*Article* **Representing 3/2-Institutions as Stratified Institutions**

**R ˘azvan Diaconescu**

Simion Stoilow Institute of Mathematics of the Romanian Academy, 010702 Bucharest, Romania; razvansdiaconescu@gmail.com

**Abstract:** On the one hand, the extension of ordinary institution theory, known as the theory of stratified institutions, is a general axiomatic approach to model theories where the satisfaction is parameterized by states of the models. On the other hand, the theory of 3/2-institutions is an extension of ordinary institution theory that accommodates the partiality of the signature morphisms and its syntactic and semantic effects. The latter extension is motivated by applications to conceptual blending and software evolution. In this paper, we develop a general representation theorem of 3/2-institutions as stratified institutions. This enables a transfer of conceptual infrastructure from stratified to 3/2-institutions. We provide some examples in this direction.

**Keywords:** institution theory; category theory; stratified institutions; 3/2-institutions; categorical model theory

**MSC:** 18N10; 03C95; 68Q65; 68T27
