Probabilistic Knowledge Spaces: A Review

  • Jean-Claude Falmagne
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 17)


This paper outlines the essential ideas of a theory for the efficient assessment of knowledge. The key concept is that of a knowledge space, that is, a basic set Q of questions or problems in a given domain of information, equipped with a distinguished family K of subsets. The family K is assumed to be closed under union, and its elements are knowledge states. The equivalence between this concept and other useful ones is spelled out. A practical implementation of computerized, robust knowledge assessment devices requires a probabilistic framework. These developments are also briefly summarized. All the results have been presented at length elsewhere, and are either in press or published.


Knowledge State Probabilistic Framework Hasse Diagram Galois Connection Knowledge Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag New York Inc. 1989

Authors and Affiliations

  • Jean-Claude Falmagne
    • 1
  1. 1.Irvine Research Unit in Mathematical Behavioral Sciences, School of Social ScienceUniversity of California at IrvineIrvineUSA

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