The Combinatorics of \textit{Salva Veritate} Principles
This work addresses foundational issues in formal linguistics and logic, offering incremental insights into the expressive power of compositional languages.
The paper tackles the problem of understanding the combinatorial implications of compositionality in languages, demonstrating that languages with salva veritate substitutions must satisfy a specific combinatorial constraint.
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.