An institutional view on relative expressivity
There are several different ways to rank logics in terms of
their expressive power depending on the criteria that we use to
measure expressiveness. Two major model-theoretic directions have
emerged over the years. One treats expressive power as the capacity of
a logical language to capture or specify certain classes of
structures, while the other is concerned with invariance or
(in)distinguishability properties. Both approaches deal, in general,
with languages that are interpreted over the same, or very similar,
models such as algebras, first-order structures, Kripke frames,
etc. It is possible as well to compare logics that employ different
notions of model, but it is not so straightforward, as it involves
relative measures of expressivity. The aim of this talk is to use the
theory of institutions in order to explore some early high-level ideas
on how to measure and compare the expressive power of arbitrary
logics, related by comorphisms. We will use stratified institutions
and a handful of modal logics to illustrate the concepts and
properties obtained at the abstract level.
Ionuț Țuțu
Last modified: Mon Oct 19 2026