# Subsumption

**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.

## Cross References

### Recommended Reading

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