*1.2. 3/2-Institutions*

Although in mainstream institution theory signature morphisms are considered in their full generality, they are always implicitly assumed to be total. However, there are few contexts that on the one hand require partial translations between signatures, and on the other hand require an institution theoretic treatment. Two such contexts are conceptual blending [9–11] and software evolution [12]. In [13], we have developed an extension of the ordinary concept of institution [1,3] that accommodates implicitly partiality of the signature morphisms in order to constitute foundations for the above-mentioned application domains. This new structure is called *3/2-institution*, and mathematically, is significantly more complex than ordinary institutions. One way to develop the theory of 3/2-institutions is by representing them in another institution theory that enjoys a higher level of development, and through such a representation to import concepts and results from there. With this paper, we take a few steps in this direction.

The semantic effect of the (implicit) partiality of the signature morphisms in 3/2 institutions is that the reduct of a model with respect to a given signature morphism is a *set* of models rather than a single model. This goes at the heart of our representation of 3/2-institutions as stratified institutions: in the representation the states of a model consists of the set of its reducts (with respect to a given signature morphism).
