Journal of Logic, Language and Information

, Volume 26, Issue 2, pp 89–108 | Cite as

A Constructive Solution to the Ranking Problem in Partial Order Optimality Theory

Article
First Online:

Abstract

Partial order optimality theory (PoOT) (Anttila and Cho in Lingua 104:31–56, 1998) is a conservative generalization of classical optimality theory (COT) (Prince and Smolensky in Optimality theory: constraint interaction in generative grammar, Blackwell Publishers, Malden, 1993/2004) that makes possible the modeling of free variation and quantitative regularities without any numerical parameters. Solving the ranking problem for PoOT has so far remained an outstanding problem: allowing for free variation, given a finite set of input/output pairs, i.e., a dataset, \(\Delta \) that a speaker S knows to be part of some language L, how can S learn the set of all grammars G under some constraint set C compatible with \(\Delta \)?. Here, allowing for free variation, given the set of all PoOT grammars GPoOT over a constraint set C , for an arbitrary \(\Delta \), I provide set-theoretic means for constructing the actual set G compatible with \(\Delta \). Specifically, I determine the set of all STRICT ORDERS of C that are compatible with \(\Delta \). As every strict total order is a strict order, our solution is applicable in both PoOT and COT, showing that the ranking problem in COT is a special instance of a more general one in PoOT.

Keywords

Optimality theory Classical optimality theory Partial order optimality theory Formal linguistics Linguistics Honology Formal phonology Order theory Set theory Ranking problem 
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References

  1. Anttila, A. (1997). Deriving variation from grammar. In R. van Hout, F. Hinskens, & L. Wetzels (Eds.), Variation, change and phonological theory (pp. 35–68).Google Scholar
  2. Anttila, A. (2009). Derived environment effects in colloquial helsinki finnish. In K. Hanson & S. Inkelas (Eds.), The nature of the word: Essays in honor of Paul Kiparsky (pp. 433–460). Cambridge, MA: MIT Press.Google Scholar
  3. Anttila, A., & Andrus, C. (2006). T-Orders. Stanford: Stanford University.Google Scholar
  4. Anttila, A., & Cho, Y. Y. (1998). Variation and change in optimality theory. Lingua, 104, 31–56.CrossRefGoogle Scholar
  5. Blutner, R. (1999). Some aspects of optimality in natural language interpretation. In H. de Hoop & H. de Swart (Eds.), Papers on optimality theoretic semantics (pp. 1–21). Utrecht: Utrecht Institute of Linguistics OTS.Google Scholar
  6. Boersma, P. (1997). How we learn variation, optionality, and probability. IFA Proceedings, 21, 43–58.Google Scholar
  7. Brasoveanu, A., & Prince, A. (2005). Ranking and necessity. In Part I. Rutgers Optimality Archive-794.Google Scholar
  8. Brasoveanu, A., & Prince, A. (2011). Ranking and necessity: The fusional reduction algorithm. Natural Language and Linguistic Theory, 29, 3–70.CrossRefGoogle Scholar
  9. Davey, B. A., & Priestley, H. A. (2002). Introduction to lattices and order. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  10. Jäger, G. (2003). Gradient constraints in finite state OT: The unidirectional and the bidirectional case. Natural Language Engineering, 9(1), 21–38.CrossRefGoogle Scholar
  11. Legendre, G. (2001). Optimality theoretic syntax. An introduction to optimality theory in syntax. Cambridge, MA: MIT Press.Google Scholar
  12. McCarthy, J. J. (2008). Doing optimality theory. Oxford: Blackwell Publishers.CrossRefGoogle Scholar
  13. Prince, A. (2002). Entailed ranking arguments. Rutgers Optimality Archive-500.Google Scholar
  14. Prince, A., & Smolensky, P. (1993/2004). Optimality theory: Constraint interaction in generative grammar. Malden, MA: Blackwell Publishers.Google Scholar
  15. Tesar, B. (1995). Computational optimality theory. Ph.D. thesis, University of Colorado at Boulder.Google Scholar
  16. Tesar, B., & Paul, S. (1993). The learnability of optimality theory: An algorithm and some basic complexity results. Rutgers Optimality Archive-2.Google Scholar
  17. Zeevat, H. (2001). The asymmetry of optimality theoretic syntax and semantics. Journal of Semantics, 17(3), 243–262.CrossRefGoogle Scholar
  18. Zwarts, J. (2004). Competition between word meanings: The polysemy of (A)round. In C. Meier & M. Weisgerber (Eds.), Proceedings of SuB8. Konstanz: University of Konstanz, Linguistics Working Papers.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.200 Winchester Circle Apt G16Los GatosUSA

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