Analyzing frame conditions in UML/OCL models: consistency equivalence and independence

In behavioral modeling using UML/OCL, operation contracts defined by pre- and postconditions describe the effects on model elements (such as attributes, links, etc.) that are enforced by an operation. However, it is usually not clearly stated which model elements can be affected and which shall not, although this information is essential in order to obtain a comprehensive description. A promising solution to this so-called frame problem is to define additional frame conditions. However, properly defining frame conditions which complete the model description in the intended way is a non-trivial, tedious and error-prone task. While for UML/OCL models in general, methods for validation and verification are available, no analysis methods for frame conditions exist so far that could support the designer in this process. In this work, we close this gap and propose a set of primary analysis objectives (namely consistency, equivalence, and independence) that provide substantial information about the correctness and adequateness of given frame conditions. Moreover, we formalize these objectives as to be able to conduct the corresponding analyses in an automatic fashion using the deductive power of established approaches for model validation and verification. Finally, we discuss how the resulting methodology can actually be applied and demonstrate its potential for elaborated analyses of frame conditions.