Abstract Model Theory Results in the Framework of the Institutions: Towards logics combination.
The importance of Craig interpolation for structuration and modularity of axiomatic style specifications have been shown by many works. In order to give sufficient conditions to Craig interpolation in a suitable framework for computer science, we've studied a propery equivalent to Craig interpolation in standard model theory: Robinson consistency. To do so, we had to generalize the notions of complete diagrams and elementary morphisms in a specialization of institutions. This allowed the generalization of other classical standard model theory results such as Löwenheim-Skolem theorem and Tarski chain union. Finally, since formulae constructors are explicite in our framework, we've studied logic combination and the preservation of both Craig interpolation and Robinson consistency through combination.