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The Subsumption Lattice and Query Learning

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Algorithmic Learning Theory (ALT 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3244))

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Abstract

The paper identifies several new properties of the lattice induced by the subsumption relation over first-order clauses and derives implications of these for learnability. In particular, it is shown that the length of subsumption chains of function free clauses with bounded size can be exponential in the size. This suggests that simple algorithmic approaches that rely on repeating minimal subsumption-based refinements may require a long time to converge. It is also shown that with bounded size clauses the subsumption lattice has a large branching factor. This is used to show that the class of first-order length-bounded monotone clauses is not properly learnable from membership queries alone. Finally, the paper studies pairing, a generalization operation that takes two clauses and returns a number of possible generalizations. It is shown that there are clauses with an exponential number of pairing results which are not related to each other by subsumption. This is used to show that recent pairing-based algorithms can make exponentially many queries on some learning problems.

This work has been partly supported by NSF Grant IIS-0099446

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Author information

Authors and Affiliations

  1. Department of Computer Science, Tufts University, Medford, MA, 02155, USA

    Marta Arias & Roni Khardon

Authors
  1. Marta Arias
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  2. Roni Khardon
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Editor information

Editors and Affiliations

  1. David R. Cheriton School of Computer Science University of Waterloo,  

    Shoham Ben-David

  2. Department of Computer & Information Sciences, University of Delaware, 103 Smith Hall, DE 19716, Newark

    John Case

  3. Dept. of Information Technology and Electronics, Ishinomaki Senshu University,  

    Akira Maruoka

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Arias, M., Khardon, R. (2004). The Subsumption Lattice and Query Learning. In: Ben-David, S., Case, J., Maruoka, A. (eds) Algorithmic Learning Theory. ALT 2004. Lecture Notes in Computer Science(), vol 3244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30215-5_31

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  • DOI: https://doi.org/10.1007/978-3-540-30215-5_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23356-5

  • Online ISBN: 978-3-540-30215-5

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