The concept of many-logics modal systems was recently introduced by Alfredo R. Freire and Manuel A. Martins. In this framework, each state is associated with a sub-lattice of a common lattice L. These sub-lattices serve as local truth spaces, where we interpret formulas based on the logic paradigm of a specific state. This allows for a model where the local interpretation of formulas can be done in various lattices such as the standard 2-value lattice, the 3-value lattice, or even the [0, 1]-lattice, as all of these are sub-lattices of the latter. Furthermore, the use of modalities allows for the interpretation of a formula to incorporate all of these logic paradigms simultaneously.

In this talk, we explore the first steps in this direction by formalizing this logic as an institution. This formalisation opens the door to using all the solid institution-independent machinery for formal program development of Sannella and Tarlecki. We investigate the applicability of this specification framework to design systems whose configurations requirements have different nature – for instance, when we have fuzzy and classic assumptions about the same entity, depending on the configuration of the system. On the other hand, we employ this machinery as a meta-level framework to assist the design development process by approaching states as design stages, and the transition as development steps. This shall provide a logic to talk about the heterogeneous development process. Eventually, having the specification building operators characterized (union, hiding, etc), the architectural decisions on this process shall be reflected in our models.