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Notational equivalence in tonal geometry

Published online by Cambridge University Press:  11 August 2020

Chris Oakden
Chris Oakden*
Affiliation:
Rutgers University
*
*E-mail: chris.oakden@rutgers.edu.
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Abstract

This paper employs a computational framework to demonstrate that two competing feature-geometric models of tonal representation are notationally equivalent. A model-theoretic analysis of these structures using a low-complexity logic yields two main results. First, the current study demonstrates that the models do not differ in their empirical coverage of assimilatory tone-sandhi processes in Chinese dialects, contrary to previous claims. Second, the models are shown to be bi-interpretable (using a more restrictive definition of bi-interpretability than earlier studies), thus providing a formally rigorous demonstration that the differences between the structures of the models are superficial, rather than substantive. The computational characterisation pursued here is well suited to questions of notational equivalence, because it allows for a principled comparison of the empirical coverage and structural content of two models using a single formalism.

Type
Articles
Information
Phonology , Volume 37 , Issue 2 , May 2020 , pp. 257 - 296
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Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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Footnotes

I wish to thank the associate editor and three anonymous reviewers for helpful feedback and suggestions. Additionally, I am indebted to Adam Jardine for extensive comments on earlier versions of this paper, as well as insightful suggestions from Robin Karlin, Yimei Xiang and students in the Rutgers Spring 2019 Seminar in Phonology. All remaining errors are my own.

References

Baković, Eric (2000). Harmony, dominance and control. PhD dissertation, Rutgers University.Google Scholar
Bao, Zhiming (1990). On the nature of tone. PhD dissertation, MIT.Google Scholar
Chan, Marjorie K. M. (1991). Contour-tone spreading and tone sandhi in Danyang Chinese. Phonology 8. 237–259.CrossRefGoogle Scholar
Chandlee, Jane (2014). Strictly local phonological processes. PhD dissertation, University of Delaware.Google Scholar
Chandlee, Jane & Heinz, Jeffrey (2018). Strict locality and phonological maps. LI 49. 23–60.Google Scholar
Chandlee, Jane & Jardine, Adam (2019a). Autosegmental Input Strictly Local functions. Transactions of the Association for Computational Linguistics 7. 157–168.CrossRefGoogle Scholar
Chandlee, Jane & Jardine, Adam (2019b). Quantifier-free least fixed point functions for phonology. In de Groote, Philippe, Drewes, Frank & Penn, Gerald (eds.) Proceedings of the 16th Meeting on the Mathematics of Language. Toronto: Association for Computational Linguistics. 50–62.CrossRefGoogle Scholar
Chandlee, Jane & Lindell, Steven (to appear). A logical characterization of strictly local functions. In Heinz, Jeffrey (ed.) Doing computational phonology. Oxford: Oxford University Press.Google Scholar
Chen, Matthew Y. (2000). Tone sandhi: patterns across Chinese dialects. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Chomsky, Noam (1972). Studies on semantics in generative grammar. The Hague: Mouton.CrossRefGoogle Scholar
Chomsky, Noam & Halle, Morris (1968). The sound pattern of English. New York: Harper & Row.Google Scholar
Courcelle, Bruno (1994). Monadic second-order definable graph transductions: a survey. Theoretical Computer Science 126. 53–75.CrossRefGoogle Scholar
Danis, Nick & Jardine, Adam (2019). Q-Theory Representations are logically equivalent to Autosegmental Representations. In Proceedings of the Society for Computation in Linguistics. Vol. 2. 29–38. https://doi.org/10.7275/tvj1-k306.Google Scholar
de Lacy, Paul (2002). The interaction of tone and stress in Optimality Theory. Phonology 19. 1–32.CrossRefGoogle Scholar
Duanmu, San (1990). A formal study of syllable, tone, stress and domain in Chinese languages. PhD dissertation, MIT.Google Scholar
Duanmu, San (1994). Against contour tone units. LI 25. 555–608.Google Scholar
Enayat, Ali & Wijksgatan, Olof (2013). Interpretations and mathematical logic: a tutorial. https://gup.ub.gu.se/file/167690.Google Scholar
Enderton, Herbert B. (2001). A mathematical introduction to logic. 2nd edn.San Diego: Academic Press.Google Scholar
Filiot, Emmanuel (2015). Logic-automata connections for transformations. In Banerjee, Mohua & Krishna, Shankara Narayanan (eds.) Logic and its applications: proceedings of the 6th Indian Conference, ICLA 2015. Heidelberg: Springer. 30–57.CrossRefGoogle Scholar
Friedman, Harvey M. & Visser, Albert (2014). When bi-interpretability implies synonymy. Logic Group Preprint Series 320. 1–19.Google Scholar
Fromkin, Victoria A. (ed.) (2000). Linguistics: an introduction to linguistic theory. Malden, Mass. & Oxford: Blackwell.Google Scholar
Goldsmith, John A. (1976). Autosegmental phonology. PhD dissertation, MIT.Google Scholar
Heinz, Jeffrey (2018). The computational nature of phonological generalizations. In Hyman, Larry M. & Plank, Frans (eds.) Phonological typology. Berlin & New York: Mouton de Gruyter. 126–195.CrossRefGoogle Scholar
Hou, Jing-Yi (1980). Pingyao fangyan de liandu biandiao. [Tone sandhi in the Pingyao dialect.] Fangyan 1980. 1–14.Google Scholar
Kawahara, Shigeto (2004). Locality in echo epenthesis: comparison with reduplication. NELS 34. 295–309.Google Scholar
Kawahara, Shigeto (2007). Copying and spreading in phonological theory: evidence from echo epenthesis. In Bateman, Leah, O'Keefe, Michael, Reilly, Ehren & Werle, Adam (eds.) Papers in Optimality Theory III. Amherst: GLSA. 111–143.Google Scholar
Kitto, Catherine & de Lacy, Paul (1999). Correspondence and epenthetic quality. Toronto Working Papers in Linguistics 16:2. 181–200.Google Scholar
Libkin, Leonid (2004). Elements of finite model theory. Berlin: Springer.CrossRefGoogle Scholar
Lombardi, Linda (2001). Why Place and Voice are different: constraint-specific alternations in Optimality Theory. In Lombardi, Linda (ed.) Segmental phonology in Optimality Theory: constraints and representations. Cambridge: Cambridge University Press. 13–45.CrossRefGoogle Scholar
Lü, Shuxiang (1980). Danyang fangyan de shengdiao xitong. [The tonal system of the Danyang dialect.] Fangyan 1980. 85–122.Google Scholar
McCarthy, John J. (1986). OCP effects: gemination and antigemination. LI 17. 207–263.Google Scholar
McCarthy, John J. (1988). Feature geometry and dependency: a review. Phonetica 45. 84–108.CrossRefGoogle Scholar
McCarthy, John J. (2010). Autosegmental spreading in Optimality Theory. In Goldsmith, John A., Hume, Elizabeth & Wetzels, W. Leo (eds.) Tones and features: phonetic and phonological perspectives. Berlin & Boston: De Gruyter Mouton. 195–222.Google Scholar
Pulleyblank, Douglas (2002). Harmony drivers: no disagreement allowed. BLS 28. 249–267.CrossRefGoogle Scholar
Rose, Phil (1990). Acoustics and phonology of complex tone sandhi: an analysis of disyllabic lexical tone sandhi in the Zhenhai variety of Wu Chinese. Phonetica 47. 1–35.CrossRefGoogle Scholar
Shih, Stephanie S. & Inkelas, Sharon (2018). Autosegmental aims in surface-optimizing phonology. LI 50. 137–196.Google Scholar
Strother-Garcia, Kristina (2018). Imdlawn Tashlhiyt Berber syllabification is quantifier-free. In Gaja Jarosz, Brendan O'Connor & Joe Pater (eds.) Proceedings of the Society for Computation in Linguistics (SCiL) 2018. 145–153. https://scholarworks.umass.edu/scil/vol1/iss1/16.Google Scholar
Strother-Garcia, Kristina & Heinz, Jeffrey (2017). Logical foundations of syllable representations. Poster presented at the 2017 Annual Meeting on Phonology, New York University. Available (April 2020) at https://cpb-us-w2.wpmucdn.com/sites.udel.edu/dist/d/3991/files/2017/09/AMP_2017_poster-25s5vzd.pdf.Google Scholar
Yan, Sen (1981). Gaoan (Laowu Zhoujia) fangyan de yuyin xitong. [The phonetic system of Gao'an (Laowu Zhoujia).] Fangyan 1981. 104–121.Google Scholar
Yip, Moira (1989). Contour tones. Phonology 6. 149–174.CrossRefGoogle Scholar
Yip, Moira (2002). Tone. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Younes, Rebecca (1983). The representation of geminate consonants. Ms, University of Texas, Austin.Google Scholar
Zhang, Hongnian (1985). Zhenjiang fangyan de liandu biandiao. [Tone sandhi in the Zhenjiang dialect.] Fangyan 1985. 191–204.Google Scholar
Zhang, Jie (2014). Tones, tonal phonology, and tone sandhi. In James Huang, C.-T., Audrey Li, Y.-H. & Simpson, Andrew (eds.) The handbook of Chinese linguistics. Malden, Mass.: Wiley. 443–464.CrossRefGoogle Scholar
Zhengzhang, Shangfang (1964). Wenzhou fangyan de liandu biandiao. [Wenzhou dialect tone sandhi.] Zhongguo Yuwen 1964. 106–152.Google Scholar
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