On the fragility of interpolation

We study a version of Craig interpolation formulated in the framework of the theory of institutions. This formulation proved crucial in the development of a number of key results concerning foundations of software specification and formal development. We investigate the fragility of interpolation properties of an institution when the institution is extended by adding new models and sentences. We point out that some interpolation properties remain stable under such extensions, even if quite arbitrary new models and sentences are permitted. We give complete characterisations of such situations for institution extensions by new models, by new sentences, as well as by new models and sentences, respectively.