# The Combinatorics of textitSalva Veritate Principles

arXiv: https://arxiv.org/abs/2201.05173 · HTML: https://mlsanity.com/paper/2201.05173/

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- First posted on arXiv 13 Jan 2022.

## Abstract (arXiv)

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.