Is Word Order Asymmetry Mathematically Expressible?

Koji Arikawa

doi:10.5964/bioling.8967

Abstract

The computational procedure for human natural language (CHL) shows an asymmetry in unmarked orders for S, O, and V. Following Lyle Jenkins, it is speculated that the asymmetry is expressible as a group-theoretical factor (included in Chomsky’s third factor): “[W]ord order types would be the (asymmetric) stable solutions of the symmetric still-to-be-discovered ‘equations’ governing word order distribution”. A possible “symmetric equation” is a linear transformation f(x) = y, where function f is a set of merge operations (transformations) expressed as a set of symmetric transformations of an equilateral triangle, x is the universal base vP input expressed as the identity triangle, and y is a mapped output tree expressed as an output triangle that preserves symmetry. Although the symmetric group S3 of order 3! = 6 is too simple, this very simplicity is the reason that in the present work cost differences are considered among the six symmetric operations of S3. This article attempts to pose a set of feasible questions for future research.

Highlights

ProblemI would like to pose the question of whether the following phenomenon can be mathematically (Galois theoretically) expressed.1I am grateful to the editors and anonymous reviewers for their patience in assessing this challenging article over the past two years
He claims that it may be a mathematically feasible way to express and translate the unmarked word order asymmetry into a language of geometrical cost calculation that leads us to ISSN 1450–3417
Problems, let us first look at what typological studies have found with respect to the probability of unmarked word order asymmetry and see how far we can go within the geometrical cost approach

Summary

Koji Arikawa

The computational procedure for human natural language (CHL) shows an asymmetry in unmarked orders for S, O, and V. Following Lyle Jenkins, it is speculated that the asymmetry is expressible as a group-theoretical factor (included in Chomsky’s third factor): “[W]ord order types would be the (asymmetric) stable solutions of the symmetric still-to-be-discovered ‘equations’ governing word order distribution”. A possible “symmetric equation” is a linear transformation f(x) = y, where function f is a set of merge operations (transformations) expressed as a set of symmetric transformations of an equilateral triangle, x is the universal base vP input expressed as the identity triangle, and y is a mapped output tree expressed as an output triangle that preserves symmetry. The symmetric group S3 of order 3! = 6 is too simple, this very simplicity is the reason that in the present work cost differences are considered among the six symmetric operations of.