Encyclopedia of Machine Learning

2010 Edition
| Editors: Claude Sammut, Geoffrey I. Webb

Subsumption

  • Claude Sammut
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30164-8_800

Subsumption provides a syntactic notion of generality. Generality can simply be defined in terms of the cover of a concept. That is, a concept, C, is more general than a concept, C, if C covers at least as many examples as C (see  Learning as Search). However, this does not tell us how to determine, from their syntax, if one sentence in a concept description language is more general than another. When we define a subsumption relation for a language, we provide a syntactic analogue of generality (Lavrač & Dčeroski, 1994). For example, θ-subsumption (Plotkin, 1970) is the basis for constructing generalization lattices in  inductive logic programming (Shapiro, 1981). See  Generality of Logic for a definition of θ-subsumption. An example of defining a subsumption relation for a domain specific language is in the LEX program (Mitchell, Utgoff, & Banerji, 1983), where an ordering on mathematical expressions is given.

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Recommended Reading

  1. Lavrač, N., & Džeroski, S. (1994). Inductive Logic Programming: Techniques and applications. Chichester: Ellis Horwood.MATHGoogle Scholar
  2. Mitchell, T. M., Utgoff, P. E., & Banerji, R. B. (1983). Learning by experimentation: Acquiring and refining problem-solving heuristics. In R. S. Michalski, J. G. Carbonell, & T. M. Mitchell (Eds.), Machine learning: An artificial intelligence approach. Palo Alto: Tioga.Google Scholar
  3. Plotkin, G. D. (1970). A note on inductive generalization. In B. Meltzer & D. Michie (Eds.), Machine intelligence (Vol. 5, pp. 153–163). Edinburgh University Press.Google Scholar
  4. Shapiro, E. Y. (1981). An algorithm that infers theories from facts. In Proceedings of the seventh international joint conference on artificial intelligence, Vancouver (pp. 446–451). Los Altos: Morgan Kaufmann.Google Scholar

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  • Claude Sammut

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