On case-based represent ability and learnability of languages

  • Christoph Globig
  • Steffen Lange
Selected Papers Analogical and Inductive Inference
Part of the Lecture Notes in Computer Science book series (LNCS, volume 872)


Within the present paper we investigate case-based representability as well as case-based learnability of indexed families of uniformly recursive languages. Since we are mainly interested in case-based learning with respect to an arbitrary fixed similarity measure, case-based learnability of an indexed family requires its represent ability, first.

We show that every indexed family is case-based representable by positive and negative cases. If only positive cases are allowed the class of representable families is comparatively small. Furthermore, we present results that provide some bounds concerning the necessary size of case bases.

We study, in detail, how the choice of a case selection strategy influences the learning capabilities of a case-based learner. We define different case selection strategies and compare their learning power to one another. Furthermore, we elaborate the relations to Gold-style language learning from positive and both positive and negative examples.


Similarity Measure Case Base Formal Language Representative Case Recursive Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Christoph Globig
    • 1
  • Steffen Lange
    • 2
  1. 1.University of KaiserslauternKaiserslauternGermany
  2. 2.HTWK LeipzigLeipzigGermany

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