Interpolation in Grothendieck Institutions
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Grothendieck institutions have recently emerged as an important
mathematical structure underlying heterogenuous multi-logic
On the other hand, interpolation properties of logics underlying
specification formalisms play an important role in the study of
In this paper we solve the interpolation problem for Grothendieck
Our main result can be used in the applications in several different
It can be used to establish interpolation properties for multi-logic
Grothendieck institutions, but also to lift interpolation properties
from unsorted logics to their many sorted variants.
The importance of the latter resides in the fact that, unlike other
structural properties of logics, many sorted interpolation is a
non-trivial generalization of unsorted interpolation.
The concepts, results, and the applications discussed in this paper
are illustrated with several examples from conventional logic and
algebraic specification theory.