Interpolation in Grothendieck Institutions

It is well known that interpolation properties of logics underlying speci.cation formalisms play an important role in the study of structured speci.cations, they have also many other useful logical consequences. In this paper, we solve the interpolation problem for Grothendieck institutions which have recently emerged as an important mathematical structure underlying heterogenous multi-logic speci.cation. Our main result can be used in the applications in several di2erent ways. 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 generalisation of unsorted interpolation. The concepts, results, and the applications discussed in this paper are illustrated with several examples from conventional logic and algebraic speci.cation theory. c © 2003 Elsevier B.V. All rights reserved.