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Swap distance minimization in SOV languages. Cognitive and mathematical foundations

Ramon Ferrer-i-Cancho, Savithry Namboodiripad

TL;DR

This study formalizes swap distance minimization as a gradient constraint on word order by introducing word order rotation and a permutation-ring framework. It tests three flexible SOV languages—Korean, Malayalam, and Sinhalese—using acceptability, reaction-time, error, and corpus data, analyzed through Kendall $\tau$ correlations and a Monte Carlo global analysis across conditions. The results show robust swap-distance effects in Korean and Malayalam, with weaker but detectable evidence in Sinhalese, and reveal that swap distance minimization often dominates a simple canonical-order preference while co-occurring with verb-predictability pressures. Together, these findings support a gradient, language-specific view of word-order optimization and provide a quantitative framework for cross-linguistic variation in syntactic ordering and its cognitive correlates.

Abstract

Distance minimization is a general principle of language. A special case of this principle in the domain of word order is swap distance minimization. This principle predicts that variations from a canonical order that are reached by fewer swaps of adjacent constituents are lest costly and thus more likely. Here we investigate the principle in the context of the triple formed by subject (S), object (O) and verb (V). We introduce the concept of word order rotation as a cognitive underpinning of that prediction. When the canonical order of a language is SOV, the principle predicts SOV < SVO, OSV < VSO, OVS < VOS, in order of increasing cognitive cost. We test the prediction in three flexible order SOV languages: Korean (Koreanic), Malayalam (Dravidian), and Sinhalese (Indo-European). Evidence of swap distance minimization is found in all three languages, but it is weaker in Sinhalese. Swap distance minimization is stronger than a preference for the canonical order in Korean and especially Malayalam.

Swap distance minimization in SOV languages. Cognitive and mathematical foundations

TL;DR

This study formalizes swap distance minimization as a gradient constraint on word order by introducing word order rotation and a permutation-ring framework. It tests three flexible SOV languages—Korean, Malayalam, and Sinhalese—using acceptability, reaction-time, error, and corpus data, analyzed through Kendall correlations and a Monte Carlo global analysis across conditions. The results show robust swap-distance effects in Korean and Malayalam, with weaker but detectable evidence in Sinhalese, and reveal that swap distance minimization often dominates a simple canonical-order preference while co-occurring with verb-predictability pressures. Together, these findings support a gradient, language-specific view of word-order optimization and provide a quantitative framework for cross-linguistic variation in syntactic ordering and its cognitive correlates.

Abstract

Distance minimization is a general principle of language. A special case of this principle in the domain of word order is swap distance minimization. This principle predicts that variations from a canonical order that are reached by fewer swaps of adjacent constituents are lest costly and thus more likely. Here we investigate the principle in the context of the triple formed by subject (S), object (O) and verb (V). We introduce the concept of word order rotation as a cognitive underpinning of that prediction. When the canonical order of a language is SOV, the principle predicts SOV < SVO, OSV < VSO, OVS < VOS, in order of increasing cognitive cost. We test the prediction in three flexible order SOV languages: Korean (Koreanic), Malayalam (Dravidian), and Sinhalese (Indo-European). Evidence of swap distance minimization is found in all three languages, but it is weaker in Sinhalese. Swap distance minimization is stronger than a preference for the canonical order in Korean and especially Malayalam.
Paper Structure (23 sections, 1 theorem, 42 equations, 3 figures, 6 tables)

This paper contains 23 sections, 1 theorem, 42 equations, 3 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Syntactic dependency distance minimization
  3. The order of S, V and O
  4. Swap distance minimization
  5. The present article
  6. Theoretical foundations
  7. Word order rotations
  8. The correlation between a distance measure and cognitive cost
  9. Material
  10. Why SOV languages
  11. Data
  12. Methodology
  13. Kendall $\tau$ correlation
  14. Kendall $\tau$ correlation test
  15. Maximum correlation
  16. ...and 8 more sections

Key Result

Corollary 1

If $\tau(d, y) > 1/3$ then $\tau(d, y) > \tau(c, y)$. If $\tau(d, y) > 4/5$ then $\tau(d, y) > \tau(p, y), \tau(c, y)$. If $\tau(d, y) < -1/3$ then $\tau(d, y) < \tau(c, y)$. If $\tau(d, y) < -4/5$ then $\tau(d, y) < \tau(p, y), \tau(c, y)$.

Figures (3)

  • Figure 1: The word order permutation ring.
  • Figure 2: Rotations of word orders with respect to an axis at the center of the ring (marked in red). Recall that clockwise rotations have negative sign while anticlockwise rotations have positive sign. To become the canonical order SOV, (a) SOV needs a rotation of $\pm 0$ degrees, (b) SVO needs a rotation of $60$ degrees, (c) VSO needs a rotation of $120$ degrees, (d) VOS needs a rotation of $\pm 180$ degrees, (e) OSV needs a rotation of $-60$ degrees, (f) OVS needs a rotation of $-120$ degrees.
  • Figure 3: The word order permutation ring with the acceptability rank of every word order marked in red below each word order. The word order with the highest mean acceptability has rank 1, the word order with the 2nd highest mean acceptability has rank 2 and so on.

Theorems & Definitions (7)

  • proof
  • proof
  • proof
  • Corollary 1
  • proof
  • proof
  • proof