Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-28T18:14:45.156Z Has data issue: false hasContentIssue false
  • English
  • Français

Harmonic Grammar with linear programming: from linear systems to linguistic typology*

Published online by Cambridge University Press:  16 April 2010

Christopher Potts ,
Joe Pater ,
Karen Jesney ,
Rajesh Bhatt  and
Michael Becker
Christopher Potts
Affiliation:
Stanford University
Joe Pater
Affiliation:
University of Massachusetts, Amherst
Karen Jesney
Affiliation:
University of Massachusetts, Amherst
Rajesh Bhatt
Affiliation:
University of Massachusetts, Amherst
Michael Becker
Affiliation:
Harvard University
Get access Rights & Permissions [Opens in a new window]

Abstract

Harmonic Grammar is a model of linguistic constraint interaction in which well-formedness is calculated in terms of the sum of weighted constraint violations. We show how linear programming algorithms can be used to determine whether there is a weighting for a set of constraints that fits a set of linguistic data. The associated software package OT-Help provides a practical tool for studying large and complex linguistic systems in the Harmonic Grammar framework and comparing the results with those of OT. We first describe the translation from harmonic grammars to systems solvable by linear programming algorithms. We then develop a Harmonic Grammar analysis of ATR harmony in Lango that is, we argue, superior to the existing OT and rule-based treatments. We further highlight the usefulness of OT-Help, and the analytic power of Harmonic Grammar, with a set of studies of the predictions Harmonic Grammar makes for phonological typology.

Type
Articles
Information
Phonology , Volume 27 , Issue 1 , May 2010 , pp. 77 - 117
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Albright, Adam, Magri, Giorgio & Michaels, Jennifer (2008). Modeling doubly marked lags with a split additive model. In Chan, Harvey, Jacob, Heather & Kapia, Enkeleida (eds.) Proceedings of the 32nd Annual Boston University Conference on Language Development. Somerville: Cascadilla. 36–47.Google Scholar
Archangeli, Diana & Pulleyblank, Douglas (1994). Grounded phonology. Cambridge, Mass.: MIT Press.Google Scholar
BakoviĆ, Eric (2000). Harmony, dominance, and control. PhD dissertation, Rutgers University.Google Scholar
Bavin Woock, Edith & Noonan, Michael (1979). Vowel harmony in Lango. CLS 15. 20–29.Google Scholar
Bazaraa, Mokhtar S., Jarvis, John J. & Sherali, Hanif D. (2005). Linear programming and network flows. 3rd edn.Hoboken, NJ: Wiley.Google Scholar
Becker, Michael & Pater, Joe (2007). OT-Help user guide. University of Massachusetts Occasional Papers in Linguistics 36. 1–12.Google Scholar
Becker, Michael, Pater, Joe & Potts, Christopher (2007). OT-Help 1.2. Software available at http://web.linguist.umass.edu/~OTHelp/.Google Scholar
Beckman, Jill N. (1997). Positional faithfulness, positional neutralisation and Shona vowel harmony. Phonology 14. 1–46.CrossRefGoogle Scholar
Beckman, Jill N. (1998). Positional faithfulness. PhD dissertation, University of Massachusetts, Amherst.Google Scholar
Boersma, Paul & Pater, Joe (2008). Convergence properties of a gradual learning algorithm for Harmonic Grammar. Available as ROA-970 from the Rutgers Optimality Archive.Google Scholar
Boersma, Paul & Weenink, David (2009). Praat: doing phonetics by computer (version 5.1.12). http://www.praat.org/.Google Scholar
Casali, Roderic F. (1996). Resolving hiatus. PhD dissertation, University of California, Los Angeles.Google Scholar
Chvátal, Vašek (1983). Linear programming. New York: Freeman.Google Scholar
Coetzee, Andries & Pater, Joe (in press). The place of variation in phonological theory. In Goldsmith, John A., Riggle, Jason & Yu, Alan (eds.) The handbook of phonological theory. 2nd edn.Oxford: Blackwell.Google Scholar
Cormen, Thomas H., Leiserson, Charles E., Rivest, Ronald L. & Stein, Clifford (2001). Introduction to algorithms. 2nd edn.Cambridge, Mass.: MIT Press.Google Scholar
Dantzig, George B. (1982). Reminiscences about the origins of linear programming. Operations Research Letters 1. 43–48.CrossRefGoogle Scholar
Davis, Stuart (1995). Emphasis spread in Arabic and Grounded Phonology. LI 26. 465–498.Google Scholar
Dresher, B. Elan & Kaye, Jonathan D. (1990). A computational learning model for metrical phonology. Cognition 34. 137–195.CrossRefGoogle ScholarPubMed
Goldsmith, John A. (1990). Autosegmental and metrical phonology. Oxford & Cambridge, Mass.: Blackwell.Google Scholar
Goldsmith, John A. (1991). Phonology as an intelligent system. In Napoli, Donna Jo & Kegl, Judy Anne (eds.) Bridges between psychology and linguistics: a Swarthmore Festschrift for Lila Gleitman. Hillsdale: Erlbaum. 247–268.Google Scholar
Goldsmith, John A. (1993). Introduction. In Goldsmith, John A. (ed.) The last phonological rule: reflections on constraints and derivations. Chicago: University of Chicago Press. 1–20.Google Scholar
Goldsmith, John A. (1999). Introduction. In Goldsmith, John A. (ed.) Phonological theory: the essential readings. Malden, Mass. & Oxford: Blackwell. 1–16.Google Scholar
Goldwater, Sharon & Johnson, Mark (2003). Learning OT constraint rankings using a Maximum Entropy model. In Spenador, Jennifer, Eriksson, Anders & Dahl, Östen (eds.) Proceedings of the Stockholm Workshop on Variation within Optimality Theory. Stockholm: Stockholm University. 111–120.Google Scholar
Hayes, Bruce, Tesar, Bruce & Zuraw, Kie (2003). OTSoft 2.1. http://www.linguistics.ucla.edu/people/hayes/otsoft/.Google Scholar
Hayes, Bruce, Zuraw, Kie, Siptár, Péter & Londe, Zsuzsa Cziráky (2008). Natural and unnatural constraints in Hungarian vowel harmony. Ms, University of California, Los Angeles.Google Scholar
Hyman, Larry M. (2002). Is there a right-to-left bias in vowel harmony? Ms, University of California, Berkeley.Google Scholar
Ito, Junko & Mester, Armin (2003). Japanese morphophonemics: markedness and word structure. Cambridge, Mass.: MIT Press.CrossRefGoogle Scholar
Itô, Junko, Mester, Armin & Padgett, Jaye (1995). Licensing and underspecification in Optimality Theory. LI 26. 571–613.Google Scholar
Jäger, Gerhard (2007). Maximum entropy models and Stochastic Optimality Theory. In Zaenen, Annie, Simpson, Jane, King, Tracy Holloway, Grimshaw, Jane, Maling, Joan & Manning, Chris (eds.) Architectures, rules, and preferences: variations on themes by Joan W. Bresnan. Stanford: CSLI. 467–479.Google Scholar
Jesney, Karen (to appear). Licensing in multiple contexts: an argument for Harmonic Grammar. CLS 45.Google Scholar
Johnson, Mark (2002). Optimality-theoretic Lexical Functional Grammar. In Merlo, Paola & Stevenson, Suzanne (eds.) The lexical basis of sentence processing: formal, computational and experimental issues. Amsterdam & Philadelphia: Benjamins. 59–73.CrossRefGoogle Scholar
Jurgec, Peter (2009). Autosegmental spreading is a binary relation. Ms, University of Tromsø.Google Scholar
Kager, René (2005). Rhythmic licensing: an extended typology. In Proceedings of the 3rd International Conference on Phonology. Seoul: The Phonology–Morphology Circle of Korea. 5–31.Google Scholar
Kaplan, Aaron F. (2008). Noniterativity is an emergent property of grammar. PhD dissertation, University of California, Santa Cruz.Google Scholar
Kelkar, Ashok R. (1968). Studies in Hindi-Urdu. Vol. 1: Introduction and word phonology. Poona: Deccan College.Google Scholar
Keller, Frank (2000). Gradience in grammar: experimental and computational aspects of degrees of grammaticality. PhD dissertation, University of Edinburgh.Google Scholar
Keller, Frank (2006). Linear optimality theory as a model of gradience in grammar. In Fanselow, Gisbert, Féry, Caroline, Vogel, Ralf & Schlesewsky, Matthias (eds.) Gradience in grammar: generative perspectives. Oxford: Oxford University Press. 270–287.CrossRefGoogle Scholar
Legendre, Géraldine, Miyata, Yoshiro & Smolensky, Paul (1990a). Harmonic Grammar: a formal multi-level connectionist theory of linguistic well-formedness: theoretical foundations. In Proceedings of the 12th Annual Conference of the Cognitive Science Society. Hillsdale: Erlbaum. 388–395.Google Scholar
Legendre, Géraldine, Miyata, Yoshiro & Smolensky, Paul (1990b). Harmonic Grammar: a formal multi-level connectionist theory of linguistic well-formedness: an application. In Proceedings of the 12th Annual Conference of the Cognitive Science Society. Hillsdale: Erlbaum. 884–891.Google Scholar
Legendre, Géraldine, Sorace, Antonella & Smolensky, Paul (2006). The Optimality Theory–Harmonic Grammar connection. In Smolensky, & Legendre, (2006: vol. 2). 339–402.Google Scholar
Lombardi, Linda (1999). Positional faithfulness and voicing assimilation in Optimality Theory. NLLT 17. 267–302.Google Scholar
López, Marco & Still, Georg (2007). Semi-infinite programming. European Journal of Operations Research 180. 491–518.CrossRefGoogle Scholar
McCarthy, John J. (1997). Process-specific constraints in optimality theory. LI 28. 231–251.Google Scholar
McCarthy, John J. (2003). OT constraints are categorical. Phonology 20. 75–138.CrossRefGoogle Scholar
McCarthy, John J. (2006). Restraint of analysis. In BakoviĆ, Eric, Ito, Junko & McCarthy, John J. (eds.) Wondering at the natural fecundity of things: essays in honor of Alan Prince. Santa Cruz: Linguistics Research Center. 195–219.Google Scholar
McCarthy, John J. (2007). Hidden generalizations: phonological opacity in Optimality Theory. London: Equinox.Google Scholar
McCarthy, John J. (2009). Harmony in Harmonic Serialism. Ms, University of Massachusetts, Amherst. Available as ROA-1009 from the Rutgers Optimality Archive.Google Scholar
McCarthy, John J. & Prince, Alan (1993). Generalized alignment. Yearbook of Morphology 1993. 79–153.CrossRefGoogle Scholar
Noonan, Michael (1992). A grammar of Lango. Berlin & New York: Mouton de Gruyter.CrossRefGoogle Scholar
Okello, Jenny (1975). Some phonological and morphological processes in Lango. PhD dissertation, Indiana University.Google Scholar
Pater, Joe (2008). Gradual learning and convergence. LI 39. 334–345.Google Scholar
Pater, Joe (2009a). Review of Smolensky & Legendre (2006). Phonology 26. 217–226.CrossRefGoogle Scholar
Pater, Joe (2009b). Weighted constraints in generative linguistics. Cognitive Science 33. 999–1035.CrossRefGoogle ScholarPubMed
Pater, Joe (to appear). Serial Harmonic Grammar and Berber syllabification. In Borowsky, Toni, Kawahara, Shigeto, Shinya, Takahito & Sugahara, Mariko (eds.) Prosody matters: essays in honor of Elisabeth O. Selkirk. London: Equinox.Google Scholar
Poser, William J. (1982). Phonological representation and action-at-a-distance. In Hulst, Harry van der & Smith, Norval (eds.) The structure of phonological representations. Part 2. Dordrecht: Foris. 121–158.Google Scholar
Potts, Christopher, Becker, Michael, Bhatt, Rajesh & Pater, Joe (2007). HaLP: Harmonic Grammar with linear programming. Version 2. Software available at http://web.linguist.umass.edu/~halp/.Google Scholar
Prince, Alan (2002). Entailed ranking arguments. Ms, Rutgers University. Available as ROA-500 from the Rutgers Optimality Archive.Google Scholar
Prince, Alan (2003). Anything goes. In Honma, Takeru, Okazaki, Masao, Tabata, Toshiyuki & Tanaka, Shin-ichi (eds.) A new century of phonology and phonological theory: a Festschrift for Professor Shosuke Haraguchi on the occasion of his sixtieth birthday. Tokyo: Kaitakusha. 66–90.Google Scholar
Prince, Alan & Smolensky, Paul (1997). Optimality: from neural networks to Universal Grammar. Science 275. 1604–1610.CrossRefGoogle ScholarPubMed
Prince, Alan & Smolensky, Paul (2004). Optimality Theory: constraint interaction in generative grammar. Malden, Mass. & Oxford: Blackwell.CrossRefGoogle Scholar
Pruitt, Kathryn (2008). Iterative foot optimization and locality in rhythmic word stress. Ms, University of Massachusetts, Amherst.Google Scholar
Riggle, Jason (2004a). Generation, recognition, and learning in finite-state Optimality Theory. PhD dissertation, University of California, Los Angeles.Google Scholar
Riggle, Jason (2004b). Generation, recognition and ranking with compiled OT grammars. Paper presented at the 78th Annual Meeting of the Linguistic Society of America, Boston.Google Scholar
Smolensky, Paul (2006). Optimality in phonology II: harmonic completeness, local constraint conjunction, and feature domain markedness. In Smolensky, & Legendre, (2006: vol. 2). 27–160.Google Scholar
Smolensky, Paul & Legendre, Géraldine (eds.) (2006). The harmonic mind: from neural computation to optimality-theoretic grammar. 2 vols. Cambridge, Mass.: MIT Press.Google Scholar
Tesar, Bruce & Smolensky, Paul (1998a). Learnability in Optimality Theory. LI 29. 229–268.Google Scholar
Tesar, Bruce & Smolensky, Paul (1998b). Learning Optimality-Theoretic grammars. Lingua 106. 161–196.CrossRefGoogle Scholar
Walker, Rachel (2001). Positional markedness in vowel harmony. In Féry, Caroline, Green, Antony Dubach & van de Vijver, Ruben (eds.) Proceedings of HILP 5. Potsdam: University of Potsdam. 212–232.Google Scholar
Walker, Rachel (2005). Weak triggers in vowel harmony. NLLT 23. 917–989.Google Scholar
Wilson, Colin (2003). Analyzing unbounded spreading with constraints: marks, targets, and derivations. Ms, University of California, Los Angeles.Google Scholar
Wilson, Colin (2006). Learning phonology with substantive bias: an experimental and computational study of velar palatalization. Cognitive Science 30. 945–982.CrossRefGoogle ScholarPubMed
Zoll, Cheryl (1996). Parsing below the segment in a constraint-based framework. PhD dissertation, University of California, Berkeley.Google Scholar
Zoll, Cheryl (1998). Positional asymmetries and licensing. Ms, MIT. Available as ROA-282 from the Rutgers Optimality Archive.Google Scholar