The Axiomatic Approach to Non-Classical Model Theory

Institution theory represents the fully axiomatic approach to model in which all components of logical systems are treated abstractly by reliance on category theory. Here, we survey some developments over last decade or so concerning institution theoretic non-classical aspects Our focus will be many-valued truth and models with states, addressed two extensions ordinary known as L-institutions stratified institutions, respectively. The discussion include relevant concepts, techniques, results from these areas.