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Constraint conjunction in weighted probabilistic grammar*

  • Stephanie S. Shih (a1)

This paper examines a key difference between constraint conjunction and constraint weight additivity, arguing that the two do not have the same empirical coverage. In particular, constraint conjunction in weighted probabilistic grammar allows for superadditive constraint interaction, where the effect of violating two constraints goes beyond the additive combination of the two constraints’ weights alone. A case study from parasitic tone harmony in Dioula d'Odienné demonstrates superadditive local and long-distance segmental feature similarities that increase the likelihood of tone harmony. Superadditivity in Dioula d'Odienné is formally captured in Maximum Entropy Harmonic Grammar by weighted constraint conjunction. Counter to previous approaches that supplant constraint conjunction with weight additivity in Harmonic Grammar, information-theoretic model comparison reveals that weighted constraint conjunction improves the grammar's explanatory power when modelling quantitative natural language patterns.

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Acknowledgements to Kie Zuraw, Eric Bakovi«, Christopher Green, Lauren Hall-Lew, Gunnar Hansson, Sharon Inkelas, Laura McPherson, Joe Pater, Brian Smith, Anne-Michelle Tessier, Colin Wilson and audiences at WCCFL 33, GLOW 38 and UCs Merced and Berkeley for discussion on various portions of this work. Thanks also to Jeff Heinz and Bill Idsardi, and two anonymous reviewers for detailed comments. Errors are inevitable in stochastic systems, and the author accepts blame for any that remain herein.

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Albright, Adam (2009). Cumulative violations and complexity thresholds: evidence from Lakhota. Paper presented at the 17th Manchester Phonology Meeting.
Anderson, David R. (2008). Model based inference in the life sciences: a primer on evidence. New York: Springer.
Anderson, David R. & Burnham, Kenneth P. (2002). Avoiding pitfalls when using information-theoretic methods. Journal of Wildlife Management 66. 912918.
Baayen, R. H. (2008). Analyzing linguistic data: a practical introduction to statistics using R. Cambridge: Cambridge University Press.
Baković, Eric (2000). Harmony, dominance and control. PhD dissertation, Rutgers University.
Bennett, William G. (2013). Dissimilation, consonant harmony, and surface correspondence. PhD dissertation, Rutgers University.
Bennett, William G. (2015a). The phonology of consonants: harmony, dissimilation, and correspondence. Cambridge: Cambridge University Press.
Bennett, William G. (2015b). Assimilation, dissimilation, and surface correspondence in Sundanese. NLLT 33. 371415.
Braconnier, C. (1982). Le système tonal du dioula d'Odienné. Abidjan: Université d'Abidjan.
Braconnier, C. (1983). Phonologie du dioula d'Odienné. Abidjan: Agence de Coopération Culturelle et Technique.
Braconnier, C. & Diaby, S. (1982). Dioula d'Odienné (parler de Samatiguila): matérial lexical. Abidjan: Institut de Linguistique Appliquée.
Burnham, Kenneth P. & Anderson, David R. (2002). Model selection and multimodel inference: a practical information-theoretic approach. 2nd edn. New York: Springer.
Burnham, Kenneth P. & Anderson, David R. (2004). Multimodel inference: understanding AIC and BIC in model selection. Sociological Methods and Research 33. 261304.
Burzio, Luigi (2002). Surface-to-surface morphology: when your representations turn into constraints. In Boucher, Paul (ed.) Many morphologies. Somerville, Mass.: Cascadilla. 142177.
Crowhurst, Megan J. & Hewitt, Mark (1997). Boolean operations and constraint interactions in Optimality Theory. Ms, University of North Carolina at Chapel Hill & Brandeis University. Available as ROA-229 from the Rutgers Optimality Archive.
Farris-Trimble, Ashley W. (2008). Cumulative faithfulness effects in phonology. PhD dissertation, Indiana University.
Frisch, Stefan A., Pierrehumbert, Janet B. & Broe, Michael B. (2004). Similarity avoidance and the OCP. NLLT 22. 179228.
Goldwater, Sharon & Johnson, Mark (2003). Learning OT constraint rankings using a Maximum Entropy model. In Spenader, Jennifer, Eriksson, Anders & Dahl, Östen (eds.) Proceedings of the Stockholm Workshop on Variation within Optimality Theory. Stockholm: Stockholm University. 111120.
Green, Christopher R. & Davis, Stuart (2014). Superadditivity and limitations on syllable complexity in Bambara words. In Farris-Trimble, Ashley W. & Barlow, Jessica A. (eds.) Perspectives on phonological theory and acquisition: papers in honor of Daniel A. Dinnsen. Amsterdam & Philadelphia: Benjamins. 223247.
Hansson, Gunnar Ólafur (2001). Theoretical and typological issues in consonant harmony. PhD dissertation, University of California, Berkeley.
Hansson, Gunnar Ólafur (2007). Blocking effects in agreement by correspondence. LI 38. 395409.
Hansson, Gunnar Ólafur (2010). Consonant harmony: long-distance interaction in phonology. Berkeley: University of California Press.
Hansson, Gunnar Ólafur (2014). (Dis)agreement by (non)correspondence: inspecting the foundations. UC Berkeley Phonology Lab Annual Report: ABC Conference Archive. Slides available (May 2017) at
Hayes, Bruce & Wilson, Colin (2008). A maximum entropy model of phonotactics and phonotactic learning. LI 39. 379440.
Hayes, Bruce, Wilson, Colin & George, Ben (2009). Maxent grammar tool. Software package. Available (May 2017) at
Hayes, Bruce, Wilson, Colin & Shisko, Anne (2012). Maxent grammars for the metrics of Shakespeare and Milton. Lg 88. 691731.
Inkelas, Sharon & Shih, Stephanie S. (2014). Unstable surface correspondence as the source of local conspiracies. NELS 44:1. 191204.
Inkelas, Sharon & Shih, Stephanie S. (2016). Tone melodies in the age of surface correspondence. CLS 51. 269283.
Ito, Junko & Mester, Armin (1998). Markedness and word structure: OCP effects in Japanese. Ms, University of California, Santa Cruz. Available as ROA-255 from the Rutgers Optimality Archive.
Ito, Junko & Mester, Armin (2003). Japanese morphophonemics: markedness and word structure. Cambridge, Mass.: MIT Press.
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. 467479.
Jäger, Gerhard & Rosenbach, Anette (2006). The winner takes it all – almost: cumulativity in grammatical variation. Linguistics 44. 937971.
Jesney, Karen (2014). Complex process interaction: weighted constraints vs. ranked constraints and rules. Paper presented at the Interaction of Grammatical Building Blocks (IGRA): Workshop on Building Blocks, University of Leipzig. Available (May 2017) at
Kaun, Abigail R. (1995). The typology of rounding harmony: an optimality theoretic approach. PhD dissertation, University of California, Los Angeles.
Kullback, S. & Leibler, R. A. (1951). On information and sufficiency. Annals of Mathematical Statistics 22. 7986.
Legendre, Géraldine, Miyata, Yoshiro & Smolensky, Paul (1990). 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.
Lionnet, Florian (2014). Doubly triggered harmony in Laal as subphonemic Agreement by Correspondence. In Kingston, John, Moore-Cantwell, Claire, Pater, Joe & Staubs, Robert (eds.) Proceedings of the 2013 Meeting on Phonology. Available (May 2017) at
Łubowicz, Anna (2005). Locality of conjunction. WCCFL 24. 254262.
Pater, Joe (2016). Universal Grammar with weighted constraints. In McCarthy, John J. & Pater, Joe (eds.) Harmonic Grammar and Harmonic Serialism. London: Equinox. 146.
Pater, Joe & Moreton, Elliot (2012). Structurally biased phonology: complexity in learning and typology. The EFL Journal 3:2. 144.
Potts, Christopher, Pater, Joe, Jesney, Karen, Bhatt, Rajesh & Becker, Michael (2010). Harmonic Grammar with linear programming: from linear systems to linguistic typology. Phonology 27. 77117.
Prince, Alan & Smolensky, Paul (1993). Optimality Theory: constraint interaction in generative grammar. Ms, Rutgers University & University of Colorado, Boulder. Published 2004, Malden, Mass. & Oxford: Blackwell.
Rhodes, Russell (2012). Vowel harmony as Agreement by Correspondence. Annual Report of the UC Berkeley Phonology Laboratory. 138–168. Available (May 2017) at
Rose, Sharon & Walker, Rachel (2004). A typology of consonant agreement as correspondence. Lg 80. 475531.
Sasa, Tomomasa (2009). Treatment of vowel harmony in Optimality Theory. PhD dissertation, University of Iowa.
Shih, Stephanie S. (2013). Consonant–tone interaction as Agreement by Correspondence. Ms, Stanford University & University of California, Berkeley. Available (May 2017) at
Shih, Stephanie S. (2014). Towards optimal rhythm. PhD dissertation, Stanford University.
Shih, Stephanie S. & Inkelas, Sharon (2014). A subsegmental correspondence approach to contour tone (dis)harmony patterns. In Kingston, John, Moore-Cantwell, Claire, Pater, Joe & Staubs, Robert (eds.) Proceedings of the 2013 Meeting on Phonology. Available (May 2017) at
Smolensky, Paul (1993). Harmony, markedness, and phonological activity. Paper presented at Rutgers Optimality Workshop. Available as ROA-87 from the Rutgers Optimality Archive.
Smolensky, Paul (2006). Optimality in phonology II: harmonic completeness, local constraint conjunction, and feature domain markedness. In Smolensky, Paul & Legendre, Géraldine (eds.) The harmonic mind: from neural computation to optimality-theoretic grammar. Vol. 2: Linguistic and philosophical implications. Cambridge, Mass.: MIT Press. 27160.
Smolensky, Paul & Legendre, Géraldine (eds.) (2006). The harmonic mind: from neural computation to optimality-theoretic grammar. 2 vols. Cambridge, Mass.: MIT Press.
Stone, M. (1977). An asymptotic equivalence of choice of model by cross-validation and Akaike's criterion. Journal of the Royal Statistical Society. Series B (Methodological) 39. 4447.
Walker, Rachel (2000). Long-distance consonantal identity effects. WCCFL 19. 532545.
Walker, Rachel (2009). Similarity-sensitive blocking and transparency in Menominee. Paper presented at the 83rd Annual Meeting of the Linguistic Society of America, San Francisco. Slides available (May 2017) at
Walker, Rachel (2014). Prominence-control and multiple triggers in vowel harmony: an ABC analysis. UC Berkeley Phonology Lab Annual Report: ABC Conference Archive. 202–213. Slides available (May 2017) at
Wayment, Adam (2009). Assimilation as attraction: computing distance, similarity, and locality in phonology. PhD dissertation, Johns Hopkins University.
Wilson, Colin (2006). Learning phonology with substantive bias: an experimental and computational study of velar palatalization. Cognitive Science 30. 945982.
Wilson, Colin & Obdeyn, Marieke (2009). Simplifying subsidiary theory: statistical evidence from Arabic, Muna, Shona, and Wargamay. Ms, Johns Hopkins University.
Zuraw, Kie (2002). Aggressive reduplication. Phonology 19. 395439.
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