The problem
Background in Iny
Iny (Ribeiro, 2002 2012) has regressive ATR harmony in which both input and output ATR values of triggers are important. The surface vowel inventory is as follows.
| [+ATR] | a ã ə̃ (ə) ɔ ɛ ʊ ɨ ɪ |
| [-ATR] | ə o õ e u i̘ i ĩ |
The following forms illustrate harmony occuring.
| /r-ɛ-rɔ=r-e/ | [rerore] |
| /b-∅-r-krɔ=kre/ | [bikrokre] |
| /r-ɛ-hãɗɛ=r-e/ | [rɛhãɗere] |
The following forms harmonize as well, but in a different way. What is the difference? Why?
| /brɔrɛ-dĩ/ | [broreni] |
| /wa-θɛ-rit͡ʃɔrɛ/ | [waθerit͡ʃɔrɛ] |
| /kɔɗʊ-dĩ/ | [kɔɗuni] |
| /r-ɛ-hI=r-e | [rɛhire] |
The following definitions and chart may help you sort things out. Using these analytical categories, think about how high, mid, and low vowels behave with respect to ATR harmony.
- Triggers: for some vowel \(V\) at index \(x\), \(V_x\), if underlying [+ATR] on \(V_x\) results in \(V_{x-1}\) becoming [+ATR], then \(V_x\) triggers [+ATR] harmony.
- Undergoes: for some vowel \(V\) at index \(y\), \(V_y\), if [+ATR] (underlying or derived) on \(V_{y+1}\) results in \(V_y\) becoming [+ATR], then \(V_y\) undergoes [+ATR] harmony.
- Propagates: for some vowel \(V\) at index \(V_z\), if [+ATR] (underlying or derived) on \(V_{z+1}\) results in \(V_z\) and \(V_{z-1}\) becoming [+ATR], then \(V_z\) propagates [+ATR].
Analysis
There are two natural classes we will want to refer to. Let's define those first.
- \([+\mathrm{ATR},+\mathrm{hi}]_i(x)=\)
- \([+\mathrm{ATR},-\mathrm{hi},-\mathrm{lo},-\mathrm{nas}]_o(x)=\)
Now we can define a BMRS for Iny. Assume the following output features. Hint: How are you going to capture the directionality?
- \([\mathrm{high}]_o(x)=\)
- \([\mathrm{low}]_o(x)=\)
- \([\mathrm{nasal}]_o(x)=\)
- \([\mathrm{ATR}]_o(x)=\)