**4. Many-Valued Truth Institution-Independent Model Theory**

In standard institution theory, the satisfaction relation between models and sentences is considered to be binary, *M* |= *ρ* either holds true or it does not. Many-valued institution theory considers a generalisation of ordinary institution theory where *M* |= *ρ* is not necessarily binary. Such a generalisation can be achieved, and basic concepts such as semantic consequence, the Galois connection between syntax and semantics, internal logic, but also more advanced concepts such as filtered products, preservation, interpolation, definability, logic translation, etc. do "survive" it but in a subtler form. From a pure theoretical standpoint (there are also more practical motivations), this generalisation brings further clarifications to the complex network of causal relationships underlying model

theory. This has to do with binary truth being a collapsed form of truth where many things happen somehow "by accident". Much institution-independent model theory may be developed in the many-valued truth fashion.
