (eds.) Spatial Cognition 1998. LNCS (LNAI), vol. 1404, pp. 313–336. Springer, Heidelberg (1998)
Fock, V.: Konfigurationsraum und zweite quantelung. Zeitschrift für Physik 75, 622–647 (1932)
Gabora, L.: cognitive mechanisms underlying the origin and evolution of culture (2001)
Gabora, L., Aerts, D.: Contextualizing concepts using a mathematical generalization of the quantum formalism. J. Exp. Theor. Artif. Intell. 14, 327–358 (2002)
Gabora, L., Rosch, E., Aerts, D.: Toward an ecological theory of concepts. Ecol. Psychol. 20, 84–116 (2008)
Ganter, B., Stumme, G., Wille, R. (eds.): Formal Concept Analysis. Springer, Heidelberg (2005)
Goodchild, M.: Citizens as sensors: the world of volunteered geography. GeoJournal 69, 211–221 (2007)
Jones, S., Hughes, J., Augustsson, L., Barton, D.: Report on the programming language Haskell 98 (1999)
Longley, P.A., Goodchild, M.F., Maguire, D.J., Rhind, D.W.: Geographic Information Systems and Science. Wiley, New York (2005)
Lü, L., Medo, M., Yeung, C.H., Zhang, Y.-C., Zhang, Z.-K., Zhou, T.: Recommender systems. Phys. Rep. 519, 1–49 (2012)
Montello, D.R., Freundschuh, S.: Cognition of geographic information. In: McMaster, R.B., Usery, E.L. (eds.) A Research Agenda for Geographic Information Science, pp. 61–91. CRC Press, Boca Raton (2005)
Muller, J.J.-C., Lagrange, J.J.-P., Weibel, R.: GIS and Generalization: Methodology and Practice. Taylor & Francis Group, London (1995)
Raper, J.: Geographic information science. Annu. Rev. Inf. Sci. Technol. 43, 1–117 (2009)
Rosch, E., Mervis, C.B.: Family resemblances: studies in the internal structure of categories. Cogn. Psychol. 7, 573–605 (1975)
Rosch, E.: Cognitive reference points. Cogn. Psychol. 7, 532–547 (1975)
Schmitt, I.: QQL: a DB&IR query language. VLDB J. 17, 39–56 (2007)
Smith, E., Osherson, D.: Conceptual combination with prototype concepts. Cogn. Sci. 8, 337–361 (1984)
Smith, B., Mark, D.: Ontology with human subjects testing. Am. J. Econ. Sociol. 58, 245–312 (1998)
Weiser, P., Frank, A., Abdalla, A: Process composition and process reasoning over multiple levels of detail. In: 7th International Conference, GIScience 2012, Columbus, Ohio (2012)
Zadeh, L.A.: Fuzzy sets. Inform. Control 8, 338–353 (1965)
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Hahn, J., Frank, A.U. (2014). Select the Appropriate Map Depending on Context in a Hilbert Space Model (SCOP). In: Atmanspacher, H., Haven, E., Kitto, K., Raine, D. (eds) Quantum Interaction. QI 2013. Lecture Notes in Computer Science(), vol 8369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54943-4_11
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