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a local conjunction conjoining constraint A and constraint B in domain δ is noted as {A&B}δ in this thesis. Universally, {A&B}δ is ranked higher than both A and B.
Self-conjunction, like local conjunction, is a conjoined constraint which is violated when a certain constraint is violated twice in a given domain. Tableau (8) is an example of self-conjunction proposed by Ito and Mester (1998). A self-conjunction of constraint A in domain δ is noted as A2δ. Like local conjunction, A2δ is universally ranked higher than A, usually with another constraint ranked in between.
(8) /bhidh/ → [bhid] or [bidh] (hypothetical) (Ito and Mester, 1998)5
/bhidh/ *ASP2σ IDENT([asp]) *ASP
a. bhidh *! **
b. → bidh * *
c. → bhid * *
d. bid **!
2.2 Previous OT Analyses of Mandarin
2.2.1 The Issue of Mid Vowel Assimilation
Previous research has done some analyses about the phonotactic restrictions of Mandarin. Duanmu (2007) has analyzed the phonotactic restrictions of Mandarin rhymes through OT. In his analysis, he derives two constraints to evaluate Mandarin rhymes: NC-Harmony and GN-Harmony. The former indicates that the nucleus and the
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coda of a same syllable should share the same value for [back] and [round] feature. The latter one indicates that the nucleus and the prenuclear glide of a same syllable should share the same value for [back] and [round] feature. Between the two constraints, NC-Harmony is ranked higher than GN-NC-Harmony. The examples by Duanmu are shown in (9) and (10) below.
(9) /ɥə/ → [ɥe] (Duanmu, 2007)
/ɥə/ NC-Harmony Avoid-[ø] {GN-[back], GN-[round]}
a. ɥə * *!
b. → ɥe *
c. ɥø *!
(10) /wəj/ → [wej] (Duanmu, 2007)
/wəj/ NC-Harmony GN-Harmony
a. wəj *! *
b. → wej *
c. woj *!
In tableau (9), the input /ɥə/ has no coda, so NC-Harmony is not violated by any candidates. This situation is called vacuous satisfaction, and the definition is in (11) below.
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(11) The definition of “vacuous satisfaction” (McCarthy, 2008)
When a candidate does not contain a structure that a certain constraint is against, it is stated that the constraint is vacuously satisfied by the candidate. For instance, an open syllable does vacuously satisfy a constraint requiring the coda to be voiceless.
In OT analysis, vacuous satisfaction is treated the same as nonvacuous satisfaction, though.
Let’s get back to example (9). All candidates satisfy NC-Harmony, so none is ruled out. Among the three candidates, candidate (c) completely satisfies GN-Harmony, but it contains a front rounded vowel [ø], which is not licensed in Mandarin. Therefore, it is ruled out by a higher-ranked constraint Avoid-[ø]. As for candidates (a) and (b), (a) violates GN-Harmony twice because the prenuclear glide and the nucleus has different values for both [back] and [round] features while (b) only violates GN-Harmony once, with its prenuclear glide and nucleus only differing in [round] feature. Therefore, candidate (b) is the best choice for the output form. Note that Avoid-[ø] must be ranked higher than GN-Harmony, or candidate (c) will be wrongly predicted as the winner.
Example (10) illustrates how NC-Harmony is ranked higher than GN-Harmony.
Comparing candidates (b) and (c), the former violates GN-Harmony while the latter NC-Harmony. The attested output is (b) [wej], so NC-Harmony is less violable.
Lin (2015) also analyzes the mid vowel assimilation phenomenon of different Mandarin dialects with OT approach. The research states that different dialects have different constraint rankings. Among them, the constraint ranking of Standard Mandarin is shown in (12).
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(12) The constraint ranking about mid vowel assimilation of Standard Mandarin (Lin, 2015)6
*ø >> RIME-HARMONY, GV-HARMONY >> *o >> *e
Likewise, Lin ranked the constraint *ø on the top to avoid such segment. Although Lin accidentally ranked RIME-HARMONY and GV-HARMONY the same, the used constraints are almost identical to those used by Duanmu. Both of them high-rank a constraint to restrict that V and X in a same syllable have identical values for the [back] (and also [round]) feature. However, it is observed that there are different phenomena when the X slot is filled with a nasal coda or an off-glide, as is illustrated in (13).
(13) The mid vowel assimilation when X is a nasal coda or an off-glide
/əj/ → [ej] /ə/ becomes [e] because of the [-back] feature of [j], which satisfies NC-Harmony.
/ən/ → [ən] /ə/ remains as a central vowel despite the following [-back] nasal [n].
/əw/ → [ow] /ə/ becomes [o] because of the [+back] feature of [w], which satisfies NC-Harmony.
/əŋ/ → [əŋ] /ə/ remains as a central vowel, which still satisfies NC-Harmony because of the following [+back] nasal [ŋ].
According to (13), it is assumed that the mid vowel has a different requirement of assimilation to a nasal coda from that to an off-glide. Therefore, it is necessary to
6 Lin defines the term “rime” as the structure of VX. Therefore, her RIME-HARMONY constraint has the same definition as Duanmu’s NC-Harmony in (9) and (10).
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Lin (2007) has also discussed about the difference of the mid vowel assimilation when it is preceded by a nasal coda or an off-glide. The problem does not lie in the segment filled in the X slot itself because it is observed that low vowels also assimilate to nasal codas. For example, shan [ʂan] ‘mountain’ and shang [ʂɑŋ] ‘injury’ are allowed, but *[ʂaŋ] and *[ʂɑn] are not. Therefore, it is unreasonable to argue that nasal codas do not trigger the assimilation. To solve this problem, Lin proposes a hypothesis: there are two main kinds of VX structure in Mandarin; one is diphthong and the other is
“high/low vowel + nasal.” She excludes the structure of “mid vowel + nasal” in the underlying form. In her theory, a mid vowel only precedes a nasal coda due to the condition and rule described in (14). There are no mid vowels preceding a nasal coda in the underlying forms.
(14) The [ə]-insertion condition a. Environment
When a high vowel and its following nasal coda have different values for the [back] feature, an [ə] is inserted between them.
b. Rule
∅ → ə / -cons
__ +nas
αbk βbk
c. Examples (The glide formation rule is omitted.) (i) /lun/ → [lwən] ‘wheel’
(ii) /piŋ/ → [pjəŋ] ‘ice’
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Lin’s hypothesis seems to successfully explain why mid vowels do not assimilate to nasal codas. However, she does not clearly explain why there are syllables like shen [ʂən] ‘body’ and seng [səŋ] ‘monk’, where there are no high vocoids in the syllables to trigger the [ə]-insertion rule.
Another problem lies in the example (ii) in (14c). In Taiwan accent, the word bing
‘ice’ is pronounced as [piŋ]. Other words that have the same rhyme are also pronounced this way. This pronunciation violates Lin’s RIME-HARMONY constraint in (12) and her [ə]-insertion rule in (14) because [i] is [-back] while [ŋ] is [+back]. Therefore, it is necessary to re-rank the constraints or propose new ones to fulfill the dialect spoken in Taiwan.
2.2.2 The Issue of Low Vowel Raising
Low vowel raising in Mandarin is a special phonological phenomenon that it is hard to find another similar rule in other contexts. The simplified formula is illustrated in (15).
(15) The low vowel raising rule a → e / j, ɥ __ n
Aiming at this phonological phenomenon, Hsieh (2012) has analyzed it via rule-based phonology and OT. In his research, he proposes a self-conjunction constraint called “AGREE[back]2” to rule out the ill-formed *[jan] and *[ɥan], and successfully predicts the well-formed [jen] and [ɥen]. The definition of the constraint is shown in (16).
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(16) AGREE[back]2 (Flemming, 2003; Hsieh, 2012)
Assign one violation mark for every syllable only if where there is a vowel not having the same value for the [back] feature as both of its adjacent consonants.
In Hsieh’s research, constraint (16) rules out *[jan] but is satisfied by [jen]. He follows the SPE tradition to regard the low front vowel [a] as [+back]. This theory does support constraint (16) to rule out *[jan] because [a] is [+back] while [j] and [n] are [-back]. However, if we specify [a] as [+back], other problems might be caused, as elaborated below.
First, the mid vowel assimilation and low vowel assimilation in diphthongs are no longer the same issue. As what is mentioned in section 2.2.1, the nucleus must have the same value for the [back] feature as the off-glide. The fact is that we have the rhyme [aj] (cf. [ej]) in Taiwanese Mandarin, which obviously violates the mentioned constraint if [a] is regarded as [+back]. Second, it will be difficult to explain why a low vowel is surfaced “even more retracted” as [ɑ] when preceding [+back] codas like [w] and [ŋ]
to form rhymes like [ɑw] and [ɑŋ] because [a] is already specified as [+back]. In other words, now that both [a] and [ɑ] are both [+back], then what feature distinguishes these segments?
Due to these problems, it is not suitable to specify [a] as [+back] because it will lead to more obstacles for analysis, and the constraint AGREE[back]2, therefore, cannot rule out the ill-formed *[jan] and *[ɥan]. In order to take other phonological phenomena (e.g. [aj] and [ej] are composed of a front vowel and [j]; the two segments agree with each other in [back] in rhymes like [ɑw] and [ɑŋ]) into consideration, a new constraint instead of AGREE[back]2should be proposed for low vowel raising.
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Chapter 3