b. (ML.(L.H)) (underapplication)
Õ
* *! *
(38) (P6) HM.LM.MHÆ (H.(L.M)) Base: LM.H (Å LM.MH)
(HM.(LM.MH)) FALL]u IDENT-IO-T-L *RISE *POLAR U[OCP IDENT-BOT OCP )a. (H.(L.M))
(normal application) Ö
* * **
b. (H.(L.H)) (underapplication)
Õ
* **! *
(39) (P7) LM.LM.MHÆ (LM(L.M)) Base: LM.H (Å LM.MH)
(LM.(LM.MH)) FALL]u IDENT-IO-T-L *RISE *POLAR U[OCP IDENT-BOT OCP )a. (LM.(L.M))
(normal application) Ö
* **
b. (LM.(L.H)) (underapplication)
Õ
* *! *
In sum, identity preservation is important in Chengdu tone sandhi. It causes tone sandhi to apply right-to-left in (P1)-(P3). However, if such application direction would result in marked forms, tone sandhi will apply in the reverse direction. Thus, the different tone sandhi operation directions in Chengdu tri-tonal sandhi are naturally captured by the interaction of the markedness constraint *POLAR and the faithfulness constraint IDENT-BOT.
2.5 Alternative analyses
Two alternative analyses are considered in this section and shown to fall short in accounting for Chengdu tri-tonal sandhi.
2.5.1 Problem of the rule-based analyses
In the rule-based analysis of tone sandhi, one of the most important things is to determine the domain within which tone sandhi should apply. Once the domain is determined, tone sandhi can be accounted for. For example, in accounting for
52
Beijing Mandarin, Shih (1986:102) proposes that the tone sandhi domain for Beijing Mandarin is a prosodic foot, which is defined by the rule in (40). According to the FFR rule, the domains for morphosyntactically distinct tri-tonal examples are different (e.g. (41)). As a consequence, different tonal outputs are correctly predicted.
(40) Foot Formation Rule (FFR) (Shih 1986:110) Foot (f) Construction
a. IC: Link immediate constituents into disyllabic feet.
b. DM: Scanning from left to right, string together unpaired syllables into binary feet, unless they branch to the opposite direction.
Super-foot (f’) Construction
Join any leftover monosyllable to a neighboring binary foot according to the direction of syntactic branching.
Rule-based analysis seems to work in accounting for Beijing Mandarin tone sandhi.18 However, when it comes to directional tone sandhi, such as Chengdu tone sandhi, where morphosyntactic structures seem to play no role, a rule-based analysis fails to work. The major problem is that in Chengdu, tone sandhi would operate left-to-right in some patterns and right-to-left in others, regardless of the information in morphosyntactic structures. Left-to-right application directionality implies that tone sandhi operates cyclically in the domain ((σσ)σ) while right-to-left application directionality implies tone sandhi applies cyclically in the domain (σ(σσ)). Since there is no objective way to determine the rule application directions, there is no objective way to determine the tone sandhi domain within which tone sandhi operates as well. Thus, stipulations of the directions in which the tone sandhi rules should apply are indispensable.
Though it has been proposed in the present study that the tonal domain for
18 There are still some residual problems left unresolved in the rule-based analysis for Beijing Mandarin tone sandhi. Please refer to Shih (1986:136), Zhang N. (1997) and Lin (2000a, 2001, 2004a, 2005b) for discussion.
53
Chengdu tri-tonal sandhi is (σ(σσ)), the domain proposed under the OT framework cannot be directly incorporated in the rule-based analysis. That is because tone sandhi does not always apply right-to-left in Chengdu even though the domain is (σ(σσ)). The domain (σ(σσ)) merely reflects the fact that right-to-left rule application directionality is the norm in Chengdu tone sandhi. Recall that (P4)-(P7) of the seven tonal patterns actually have the tone sandhi rules operating from left to right. In OT, the domain proposed for Chengdu tone sandhi works because in the framework, constraints are violable. The different directions are caused by the interaction of the constraints, especially the markedness constraint *POLAR and the constraint requiring output-to-output correspondence, i.e., IDENT-BOT. The domination of the markedness constraint over IDENT-BOT predicts that tone sandhi applies right-to-left to achieve identity between prosodically related outputs, unless such directionality would produce highly marked forms. In that case, tone sandhi applies left-to-right.
However, in the rule-based analysis, the different directions cannot be accounted for by a single tone sandhi domain. If the tone sandhi domain for Chengdu is assumed to be (σ(σσ)), then only the tonal patterns that are derived by right-to-left directionality (i.e., (P1)-(P3)) can be accounted for (e.g. (42)). The tonal patterns that are derived by the left-to-right directionality (i.e., (P4)-(P7)) can never be accounted for by the same domain. Thus, the conflicting directions can only resort to stipulations such as those listed in (43).
(42)
54
2.5.2 Problems of the principles
In §2.2, we have shown that neither the principle of Structure Affinity nor the principle of Temporal Sequence can function to predict tone sandhi operation directionality in Chengdu. In this section, we will test the remaining four principles, i.e., Derivational Economy, Transparency, Wellformedness and Simplicity.
We shall first consider Derivational Economy. Derivational Economy prefers tonal changes that are derived by the shortest derivational path. However, as shown below, the attested outputs are not derived by the most economical derivation path, since the attested outputs and the unattested outputs are derived by the same steps of derivation in all seven patterns.
(44)
Attested Outputs Unattested Outputs
(P1)
Next, we should consider the principle of Transparency. Transparency prefers transparent outputs to opaque outputs that are either non-surface-true or non-surface-apparent. Transparency also fails to account for Chengdu tri-tonal sandhi because as mentioned, though the outputs of (P4)-(P7) are transparent (showing normal application), those of (P1)-(P3) are opaque. As a matter of fact, the impermissible sequences observed in (P1)-(P3) also indicate that the next principle Wellformedness, which prefers a derivation that yields unmarked tonal combinations, is not able to govern the tonal changes.19
Finally, we consider the principle of Simplicity. Simplicity prefers level tones to contour tones. As illustrated below, the principle of Simplicity also fails because the attested outputs and the unattested outputs contain the same number of level tones.
19 Though there is an overlapping between the criteria of Transparency and Wellformedness, the two criteria should not be mixed. That is because though transparent outputs are always wellformed, wellformed outputs are not necessarily transparent. Some opaque outputs (particularly non-surface-apparent outputs) could be wellformed. (ref.Lin 2004b, Lin 2005a).
55
(45)