1.2.3. Institutional Model Theory as Such

The abstract axiomatic development of institutional model theory goes back to [30–32]. Those early endeavours stemmed from computing science, addressing typical issues from formal specification (such as initial semantics), but they also led to strong model–theoretic results in themselves. Even so, a systematic programme for developing an in-depth institutional model theory beyond computing science motivations arose only after 2000.

	- 1. A *new understanding* of model–theoretic phenomena that are uncontaminated by irrelevant concrete details; this led to revisions of well established concepts and facilitated access to difficult results;
	- 2. A consequence of (1) is a series of results about completeness [38,39], definability [40,41], interpolation [42–45], Löwenheim–Skolem [37,45], some instances of these representing *new important results* even in first-order model theory;
	- 3. A systematic and uniform development of *model theories for unconventional logics*, either new or older ones, which is a process of great difficulty within concrete frameworks.

Moreover, in the case of (3), the institution–theoretic approach has also led to a better understanding of the respective logics sometimes accompanied by a conceptual resetting.
