Abstraction is one of the most promising approaches to improve the performance of problem solvers. In several domains abstraction by dropping sentences of a domain description { as used in most hierarchical planners { has proven useful. In this paper we present examples which illustrate signi cant drawbacks of abstraction by dropping sentences. To overcome these drawbacks, we propose a more general view of abstraction involving the change of representation language. We have developed a new abstraction methodology and a related sound and complete learning algorithm that allows the complete change of representation language of planning cases from concrete to abstract. However, to achieve a powerful change of the representation language, the abstract language itself as well as rules which describe admissible ways of abstracting states must be provided in the domain model.This new abstraction approach is the core of Paris (Plan Abstraction and Re nement in an Integrated System), a system in which abstract planning cases are automatically learned from given concrete cases. An empirical study in the domain of process planning in mechanical engineering shows signi cant advantages of the proposed reasoning from abstract cases over classical hierarchical planning.1. Only Tenenberg's (1988) abstraction by analogical mappings and the planning system Sipe (Wilkins, 1988) contains rst approaches that allow a change of representation language.2. However, we might assume that the term X + 1 is modeled as a separate predicate in the precondition.Unfortunately, this does not change the described situation at all. 3. Because we assume many other operators besides the inc-operator, b 1 holds.