Invitational round | 10 points | 51.00% | Problem statement | Official solution | Tags: Phonology
All phrases here are of the form "A's B".
Now we can translate to English without having figured out the tones.
a. [aja βɔɾu] = chicken's fish
b. [dukɛ aitɛ] = bird's father
c. [wutu dukɛ] = car's bird
We can even translate into Abawiri, but without tones.
a. car's earth = [wutu sɔɾi]
b. bird's car = [dukɛ wutu]
c. father's rat = [aitɛ sɔkɾɛ]
d. child's fish = [dɛβi bɔɾu]
e. earth's chicken = [sɔɾi aja]
f. father's ear = [aitɛ gʷaku]
To truly complete this part, we need to figure out the tones. We have 8 data points from O1, plus 3 more from O2. I will refer to the first and second syllables of the possessor position as σ1 and σ2, and the first and second syllables of the possessed position as σ3 and σ4. So a possessive construction always has 4 syllables: σ1σ2 σ3σ4. I use 5 to mark high tone (like í), 3 to mark mid tone (like ē), and 1 to mark low tone (like à). For example, [aitɛ] appears as [àitɛ́] in the possessor position, so is recorded as σ1 = 1, σ2 = 5. In the possessed position, it appears as [àitɛ̀], so is recorded as σ3 = 1, σ4 = 1. Here's the full table of tones:
| Word | σ1 | σ2 | σ3 | σ4 |
|---|---|---|---|---|
| [aitɛ] | 1 | 5 | 1 | 1 |
| [aja] | 1 | 1; 3 | ||
| [bɔɾu] | 5 | 5 | 5 | 1 |
| [dɛβi] | 1 | 1; 5 | 1 | 1 |
| [dukɛ] | 5 | 5 | 5 | 1 |
| [gʷaku] | 5 | 1 | ||
| [sɔkɾɛ] | 1 | 3 | 1 | 1 |
| [sɔɾi] | 1 | 1 | 1 | 1 |
| [wutu] | 1 | 1 | 1 | 1 |
Notice that σ4 is always low tone, and the same word always has identical tones for σ1 and σ3. Therefore, at least the first syllable's tone is encoded directly in the word (lexical tones), and the last syllable of the phrase always becomes low tone. So at this point, we can already fill in tones for 3 syllables.
a. car's earth = [wùtu sɔ̀ɾì]
b. bird's car = [dúkɛ wùtù]
c. father's rat = [àitɛ sɔ̀kɾɛ̀]
d. child's fish = [dɛ̀βi βɔ́ɾù]
e. earth's chicken = [sɔ̀ɾi àjà]
f. father's ear = [àitɛ gʷákù]
We'd like to say that σ2's tone is also underlyingly encoded in the word (like Chinese, where every syllable has an underlying tone), but [dɛβi] and [aja] have two different tones for σ2. If we postulate an underlying encoding, we have to select one underlying form and explain this variation.
The [dɛ̀βí]/[dɛ̀βì] variation cannot have happened simply due to the tones of the surrounding syllables, because in 3 and 7, they are followed by [àitɛ̀] and [wùtù] respectively, so the two phrases both have σ1σ3σ4 = 111. However, we know that [aitɛ] has σ1σ2 = 15 and just changed to 11 in the σ3σ4 position, while [wutu] has σ1σ2 = 11. Perhaps it depends on the underlying tone of the next word. There's no reason to not believe that the same process has happened for all the other words as well—so let's list all possible tones of σ2 and their corresponding σ1 and σ3 contexts:
| σ2 | σ1 ____ σ3 |
|---|---|
| 5 | 11 ([aitɛ dɛβi], [dɛβi wutu]), 51 ([dukɛ sɔɾi], [dukɛ aitɛ]), 55 ([bɔɾu gʷaku]) |
| 3 | 15 ([sɔkɾɛ dukɛ], [aja βɔɾu]) |
| 1 | 11 ([dɛβi aitɛ], [aja sɔkɾɛ]), 15 ([sɔɾi βɔɾu], [wutu dukɛ]) |
This may seem really messy, but there are already a few takeaways:
Now we just need to explain how to select between the two alternatives in conditions 2 and 3. Here's IMO a real stretch: we want to form a rule that looks like "pick this alternative if the first or second word belongs to a class X, or the other alternative otherwise". In condition 2, it can't be based on the second word, because [βɔɾu] appears as a second word in both alternatives. In condition 3, it can't be based on the first word, because [dɛβi] appears as a first word in both alternatives. So only the following rules can work:
And, based on the cases of σ1σ2σ3 = 135 and 111, we can figure out that X includes [sɔkɾɛ], [aja], and [aitɛ].
I'll admit that this analysis is reverse-engineered from the solution and I have no clue how you are supposed to come up with it in a test (that the rule needs to discriminate based on the identity of the first or second word). This class X is known as "toneless words" in the official solution.
a. car's earth = [wùtu sɔ̀ɾì] → [wùtú sɔ̀ɾì] (σ1 = σ3 = 1, second word doesn't belong to class X)
b. bird's car = [dúkɛ wùtù] → [dúkɛ́ wùtu] (σ1 = 5)
c. father's rat = [àitɛ sɔ̀kɾɛ̀] → [àitɛ̀ sɔ̀kɾɛ̀] (σ1 = σ3 = 1, second word belongs to class X)
d. child's fish = [dɛ̀βi βɔ́ɾù] → [dɛ̀βì βɔ́ɾù] (σ1 = 1, σ3 = 5, first word doesn't belong to class X)
e. earth's chicken = [sɔ̀ɾi àjà] → [sɔ̀ɾì àjà] (σ1 = σ3 = 1, second word belongs to class X)
f. father's ear = [àitɛ gʷákù] → [àitɛ̄ gʷákù] (σ1 = 1, σ3 = 5, first word belongs to class X)