Qualitative Reasoning about Incomplete Categorization Rules Based on Interpolation and Extrapolation in Conceptual Spaces

  • Steven Schockaert
  • Henri Prade
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6929)


Various forms of commonsense reasoning may be used to cope with situations where insufficient knowledge is available for a given purpose. In this paper, we rely on such a strategy to complete sets of symbolic categorization rules, starting from background information about the semantic relationship of different properties and concepts. Our solution is based on Gärdenfors conceptual spaces, which allow us to express semantic relationships with a geometric flavor. In particular, we take the inherently qualitative notion of betweenness as primitive, and show how it naturally leads to patterns of interpolative reasoning. Both a semantic and a syntactic characterization of this process is presented, and the computational complexity is analyzed. Finally, some patterns of extrapolative reasoning are sketched, based on the notions of betweenness and parallelism.


Attribute Space Rule Base Categorization Rule Conceptual Space Qualitative Reasoning 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Steven Schockaert
    • 1
  • Henri Prade
    • 2
  1. 1.Department of Applied Mathematics and Computer ScienceGhent UniversityBelgium
  2. 2.Institut de Recherche en Informatique de Toulouse (IRIT), Université Paul SabatierToulouseFrance

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