A Logical Analysis of Autosegmental Approaches to Root-and-Pattern Morphology in Arabic

What it is about

Jardine (2017) showed that left-to-right association of autosegmental representations of arbitrary length is not definable in monadic second-order logic, which casts doubt on the cognitive plausibility of the autosegmental approach. Payne shows that the finite length of the Arabic consonantal root avoids this problem. She builds a relational model with three tiers (prosodic template, affixes, root) and the precedence relation, adds constraints such as "each C slot links to one element", and writes McCarthy's (1981) analysis of the fifteen binyanim of the root KTB as association transductions in first-order logic. Binyan-specific rules, the flop of reflexive [t] in binyan VIII and the erasure rule for gemination in II, V and XIII, are written as binyan-indexed transductions. The paper is formal; it reports no measurements, and it notes that the result depends on the root being finite, not on its exact length.

Ideas

I1. Write the binyan-indexed association as a finite table (binyan, template slots, affix position) and apply it in Rust, left to right, with no search. Each generated form then has a traceable chain of associations.
I2. Hebrew hitpa'el forms have the same t-infix problem as binyan VIII. Write Payne's flop rule as a rule and test it on the hitpa'el forms in MACULA. The paper names Hebrew as a possible extension.
I3. Use the paper's Table 1 (the root KTB in all fifteen binyanim, in the perfective, imperfective and participle columns) as a closed gold test for any Semitic root-and-pattern generator. The set is small and closed, so a generator either passes it or fails.

For Mova

I1 goes into languages/hbo/06-verb.md, as a verb-stem table. I2 goes into languages/hbo/07-weak-verbs.md. I3 is a test set for the same verb-stem table and for any generator in tools/hbo.

Library summary

The Research library's own summary of the paper, in our words — not the paper's text.

Written for the Research library (claude-opus-5-5) from the paper text. Original — aclanthology.org/2026.scil-main.9.pdf

Summary

Autosegmental accounts of Arabic root-and-pattern morphology, especially McCarthy (1981), map a consonantal root onto a prosodic template by associating elements from left to right. Jardine (2017) proved that such association over representations of unbounded length cannot be expressed in MSO logic, so it is not regular. That result casts doubt on whether the approach is cognitively plausible, since other morphophonological patterns are subregular.

Payne argues that Arabic avoids this problem because its roots have a bounded number of consonants. She extends Jardine's (2024) two-tier relational model to three tiers: prosodic template, affixes and root. Her model orders elements by precedence rather than successor. Over this structure she defines parallel transductions for affix association and root association. These cover all fifteen binyanim of the triconsonantal root KTB in Modern Standard Arabic and are stated entirely in First Order logic.

The result shows that McCarthy's analysis stays computationally modest for Arabic. It suggests that the restricted length of Semitic roots gives the system a real computational advantage.

Key points

The data are McCarthy's (1981) Modern Standard Arabic paradigm of KTB ("write"), covering 15 binyanim with perfective, imperfective and participle forms. The analysis handles only triconsonantal roots.
The relational signature contains precedence (<) plus two association relations, one linking affixes to the template and one linking the root to the template. It also has unary features for the template (segm, syll, one per binyan), the root, affixes and consonant phonology.
Binyan VIII's infixed reflexive [t] is placed directly in the second consonant slot, replacing McCarthy's "flop" rule. Gemination in binyanim II, V and XIII is handled by an erasure-style condition.
A worked derivation of taKaTTaB (binyan V) shows step by step how the two First Order transductions apply together.
Proposed extensions include roots of 2–5 consonants, Arabic dialects, Hebrew, and similar logical analyses of Optimality-Theoretic accounts.

Cite

The paper itself, not this card. BibTeX from the library's record of the work. DOI 10.18653/v1/2026.scil-main.9

@inproceedings{payne2026logical,
  title = {{A Logical Analysis of Autosegmental Approaches to Root-and-Pattern Morphology in Arabic}},
  author = {Payne, Sarah},
  booktitle = {Proceedings of the Society for Computation in Linguistics 2026},
  year = {2026},
  doi = {10.18653/v1/2026.scil-main.9},
  url = {https://doi.org/10.18653/v1/2026.scil-main.9}
}

References

17 references, 0 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

Muteb Alqarni. 2022. Word-formation and reduplication in standard Arabic: A new distributed morphology approach. Poznan Studies in Contemporary Linguistics, 58(3):381–418. find
Maya Arad. 2005. Roots and patterns: Hebrew morphosyntax. Springer. find
J Richakd Büchi. 1960. Weak second-order arithmetic and finite automata. Mathematical Logic Quarterly, pages 66–92. find
Noam Chomsky. 1957. Syntactic structures. Walter de Gruyter. find
Noam Chomsky. 1963. Formal properties of grammars. Handbook of math. Psychology, 2:328–418. find
George N Clements and Kevin C Ford. 1979. Kikuyu tone shift and its synchronic consequences. Linguistic inquiry, pages 179–210. find
GN Clements and SJ Keyser. 1983. From CV phonology: A generative theory of the syllable. find
John Goldsmith. 1976. Autosegmental phonology. Ph.D. thesis, Doctoral dissertation/Garland Press. find
Thomas Graf. 2022. Subregular linguistics: Bridging theoretical linguistics and formal grammar. Theoretical Linguistics, 48(3-4):145–184. find
Jeffrey Heinz. 2018. The computational nature of phonological generalizations. Phonological typology, phonetics and phonology, 23:126–195. find
Grover Hudson. 1986. Arabic root and pattern morphology without tiers. Journal of Linguistics, 22(1):85– 122. find
Adam Jardine. 2017. On the logical complexity of autosegmental representations. In Proceedings of the 15th Meeting on the Mathematics of Language, pages 22–35, London, UK. Association for Computational Linguistics. find
Adam Jardine. 2024. Autosegmental Representations in Zigula and Shambaa. In Doing Computational Phonology. find
Ronald M Kaplan and Martin Kay. 1994. Regular models of phonological rule systems. Computational linguistics, 20(3):331–378. find
John J McCarthy. 1981. A prosodic theory of nonconcatenative morphology. Linguistic inquiry, 12(3):373–418. find
Matthew A Tucker. 2011. The morphosyntax of the Arabic verb: Toward a unified syntax-prosody. find
Adam Ussishkin. 2003. Templatic effects as fixed prosody: The verbal system in Semitic. Amsterdam Studies in the Theory and History of Linguistic Science Series 4, pages 511–530. find