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world.
Thus far, it has been shown that a perception-production view better accounts for cross-linguistic loanword adaptation phenomena, which may otherwise be rendered biased if they are considered within the scope of a single production or perception process. Moreover, from a functional point of view, cue constraints, employed in building the perception grammar, suitably reflect the down-to-earth aural events.
What is needed now is an appropriate theoretic framework where the mentioned ideas may be properly couched.
2.4 Optimality Theory
Due to the key notions of violable constraints that properly model the oftentimes conflicting forces of preservation of input information and obedience to the sound system of the output language, Optimality Theory (OT, Prince and Smolensky 1993/2004, McCarthy and Prince 1995, Kager 1999) has served as a mainstream framework to model phonological processes in loanword adaptation (Yip 1993, 2002, 2006; Paradis 1995, 1996; Shinohara 2000, 2004a; Labrune 2002; Kenstowicz 2003ab;
Kang 2003; Broselow 2004, 2009; Shih 2004; Miao 2005; Lu 2006; Lü 2013; Lin 2007a, 2008ab; among many others). This section elaborates on the basic assertions and the broad architecture of OT.
2.4.1 Universality and Markedness
A broad picture that emerges from a large body of linguistic research over the past decades is the pursuit of Universal Grammar (UG), i.e. a limited set of universal properties that individual languages base their structures on. Owing to the growing effort to narrow down possible cross-linguistic phonological processes and adjustments, the early rule-based Generative Grammar (Chomsky and Halle 1968)
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was soon found untenable in that the logically “limitless” language-specific rewrite rules fail to correspond to the exploration of human’s core properties of grammars. In response, a different constraint-based approach that still inherits the central positions of the conventional derivational theory, has been taken to replace the linear-ordering rewrite rules. By definition, a constraint is a requirement in structure that may be either complied with or violated by an output form. In a constraint-based approach, typically, demands are imposed on the surface form, and any form that does not abide by the constraints is eliminated in favor of the form(s) that does. Among these theories, Optimality Theory has been recognized as the most successful.
In OT, constraints are universal, which implies that UG consists of a limited set of constraints and all of them are part of the grammars of all natural languages. The phonology of each language is represented by a distinctive ranking of a fixed set of universal constraints. To the very extreme, the number of natural languages that exist and ever existed in the world should be equal to the factorial of the total number of possible constraints. While constraint hierarchies may differ between languages, they should respect a set of universal principles, namely UG. There are two possible criteria for UG: they are either typologically or phonetically grounded. Specifically, a statement of UG that a certain segment is favored over others or one that is preferred to others in particular contexts should be motivated by either cross-linguistic evidence or articulatory or perceptual supports. Examples of UG include “syllables have onsets”, “rounded vowels are back”, “syllables are open”, “postnasal obstruents are voiced”, etc. Statements like these are embodied in Generative Phonology with an inherently relative concept of markedness: unmarked linguistic structures are cross-linguistically favored over marked ones. While this is true, a marked structure is not necessarily ill-formed per se, but it is simply less preferred in comparison to other forms. In that sense, every form or structure is marked to a certain degree. The notion
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of markedness is built into an OT grammar in the form of output constraints, which typically make straightforward statements about marked or unmarked language patterns.
2.4.2 Violability
Intrinsically, constraints are mutually in conflict, in the sense that satisfaction of a constriant necessitates violation of at least another. When two constraints are contradictory, the one that ranks higher has the priority. This central idea of constraint interaction entails another property of OT constraints: constraints are inherently violable. Given this position, language in its nature is a system of conflicting forces, because constraints are typically conflicting. OT does not, however, assert that every constraint has an equal effect in all languages, but the constraints are language-specifically ranked. A constraint that is undominated in a language, meaning that it is never violated in its phonological grammar, can be completely ineffective in another language.
The flexibility of violability, however, is accompanied by a fundamental premise of constraint interaction: violation must be minimal. In an input-output grammar of OT, the optimal output is the one (or sometimes the ones) that keeps violation to a minimum, as violation of the rest potential outputs is more serious. Violability of constraints is a critical property since it distinguishes OT from other derivational models as well as other constraint-based theories.
2.4.3 Markedness and faithfulness: tug of wars
A markedness constraint is a requirement that the output meet a certain criterion of well-formedness in phonological structure, indicating that it exclusively makes reference to the output. Markedness constraints can be either negative (27a) or
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positive (27b) statements, as exemplified below.
(27) Examples of markedness constraints a. Syllables must not have codas.
b. Syllables must have onsets.
In addition to markedness constraints, OT recognizes another type of constraint family: faithfulness. A faithfulness constraint requires that the output form preserve certain properties of the input structure. It is a force that enhances the identity between the output and the input, prohibiting differences between them. Examples of faithfulness constraints are given in (28), most of which are stated positively (but see Alderete 2001).
(28) Examples of faithfulness constraints
a. All segments in the input must be preserved in the output.
b. All segments in the output must have counterparts in the input.
As the two examples show, faithfulness constraints take both input and output into account, which indicates that, unlike markedness constraints, they are not pure output constraints. Phonologies of all languages are full of examples of unfaithful mappings, suggesting that faithfulness constraints generally rank lower compared to markedness constraints.
Markedness constraints and faithfulness constraints are conflicting by nature.
Whenever a faithfulness constraint favors an output for the preservation of a certain element, there must be a markedness constraint disfavoring it. The confronting positions between markedness and faithfulness constraints can also be understood in a broader sense: preservation of more potential lexical contrasts in a sound system can only be reached at the expense of an increase in phonological markedness.
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2.4.4 The input-output mechanism of OT
Given the fact that no single form can satisfy all constraints, there must be a device in OT that works on the selection of the form that incurs the least violation. In an OT grammar, language forms are generated through an input-output mechanism, where the function GEN(ERATOR), when applied to an input, produces an indefinite number of candidates, all of which are possible analyses of the input. When the produced candidate set is submitted to the other function EVAL(UATOR), the optimal, also termed as the “most harmonic”, output is produced by applying a language-specific constraint hierarchy to the set of candidates. The OT flowchart in (29) shows the elimination process.
(29) The OT flowchart (based on Kager 1999)
Candidate a
Candidate b Input GEN Candidate c
Candidate d Output
Candidate…
In general, an OT grammar evaluates an indefinite set of candidates, from which it selects the optimal output, which best matches the mutually conflicting constraint set. By definition, an output is “optimal” if it incurs the least violations of a set of ranked constraints. Essentially, all analyses proposed by GEN are submitted to EVAL
for parallel evaluation: all the constraints pertaining to a certain type of structure evaluate and interact within a single hierarchy, with no intermediate level involved.
C1 C2 Cn
EVAL
>> >>…
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2.4.5 Demonstration of constraint activities
Conventionally, constraint rankings of an OT grammar are demonstrated by a tableau. A tableau lists two or more output candidates vertically in random order in the leftmost column, and constraints are arranged horizontally in a descending ranking from left to right on the top row, as represented below:
(30) Sample of a tableau
Ranking: C1 >> C2,C3 >> C4
Input C1 C2 C3 C4
a. Candidate 1 *!
b. Candidate 2 *!
c. Candidate 3 *!
d. ☞Candidate 4 *
e. …
In (30), Candidate (a) violates the undominated C1 and is ruled out. A violation is indicated by an asterisk ‘*’, the fatal violation is indicated by an exclamation mark ‘!’, and the shading in the cells indicates that the violation content is no longer relevant.
Candidate (b) and (c) are eliminated too for their violations of C2 and C3 in the second level. The separating dotted line stands for irrelevant ranking between C2 and C3. Candidate (d) is selected as the optimal output, as marked by the index finger ‘☞’, despite its insignificant violation of the low-ranked C4.
In our OT analyses, however, the tableaux are given in a revised format under the name of the combination tableau (McCarthy 2008), which is based on Prince’s (2002) introduction of the comparative tableau. Unlike conventional violation tableaux, which focus on violations of constraints, a combination tableau is centered on favoring relations. To construct a combination tableau, first we draw a violation tableau, and then add W (the winner) and L (the loser) information to make a
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comparative tableau. The W and L symbols are marked in the corresponding cell (next to the asterisk, if any) by considering the constraint to see whether it favors the winners over the loser (W), the other way around (L), or neither (blank). To illustrate this format, we modify an OT analysis of English nominal plural that is originally given in Gussenhoven and Jacobs (1998). The constraints in action are listed in (31), where (31ab) are markedness constraints and (31c) to (31e) are faithfulness constraints, followed by illustrations of combination tableaux.
(31) Constraints for English plural formation (Gussenhoven and Jacobs 1998, revised) a. *SibSib: Sequences of sibilants are prohibited within the word.
b. αVoice-αVoice: Sequences of obstruents within the syllable must agree for voicing.
c. Max(imaility)-IO: Deletion of segments is prohibited. (28a) d. Dep(endency)-IO: Insertion of segments is prohibited. (28b)
e. Ident(F): A segment in the input is identical to the corresponding segment in the output.
(32) English plural formation (Gussenhoven and Jacobs 1998, revised) Ranking: *SibSib, αVoice-αVoice >> Max-IO >> Dep-IO >> Ident(F) (a) /.k s-z./ → [.k .s z.]
/.k s-z./ *SibSib Max-IO Dep-IO
a. ☞ [.k .s z.] *
b. [.k sz.] *W L
c. [.k s.] *W L
(b) /.bæk-z./ → [.bæks.]
/.bæk-z./ αVoice-αVoice Max-IO Dep-IO Ident(F)
a. ☞[.bæks.] *
b. [.bækz.] *W L
c. [.bæk.] *W L
d. [.bæ.k z.] *W L
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In (32a), the input syllable ends in a sibilant coda. The undominated markedness constraint *SibSib favors the winner over Candidate (b) for the sibilant-sibilant cluster in coda, and hence an asterisk plus “W” are marked in the corresponding cell.
Likewise, the faithfulness constraint Max-IO prefers the winner over Candidate (c) for the ignorance of the nominal plural suffix [z]. Candidate (a) serves as the winner despite its violation against the loser-favoring Dep-IO for the insertion of a vowel. In (32b), where the input ends in a stop, Candidate (b) is disfavored by the markedness constraint αVoice-αVoice for the voicing disagreement in the [kz] sequence. The faithfulness constraints Max-IO and Dep-IO favor the winner over Candidates (c) for deletion of the plural suffix [z] and over Candidate (d) for [ ]-insertion, respectively.
Candidate (a) is evaluated as optimal since its violation of the bottomed faithfulness constraint Ident(F) is minimal.
In a combination tableau, cells with W and L in a single row indicate that the constraints involved are in conflict. Moreover, in every loser row there is at least a W to the left of every L. That is, whenever a constraint favors a loser, there must be a higher-ranked constraint that favors the winner over the loser. If not, this ranking argument is rendered invalid. The OT analyses in this dissertation are all presented in this fashion such that first, it is clearly seen if the constraints involved conflict over the choice of the winner. Second, the validity of the ranking argument can be easily examined through the relative positions of Ws and Ls.