Intersection-closed classes of concepts arise naturally in many contexts and have been intensively studied in computational learning theory. In this paper, we study intersection-closed classes that contain the concepts invariant under an operation satisfying a certain algebraic condition. We give a learning algorithm in the exact model with equivalence queries for such classes. This algorithm utilizes a novel encoding scheme, which we call a signature.

The first author was supported by an NSERC Discovery Grant. The second and third authors were supported by grant TIC 2002-04470-C03 and the EU PASCAL Network of Excellence IST-2002-506778. The third author was also supported by the MEC under the program “Ramon y Cajal”, grant TIC 2002-04019-C03, and MODNET Marie Curie Research Training Network MRTN-CT-2004-512234.