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Encyclopedia of Machine Learning pp 937–938Cite as

Subsumption

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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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Generalization

Induction

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Recommended Reading

  • Lavrač, N., & Džeroski, S. (1994). Inductive Logic Programming: Techniques and applications. Chichester: Ellis Horwood.

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  • 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.

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  • 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.

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  • 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.

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    1. Claude Sammut
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    1. School of Computer Science and Engineering, University of New South Wales, Sydney, Australia, 2052

      Claude Sammut

    2. Faculty of Information Technology, Clayton School of Information Technology, Monash University, P.O. Box 63, Victoria, Australia, 3800

      Geoffrey I. Webb

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    © 2011 Springer Science+Business Media, LLC

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    Sammut, C. (2011). Subsumption. In: Sammut, C., Webb, G.I. (eds) Encyclopedia of Machine Learning. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30164-8_800

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