  Various concepts of grammatical compositionality arise in many theories of
both natural and artificial languages, and often play a key role in accounts of
the syntax-semantics interface. We propose that many instances of
compositionality should entail non-trivial combinatorial claims about the
expressive power of languages which satisfy these compositional properties. As
an example, we present a formal analysis demonstrating that a particular class
of languages which admit salva vertitate substitutions - a property which we
claim to be a particularly strong example of compositional principle - must
also satisfy a very natural combinatorial constraint identified in this paper.
