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Optimality theory is a theory of phonology that drops Chomskyan replacement rules in favor of a set of ranked constraints. It can lead to much more elegant analyses in some cases.

However, I don't understand how optimality theory can deal with phonological opacity.

Take, for example, Isthmus Nahuatl. (This example comes from an old textbook of phonology, but any errors are most likely my own.) In rule-based phonology, it is said to have two relevant rules:

[-cons] → ∅ / [+voice +sonorant] _ #
[+voice +cons +sonorant] → [-voice] / _ #

In other words, word-final vowels after voiced sonorants are deleted, and word-final sonorants become devoiced.

But notably, the first rule doesn't feed the second: given the underlying form /ʃikakíli/, we get the surface form [ʃikakíl] rather than *[ʃikakíl̥]. In rule-based phonology, this is handled through rule orderings.

How would this phenomenon be explained in optimality theory? Forms like /tájoːl/ [tájoːl̥] indicate that the "no final voiced sonorants" constraint is highly-ranked; why does this constraint mysteriously fail to apply when another constraint would apply as well? Any ranking of "no final voiced sonorants" and "no final vowels after voiced sonorants" would seem to produce *[ʃikakíl̥], which is not observed.

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    Maybe relevant: people.umass.edu/jjmccart/sympathy.pdf – ewawe Jul 28 '18 at 14:03
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    Out of curiosity, what book did the example come from? – user6726 Jul 28 '18 at 21:40
  • @user6726 I must admit I'm not sure. I only have photocopies of the relevant pages. – Draconis Jul 29 '18 at 17:39
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Unsurprisingly, this issue has plagued OT since its inception a quarter century ago. One issue is defining exactly what "problem" is: my own view is that the relevant question should not involve reifying a phenomenon (opacity), it involves comparison of analytic devices (ordering versus...). The term "opacity" was introduced by Kiparsky in 1971, but has received various definitions. The classical definition essentially said that allophonic rules (those satisfying the biuniqueness condition) are transparent, and nonallophonic rules (any neutralization or deletion) are opaque. Kiparsky was not proposing anything about the theory of grammar, the utility of the concept lies in its function in language change. In short, it's not clear what the limits of "opacity" are. However, counterfeeding as you pointed to is the most prominent form of problem case subsumed under "opacity".

Rules, Constraints, and Phonological Phenomena (Vaux & Nevins, eds.) has a paper "Ordering" that addresses some of the devices available (ca. 2000) for emulating ordering in OT. Briefly summarized and including other developments...

(1) Containment. Originally, segments were not deleted, they were simply "unparsed". That means that the winning candidate is [ʃikakíl(i)] with an unsyllabified i; because that vowel is still there, l is not really final.

(2) 2-level constraints. It has also been proposed that constraints can refer to properties of the input (remember that a tableau has the input in the NW corner, so this is conceptually an obvious possibility). The whole class of IO Faithfulness constraints exploits this possibility. So the constraint could refer to "whether the sonorant is final in the input".

(3) Constraint Conjunction: "you cannot both X and Y". You can delete a vowel, you can devoice a sonorant, but you cannot both delete a vowel and devoice a sonorant" (within a given substring). Deletion of a vowel violates Max, devoicing a vowel violates Ident, you cannot violate both constraints in a substring.

(4) Sympathy constraints. Faithfulness is extended to include a "sympathetic" candidate (the flower candidate), which is the best candidate that satisfies a particular constraint (such as Max). Then there is the sympathetic-candidate faithfulness constraint that says that the actual output has to be faithful to the flower candidate with respect to some property, in this case, the voicing of the flower candidate. The flower candidate is the best candidate (the underlying form, as it happens) that satisfies Max (which is in fact violated in the output).

(5) Operational domains. This is popular in the Optimal Domains Theory variant and used sometimes in mainstream versions (especially for reduplication). Basically, you can bracket a string various ways, and state constraints with respect to that bracketing. Maybe the devoicing rule requires the sonorant to be adjacent to the bracket "}", which is assigned to the end of the word but not inside CV.

(6) Limited serial derivation. Lexical phonology versions of OT have multiple passes through the phonology. Final vowel deletion could be assigned to a different stratum, and constraint ranking can be different across strata.

(7) Candidate chains. This is whole nother kettle of fish, and I have to admit that I don't understand all of the details of how it is implemented. The idea is very simple, though, and was necessary in order to implement Sympathy theory without actual derivations. The problem in ST is that the evaluation of candidate A with respect to sympathy constraint Z depends on identifying flower candidate B, which requires evaluating all candidates for all constraints. That's a serial derivation, or looks like one.

This can be solved by generating not just a "phonetic" candidate, but also a proposed "sympathetic" candidate. So for example, if you need /niduura/ to generate the flower candidate nduura to guide selection of the phonetic candidate ninuura, you simply pair {ninuura, nduura} as well as many others like {ninuura, niduura} and so on – the first member of the n-tuple is the one pronounced, the second is the flower candidate. The pairing is simply the Cartesian product of the candidate set with itself.

This can be extended to have longer n-tuples of candidates such as {dosk'a, do:sk'a, du:sk'a} – this is a Yawelmani form, where o, o: trigger rounding of /a/, but surface [o] can derive from /u:/, and such an [o] does not condition harmony. Candidate chains amounts to selecting the correct n-tuple with the desired phonetic form, and that chain of candidates that leads to the phonetic form. There are various complications involving "Prec" constraints ("all violations of Max must precede any violations of Dep"), plus a limit on Gen, where adjacent candidates within a candidate n-tuple differ in "one thing".

I think that "Harmonic serialism" has gained ascendancy these days. In essence, rule ordering is back.

The dissertation by Bye also proposes a theory of "virtual phonology" to handle opacity, f.y.i.

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Taking the problem to be to explain why the final [l] of [ʃikakíl] does not devoice, my best guess is that that [l] is long, or at least has some fortis articulation that prevents weakening it to voiceless [l]. I do see that this is not consistent with the facts as given, since it is transcribed as just a single final [l], not *[ʃikakíll], yet sometimes such phonetic details escape mention.

If this were correct, the example would not be relevant to the choice between replacement rule vs. optimality theory, neither of which, in any case, appears to offer any explanation of what is going on.

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  • The example presented here is simplified, but the textbook provides many more examples: it does seem to be a consistent rule in Isthmus Nahuatl that final vowels after voiced sonorants disappear, and final voiced sonorants devoice, but that these two rules never both apply to the same word. – Draconis Jul 28 '18 at 20:48

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