Principles and Parameters: a coding theory perspective

TL;DR

This paper introduces a novel approach to linguistic parameter comparison by applying error-correcting code theory, enabling quantitative analysis of syntactic variability within and across language families.

Contribution

It develops a coding theory framework for the Longobardi's PCM, linking linguistic parameter analysis to classical bounds in coding theory for the first time.

Findings

Codes within the same language family lie below the Gilbert-Varshamov bound.

Codes across different families can surpass the asymptotic bound, indicating higher variability.

The approach provides a quantitative measure of syntactic diversity.

Abstract

We propose an approach to Longobardi's parametric comparison method (PCM) via the theory of error-correcting codes. One associates to a collection of languages to be analyzed with the PCM a binary (or ternary) code with one code words for each language in the family and each word consisting of the binary values of the syntactic parameters of the language, with the ternary case allowing for an additional parameter state that takes into account phenomena of entailment of parameters. The code parameters of the resulting code can be compared with some classical bounds in coding theory: the asymptotic bound, the Gilbert-Varshamov bound, etc. The position of the code parameters with respect to some of these bounds provides quantitative information on the variability of syntactic parameters within and across historical-linguistic families. While computations carried out for languages belonging to the same family yield codes below the GV curve, comparisons across different historical families can give examples of isolated codes lying above the asymptotic bound.