  We define and study the problem of modular concept learning, that is,
learning a concept that is a cross product of component concepts. If an
element's membership in a concept depends solely on it's membership in the
components, learning the concept as a whole can be reduced to learning the
components. We analyze this problem with respect to different types of oracle
interfaces, defining different sets of queries. If a given oracle interface
cannot answer questions about the components, learning can be difficult, even
when the components are easy to learn with the same type of oracle queries.
While learning from superset queries is easy, learning from membership,
equivalence, or subset queries is harder. However, we show that these problems
become tractable when oracles are given a positive example and are allowed to
ask membership queries.
