The Combinatorics of \textit{Salva Veritate} Principles

TL;DR

This paper explores the combinatorial implications of salva veritate principles in language, showing that certain compositional properties impose specific constraints on the expressive power of languages.

Contribution

It introduces a formal analysis linking salva veritate compositionality to natural combinatorial constraints in language expressiveness.

Findings

Languages with salva veritate properties must satisfy specific combinatorial constraints

The analysis reveals a strong connection between compositionality and expressive power

Provides a formal framework for understanding language compositionality

Abstract

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.