# Borrowing Interpolation(*abstract*)

We present a generic method for establishing interpolation properties by
`borrowing' across logical systems.
The framework used is that of the so-caled `institution theory' which is
a categorical abstract model theory providing a formal definition for the
informal concept of `logical system' and a mathematical concept of
`homomorphism' between logical systems.
We develop three different styles or patterns to apply the proposed
borrowing interpolation method.
These three ways are illustrated by the development of a series of
concrete interpolation results for logical systems that are used in
mathematical logic or in computing science, most of these
interpolation properties apparently being new results.
These logical systems include fragments of (classical many sorted)
first order logic with equality, preordered algebra and its Horn
fragment, partial algebra, higher order logic.
Applications are also expected for many other logical systems,
including membership algebra, various types of order sorted algebra,
the logic of predefined types, etc., and various combinations of the
logical systems discussed here.

back to Selected Publications