Probabilistic and quantum institutions revisited

We revisit quantum institutions as in [2] and solve some problems identified therein. Global, probabilistic and quantum exogenous enrichments of logics are adapted to a new notion of global model. For simplicity sake, all the constructions are presented in the realm of satisfaction systems, which proves to be an appropriate framework for defining the new logics. It also provides suitable constructions for studying the relationship between these enrichments and compare them with the constructions of [2]. Nevertheless, all the constructions are shown to be easily extended to institutions.