Select the Appropriate Map Depending on Context in a Hilbert Space Model (SCOP)

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.

[1]  Daniel R. Montello,et al.  Cognition of Geographic Information , 2005 .

[2]  Edward E. Smith,et al.  Conceptual Combination with Prototype Concepts , 1984, Cogn. Sci..

[3]  M. Goodchild,et al.  Geographic Information Systems and Science (second edition) , 2001 .

[4]  V. Fock Konfigurationsraum und zweite Quantelung , 1932 .

[5]  E. Rosch,et al.  Family resemblances: Studies in the internal structure of categories , 1975, Cognitive Psychology.

[6]  Diederik Aerts,et al.  A Quantum Model for the Ellsberg and Machina Paradoxes , 2012, QI.

[7]  Sophie Ahrens,et al.  Recommender Systems , 2012 .

[8]  Diederik Aerts,et al.  The Guppy Effect as Interference , 2012, QI.

[9]  Gerd Stumme,et al.  Formal Concept Analysis , 2009, Handbook on Ontologies.

[10]  John Hughes,et al.  Report on the Programming Language Haskell 98 , 1999 .

[11]  Diederik Aerts,et al.  A Quantum Structure Description of the Liar Paradox , 1999 .

[12]  Liane Gabora,et al.  Cognitive mechanisms underlying the creative process , 2002, Creativity & Cognition.

[13]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[14]  M. Goodchild Citizens as sensors: the world of volunteered geography , 2007 .

[15]  Diederik Aerts,et al.  Contextualizing concepts using a mathematical generalization of the quantum formalism , 2002, J. Exp. Theor. Artif. Intell..

[16]  Diederik Aerts,et al.  General Quantum Modeling of Combining Concepts: A Quantum Field Model in Fock Space , 2007, 0705.1740.

[17]  L. Gabora,et al.  Cognitive Mechanisms Underlying the Origin and Evolution of Culture , 2001 .

[18]  Diederik Aerts,et al.  Toward an Ecological Theory of Concepts , 2008, 0803.2567.

[19]  Robert B McMaster,et al.  A Research Agenda for Geographic Information Science , 2004 .

[20]  Robert Weibel,et al.  GIS and generalization: methodology and practice. , 1995 .

[21]  Diederik Aerts,et al.  A Theory of Concepts and Their Combinations II: A Hilbert Space Representation , 2004 .

[22]  Diederik Aerts,et al.  A theory of concepts and their combinations I: The structure of the sets of contexts and properties , 2005 .

[23]  Bettina Berendt,et al.  Spatial Representation with Aspect Maps , 1998, Spatial Cognition.

[24]  Diederik Aerts,et al.  Intrinsic contextuality as the crux of consciousness , 2013, 1310.7672.

[25]  E. Rosch Cognitive reference points , 1975, Cognitive Psychology.

[26]  Barry Smith,et al.  Ontology with Human Subjects Testing: An Empirical Investigation of Geographic Categories , 1998 .

[27]  Ingo Schmitt,et al.  QQL: A DB&IR Query Language , 2007, The VLDB Journal.