Principles and Parameters: a coding theory perspective
This work addresses the challenge of quantifying linguistic diversity for historical-linguistic analysis, representing an incremental application of coding theory to an existing method.
The authors tackled the problem of analyzing syntactic parameter variability across languages by applying error-correcting code theory to Longobardi's parametric comparison method, resulting in quantitative insights such as codes below the Gilbert-Varshamov curve for within-family comparisons and isolated codes above the asymptotic bound for cross-family comparisons.
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.