Optimality theory

 

  • Optimality theory is also criticized as being an impossible model of speech production/perception: computing and comparing an infinite number of possible candidates would take an infinitely long time to process.

  • There are two basic types of constraints:

    Faithfulness constraints require that the observed surface form (the output) match the underlying or lexical form (the input) in some particular way; that is, these constraints require identity between input and output forms.

  • Example
    As a simplified example, consider the manifestation of the English plural:

    /dɒɡ/ + /z/ → [dɒɡz] (dogs)
    /kæt/ + /z/ → [kæts] (cats)
    /dɪʃ/ + /z/ → [dɪʃɪz] (dishes)
    Also consider the following constraint set, in descending order of domination:
    No matter how the constraints are re-ordered, the allomorph [ɪs] will always lose to [ɪz].

  • [12]
    Alignment constraints
    Local conjunctions
    Two constraints may be conjoined as a single constraint, called a local conjunction, which gives only one violation each time both constraints are violated within a given domain, such as a segment, syllable or word.

  • Brasoveanu and Prince (2005) describe a process known as fusion and the various ways of presenting data in a comparative tableau in order to achieve the necessary and sufficient conditions for a given argument.

  • The source of this issue may be in terminology: the term theory is used differently here than in physics, chemistry, and other sciences.

  • For example, a language without complex clusters must be able to deal with an input such as /flask/.

  • If grammars differ only by having different rankings of Con, then the set of possible human languages is determined by the constraints that exist.

  • [2]
    Overview
    There are three basic components of the theory:

    Generator (Gen) takes an input, and generates the list of possible outputs, or candidates,
    Constraint component (Con) provides the criteria, in the form of strictly ranked violable constraints, used to decide between candidates, and
    Evaluator (Eval) chooses the optimal candidate based on the constraints, and this candidate is the output.

  • Other theories within OT are concerned with issues like the need for derivational levels within the phonological domain, the possible formulations of constraints, and constraint interactions other than strict domination.

  • Although much of the interest in OT has been associated with its use in phonology, the area to which OT was first applied, the theory is also applicable to other subfields of linguistics (e.g.

  • Idsardi (2006) argues this position, though other linguists dispute this claim on the grounds that Idsardi makes unreasonable assumptions about the constraint set and candidates, and that more moderate instantiations of OT do not present such significant computational problems (see Kornai (2006) and Heinz, Kobele and Riggle (2009)).

  • There have been a number of proposals designed to account for it, but most of the proposals significantly alter OT’s basic architecture and therefore tend to be highly controversial.

  • Some constraints are sometimes used as a “cover constraint”, standing in for a set of constraints that are not fully known or important.

  • However, it may not be possible to distinguish all of these potential grammars, since not every constraint is guaranteed to have an observable effect in every language.

  • Two total orders on the constraints of Con could generate the same range of input–output mappings, but differ in the relative ranking of two constraints which do not conflict with each other.

  • These sorts of problems are the reason why most linguists utilize a lattice graph to represent necessary and sufficient rankings, as shown below.

  • The first row reveals that either *SS or Agree must dominate Dep, based on the comparison between [dɪʃɪz] and [dɪʃz].

  • Specific instantiations of OT may make falsifiable predictions, in the same way specific proposals within other linguistic frameworks can.

  • OT differs from other approaches to phonological analysis, which typically use rules rather than constraints.

  • In derivational phonology, effects that are inexplicable at the surface level but are explainable through “opaque” rule ordering may be seen; but in OT, which has no intermediate levels for rules to operate on, these effects are difficult to explain.

  • In Balangao, NoCoda is not ranked high enough to be always obeyed, as witnessed in roots like taynan (faithfulness to the input prevents deletion of the final /n/).

  • Completely distinct from these, there are sub-theories which have been proposed entirely within OT, such as positional faithfulness theory, correspondence theory (McCarthy and Prince 1995), sympathy theory, stratal OT, and a number of theories of learnability, most notably by Bruce Tesar.

  • [13]
    Eval: definition of optimality
    In the original proposal, given two candidates, A and B, A is better, or more “harmonic”, than B on a constraint if A incurs fewer violations than B.

  • What predictions are made, and whether they are testable, depends on the specifics of individual proposals (most commonly, this is a matter of the definitions of the constraints used in an analysis).

  • Part of language acquisition can then be described as the process of adjusting the ranking of these constraints.

  • So far, the following rankings have been shown to be necessary:

    *SS, Max ≫ Dep ≫ Ident
    While it is possible that Agree can dominate Dep, it is not necessary; the ranking given above is sufficient for the observed [dɪʃɪz] to emerge.

  • The opacity of such phenomena finds no straightforward explanation in OT, since theoretical intermediate forms are not accessible (constraints refer only to the surface form and/or the underlying form).

  • Each of the constraints’ names may be suffixed with “-IO” or “-BR”, standing for input/output and base/reduplicant, respectively—the latter of which is used in analysis of reduplication—if desired.

  • [36] Constraints cover both the relations between sound and letter as well as preferences for spelling itself.

  • [28][irrelevant citation]
    Theories within optimality theory
    In practice, implementations of OT often make use of many concepts of phonological theories of representations, such as the syllable, the mora, or feature geometry.

  • The tableau for /kæt/ + /z/ contains rows with a single W and a single L. This shows that Agree, Max, and Dep must all dominate Ident; however, no ranking can be established between those constraints on the basis of this input.

  • This also means that constraints are violable; the winning (i.e.

  • Use outside of phonology
    Optimality theory is most commonly associated with the field of phonology, but has also been applied to other areas of linguistics.

  • [7][8] Parse and Fill serve essentially the same functions as Max and Dep, but differ in that they evaluate only the output and not the relation between the input and output, which is rather characteristic of markedness constraints.

  • Under McCarthy and Prince’s analysis, this is because faithfulness to the input does not apply to reduplicated material, and NoCoda is thus free to prefer ma-tayna-taynan over hypothetical ma-taynan-taynan (which has an additional violation of NoCoda).

  • Based on this tableau, the following ranking has been established:

    Agree, Max, Dep ≫ Ident
    The tableau for /dɪʃ/ + /z/ shows that several more rankings are necessary in order to predict the desired outcome.

  • Frequently, such alterations add new types of constraints (which are not universal faithfulness or markedness constraints), or change the properties of Gen (such as allowing for serial derivations) or Eval.

  • Markedness constraints motivate changes from the underlying form, and faithfulness constraints prevent every input from being realized as some completely unmarked form (such as [ba]).

  • Neither of these are truthful, which is a failing of writing out rankings in a linear fashion like this.

  • [5] If rankings with ties are allowed, then the number of possibilities is an ordered Bell number rather than a factorial, allowing a significantly larger number of possibilities.

  • Within a language, a constraint may be ranked high enough that it is always obeyed; it may be ranked low enough that it has no observable effects; or, it may have some intermediate ranking.

  • In this view, OT is taken to be a model of linguistic competence and is therefore not intended to explain the specifics of linguistic performance.

  • A is “optimal” in its candidate set if it is better on the constraint hierarchy than all other candidates.

  • Max and Dep replace Parse and Fill proposed by Prince and Smolensky (1993), which stated “underlying segments must be parsed into syllable structure” and “syllable positions must be filled with underlying segments”, respectively.

  • Gen is free to generate any number of output candidates, however much they deviate from the input.

 

Works Cited

[‘1. “Optimality”. Proceedings of the talk given at Arizona Phonology Conference, University of Arizona, Tucson, Arizona.
2. ^ Prince, Alan, and Smolensky, Paul (1993) “Optimality Theory: Constraint interaction in generative grammar.” Technical Report CU-CS-696-93, Department of Computer Science, University of Colorado at Boulder.
3. ^ Kager (1999), p. 20.
4. ^ Prince, Alan (2004). Optimality Theory: Constraint Interaction in Generative Grammar. Paul Smolensky. Malden, MA: Blackwell Pub. ISBN 978-0-470-75940-0. OCLC 214281882.
5. ^ Merchant, Nazarré; Riggle, Jason (2016-02-01). “OT grammars, beyond partial orders: ERC sets and antimatroids”. Natural Language & Linguistic Theory. 34 (1): 241–269. doi:10.1007/s11049-015-9297-5. ISSN 1573-0859. S2CID 254861452.
6. ^ Ellison, T. Mark; Klein, Ewan (2001), “Review: The Best of All Possible Words (review of Optimality Theory: An Overview, Archangeli, Diana & Langendoen, D. Terence, eds., Blackwell, 1997)”, Journal of Linguistics, 37 (1): 127–143, JSTOR 4176645.
7. ^ Prince & Smolensky (1993), p. 94.
8. ^ Jump up to:a b McCarthy (2008), p. 27.
9. ^ McCarthy (2008), p. 209.
10. ^ Kager (1999), pp. 99–100.
11. ^ McCarthy (2008), p. 224.
12. ^ Kager (1999), pp. 29–30.
13. ^ Jump up to:a b Kager (1999), pp. 392–400.
14. ^ McCarthy (2008), pp. 214–20.
15. ^ Frank, Robert; Satta, Giorgio (1998). “Optimality theory and the generative complexity of constraint violability”. Computational Linguistics. 24 (2): 307–315. Retrieved 5 September 2021.
16. ^ Tesar & Smolensky (1998), pp. 230–1, 239.
17. ^ McCarthy (2001), p. 247.
18. ^ Chomsky (1995)
19. ^ Dresher (1996)
20. ^ Hale & Reiss (2008)
21. ^ Halle (1995)
22. ^ Idsardi (2000)
23. ^ Idsardi (2006)
24. ^ Heinz, Jeffrey; Kobele, Gregory M.; Riggle, Jason (April 2009). “Evaluating the Complexity of Optimality Theory”. Linguistic Inquiry. 40 (2): 277–288. doi:10.1162/ling.2009.40.2.277. ISSN 0024-3892. S2CID 14131378.
25. ^ Kornai, András (2006). “Is OT NP-hard?” (PDF).
26. ^ Kager, René (1999). Optimality Theory. Section 1.4.4: Fear of infinity, pp. 25–27.
27. ^ Prince, Alan and Paul Smolensky. (2004): Optimality Theory: Constraint Interaction in Generative Grammar. Section 10.1.1: Fear of Optimization, pp. 215–217.
28. ^ de Lacy (editor). (2007). The Cambridge Handbook of Phonology, p. 1.
29. ^ McCarthy, John (2001). A Thematic Guide to Optimality Theory, Chapter 4: “Connections of Optimality Theory”.
30. ^ Legendre, Grimshaw & Vikner (2001)
31. ^ Trommer (2001)
32. ^ Wolf (2008)
33. ^ Hendriks, Petra, and Helen De Hoop. “Optimality theoretic semantics”. Linguistics and philosophy 24.1 (2001): 1-32.
34. ^ Blutner, Reinhard; Bezuidenhout, Anne; Breheny, Richard; Glucksberg, Sam; Happé, Francesca (2003). Optimality Theory and Pragmatics. Springer. ISBN 978-1-349-50764-1.
35. ^ Wiese, Richard (2004). “How to optimize orthography”. Written Language and Literacy. 7 (2): 305–331. doi:10.1075/wll.7.2.08wie.
36. ^ Hamann, Silke; Colombo, Ilaria (2017). “A formal account of the interaction of orthography and perception”. Natural Language & Linguistic Theory. 35 (3): 683–714. doi:10.1007/s11049-017-9362-3. hdl:11245.1/bab74c16-4f58-4b1f-9507-cd51fbd6ae49. S2CID 254872721.
37. Brasoveanu, Adrian, and Alan Prince (2005). Ranking & Necessity. ROA-794.
38. Chomsky (1995). The Minimalist Program. Cambridge, Massachusetts: The MIT Press.
39. Dresher, Bezalel Elan (1996): The Rise of Optimality Theory in First Century Palestine. GLOT International 2, 1/2, January/February 1996, page 8 (a humorous introduction for novices)
40. Hale, Mark, and Charles Reiss (2008). The Phonological Enterprise. Oxford University Press.
41. Halle, Morris (1995). Feature Geometry and Feature Spreading. Linguistic Inquiry 26, 1-46.
42. Heinz, Jeffrey, Greg Kobele, and Jason Riggle (2009). Evaluating the Complexity of Optimality Theory. Linguistic Inquiry 40, 277–288.
43. Idsardi, William J. (2006). A Simple Proof that Optimality Theory is Computationally Intractable. Linguistic Inquiry 37:271-275.
44. Idsardi, William J. (2000). Clarifying opacity. The Linguistic Review 17:337-50.
45. Kager, René (1999). Optimality Theory. Cambridge: Cambridge University Press.
46. Kornai, Andras (2006). Is OT NP-hard?. ROA-838.
47. Legendre, Géraldine, Jane Grimshaw and Sten Vikner. (2001). Optimality-theoretic Syntax. MIT Press.
48. McCarthy, John (2001). A Thematic Guide to Optimality Theory. Cambridge: Cambridge University Press.
49. McCarthy, John (2007). Hidden Generalizations: Phonological Opacity in Optimality Theory. London: Equinox.
50. McCarthy, John (2008). Doing Optimality Theory: Applying Theory to Data. Blackwell.
51. McCarthy, John and Alan Prince (1993): Prosodic Morphology: Constraint Interaction and Satisfaction. Rutgers University Center for Cognitive Science Technical Report 3.
52. McCarthy, John and Alan Prince (1994): The Emergence of the Unmarked: Optimality in Prosodic Morphology. Proceedings of NELS.
53. McCarthy, John J. & Alan Prince. (1995). Faithfulness and reduplicative identity. In J. Beckman, L. W. Dickey, & S. Urbanczyk (Eds.), University of Massachusetts occasional papers in linguistics (Vol. 18, pp. 249–384). Amherst, Massachusetts: GLSA Publications.
54. Merchant, Nazarre & Jason Riggle. (2016) OT grammars, beyond partial orders: ERC sets and antimatroids. Nat Lang Linguist Theory, 34: 241. doi:10.1007/s11049-015-9297-5
55. Moreton, Elliott (2004): Non-computable Functions in Optimality Theory. Ms. from 1999, published 2004 in John J. McCarthy (ed.), Optimality Theory in Phonology.
56. Pater, Joe. (2009). Weighted Constraints in Generative Linguistics. “Cognitive Science” 33, 999–1035.
57. Prince, Alan (2007). The Pursuit of Theory. In Paul de Lacy, ed., Cambridge Handbook of Phonology.
58. Prince, Alan (2002a). Entailed Ranking Arguments. ROA-500.
59. Prince, Alan (2002b). Arguing Optimality. In Coetzee, Andries, Angela Carpenter and Paul de Lacy (eds). Papers in Optimality Theory II. GLSA, UMass. Amherst. ROA-536.
60. Prince, Alan and Paul Smolensky. (1993/2002/2004): Optimality Theory: Constraint Interaction in Generative Grammar. Blackwell Publishers (2004) [1](2002). Technical Report, Rutgers University Center for Cognitive Science and Computer Science Department, University of Colorado at Boulder (1993).
61. Tesar, Bruce and Paul Smolensky (1998). Learnability in Optimality Theory. Linguistic Inquiry 29(2): 229–268.
62. Trommer, Jochen. (2001). Distributed Optimality. PhD dissertation, Universität Potsdam.
63. Wolf, Matthew. (2008). Optimal Interleaving: Serial Phonology-Morphology Interaction in a Constraint-Based Model. PhD dissertation, University of Massachusetts. ROA-996.
Photo credit: https://www.flickr.com/photos/sophiea/4860145119/’]