Constraint against multiple identical linkage in OT

Question

I confess this question is rather theory-internal, but it may be very trivial for someone who follows the theoretical literature well. I am thinking of a type of constraint and want to know if such a thing has been proposed before, in the OT literature or elsewhere.

Imagine a representation where X is a root node, and i and j are features of the same type (e.g. they are both tone features), and imagine further that i and j are both linked to X, so you have a representation like

  X
 /\
i j

If i and j are different, then there is a contour. Now what if i and j are the same? Has there been discussion on a constraint against, as it were, "trivial contours?"

[subsequently added] Also, let's say that we want to ban the above representation, but still permit

X X
| |
i j

So a simple OCP rule will not suffice. Then further suppose that

  X
 /\
i j

when i and j are different, is also permitted.

[a second addition] To narrow the problem further, let's say that three elements, i,i,j are to be linked to two nodes, X1 and X2. The two possibilities where every element is associated with some node, and every node is associated with some element are:

X1  X2   X1 X2
/\  |     | /\
i i j     i i j

Both of these have one OCP violation, and one violation of NoContour, so these two constraints cannot be used in combination to solve the problem.

Answer 1

Your wanting a constraint against “trivial contours” ignores the fact that these may not be as trivial as you might suppose. Suppose you have a language with tones {L, LH, HL, H} and no vowel length. Then you could have a vowel like [V̌] which would be something like

  V
 / \
L   H

Now suppose you have another vowel in this language that has two high tone features.

  V
 / \
H   H

Since there’s no vowel length, we would expect this to be something like [V́], i.e. just a vowel with a high tone. Our description predicts this should be equivalent to

V
|
H

right? The language shouldn’t have any difference between one and two features. But suppose the language also said that it was okay to spread the second part of the contour onto a subsequent sonorant.

  V R
 / \|
L   H

So there should be a sequence like [V̀Ŕ] or [V̌Ŕ] arising from the above structure. If L is the unmarked tone then this should be a marked form with high tone on the sonorant. Contrast this with the following:

V R
|
H

Here the R gets the default tone which is L, so producing [V́R̀]. Now with L unmarked but a vowel with two H features then with a following sonorant we’d get

  V R
 / \|
H   H

which would show up as [V́Ŕ]. That’s a marked form, different from the unmarked [V́R̀] that should happen if L is the default, unmarked tone. This context is not exactly trivial but it does result from the “trivial contours” you describe if you expand the situation to include tone spread to sonorants which is a fairly common phenomenon.

I know this isn’t really an answer for you. I can’t point to any literature offhand, but I think that you’d need some good data to justify prohibiting such forms. Just because they seem trivial in the trivial case doesn’t mean that they continue to be trivial in nontrivial situations. To test your hypothesis I’d look for something in western Africa where the Bantu and Bantoid languages have tone systems like this.

(I’m handwaving about ‘marked’ and ‘unmarked’ because everybody does, but in a real article these terms would need to be well defined.)

Answer 2

[Here is an answer whose substance was suggested to me by Diana Archangeli]

The form of the OCP I was assuming was a somewhat classical one, more or less like Goldsmith's (1976:272) formulation:

At the phonetic level, any conti[g]uous identical (auto)segments must be
collapsed into each other. 

Under this formulation, OCP does not prefer either of:

X1  X2   X1 X2
/\  |     | /\
i i j     i i j

since it is just evaluating the surface sequence [i i j]. However, a generalized OCP, as proposed by Suzuki (1998:64) can distinguish between the two. Here is Suzuki's formulation:

Generalized OCP (GOCP)
In the scheme *X...X where “...” is intervening material, a sequence of two Xs is
   prohibited in some domain D.

The key is to recognize that the GOCP could apply cyclically, first at one domain, then at a higher domain, since it can apply to all domains generally. So [[i i] [j]] contains two violations of GOCP, first for [i i], then for [i i j], while [[i] [i j]] contains only one violation, for [i i j].

As @James C. points out, I did not consider representations where one of the featural elements was multiply-linked. Ranking No-Spread (McCarthy 1995:53) high enough, however, can rule out such representations.

Goldsmith, J. 1976. Autosegmental phonology. PhD. thesis, MIT.

McCarthy, J. 1995. Extensions of Faithfulness: Rotuman Revisited. ROA-110.

Suzuki, K. 1998. A typological investigation of dissimilation. PhD. thesis, University of Arizona