**5. Conclusions**

Standard institutional model theory has undergone a high level of development as partially shown in [44]. On the other hand, although non-classical institutional model theory, in its stratified and L-institution forms, has advanced significantly over the past decade, it still lags behind the standard version. This is because of two main factors: time scale and mathematical difficulty. While standard institutional model theory has been developed over approximately four decades, the non-classical version is much younger. Then, of course, the latter is mathematically more difficult than the former; it is enough only to compare the basic definition in order to obtain an understanding of this. However, we have already seen that many non-classical developments may benefit from classical ones. At the same time, non-classical institution model theory has aspects that cannot be related to classical developments. All these mean that a lot of interesting theoretical problems await in non-classical institutional model theory, and we hope that in the next decade or so, many of them will be addressed.

In addition, there is something to be addressed that is at least as important as the theoretical problems: namely, to find new relevant applications. For instance, due to the highly abstract nature of this approach, which goes hand-in-hand with the axiomatic method, it has a strong potential to accomodate a wide class of old and new formalisms especially from computing science. However, all these require a thorough exploration.

**Funding:** This work was supported by a grant of the Romanian Ministry of Education and Research, CNCS–UEFISCDI, project number PN-III-P4-ID-PCE-2020-0446, within PNCDI III.

**Conflicts of Interest:** The author declares no conflict of interest.
