ANÁLISIS DE LOS REQUISITOS

One o f the core assumptions o f the theory is that all grammars are essentially language-specific hierarchies o f universal and violable constraints. In this view, the process o f language acquisition equates learning o f a constraint hierarchy o f the target language grammar, specifically via re-ranking o f relevant constraints. This leads to the development o f a learning principle known as Constraint Demotion (CD), the basis for a

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group o f ‘algorithms’ such as Recursive Constraint Demotion (RCD) algorithm (Tesar and Smolensky 1996, 1998, 2000), which are presumed to deduce relevant constraint rankings from linguistic forms. A nontrivial assumption about the learning theory is that the ‘input’ and ‘output’ are already given, and that the input —► output mapping and the inaudible structure o f the output is already known to the learner. The algorithm demonstrates that it is possible to construct rankings on the basis o f the given input and output forms (= ‘linguistically structured’ representations), provided a given set o f universal constraints. The working principle o f the algorithm is that the constraints violated in the optimal output must be ‘dominated’ by some other constraints. Cross examination o f the attested output form vs. the suboptimal candidates, or the ‘loser/winner’ pairs, provides key information on the identification o f constraints involved, and the known pairing o f the output to the input leads the way to deduce the relevant hierarchy o f constraints consistent with the given data. In the remainder o f the section we w ill learn the key principles and operations o f the algorithm and see how it deduces the target rdk ranking using real data from Japanese.

T h e in itia l h ie ra r c h y

This is how the RCD algorithm works. Let us start from the initial state o f the algorithm (87) in which all constraints to are in one ‘stratum’ indicated by ‘{ } ’, unranked with respect to one another. That is, all constraints are undominated. A hierarchy is conventionally notated as d€, and the initial state as ^ o-

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(87) Initial state o f the constraints hierarchy { C i , C2, C3. . . C q }

In the case o f rdk the initial state should look like the following (8 8).

(8 8) The initial constraint hierarchy for rdk

{O C P [+ voice, - s o n ] , *[+ voice, - s o n ], Reauze-Morpheme, M AX [voice], MAX[assoc.], DEP[voice],DEP[assoc.], UNIFORMITY[voice],. . . }

• Step 1 —> cf€\

Let us first take the simplest rdk case ori-gami as an example to see how the first ranking is initiated on the basis o f the given surface form. The task o f the algorithm is “to deduce the constraint hierarchy under which the given surface form emerges as the optimal output o f the given input form” (Kager 1999:301). That is, to find the ranking that makes the given surface form [ori-gami] the most harmonic output o f the given input /ori + p + kami/. The critical information on which the algorithm relies is a list o f constraint violations for mark-data pair(s). It is a pair o f suboptimal/optimal (loser/winner) candidates, in our case [ori-kami] -< [ori-gami]. The algorithm then constructs a list o f constraint violations made by the suboptimal candidate and the optimal candidate as exemplified below in (89).

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(89) Mark-data (Step 1): orikami -< origami [v]p

input suboptimal -< optimal

(loser) (winner)

loser-marks

(CfojCT-)

winner-marks

(Cip:MMgr)

/o ri+ p + k a m i/ orikami -< origam i [v]p ♦Realize-Morpheme ♦Ma x[qssoc.] ’*‘MAX[assoc.] ♦DEP[assoc.] ♦DEP[voice] ♦ ♦ [+ voice, - s o n ] constraints constraints violated by the loser violated l y die winner

Here, a constraint violation is marked by an asterisk (**’) before the name o f the constraint. iMser-marks (Cfaser) list all the violation marks o f the suboptimal candidate, while winner-marks H^inner) list all the violation marks o f the optimal candidate. Any pair that carries information shared by the loser and winner is o f no value and must be ‘cancelled (or struck) out’. This method is called M ark Cancellation (90) first introduced by Prince and Smolensky (1993), which is applied to the violations o f MAX[assoc.] in (89).

(90) Mark Cancellation

For each pair (loser-marks, wiimer-marks) in mark-data:

a. For each occurrence o f a mark *C in both loser-marks and winner-marks in the same pair, remove that occurrence o f *C fi*om both.

b. If, as a result, no wiimer-marks remain, remove the pair fi*om mark-data. c. If, after the preceding steps, a row o f the mark-data table contains multiple

tokens o f the same type o f mark, duplicates are eliminated, leaving at most one token o f each type.

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Now, all the necessary information is ready for RCD to operate. The remaining imcancelled marks are to be relatively ranked according to the principle o f constraint demotion (Tesar and Smolensky 2000:36) given in (91).

(91) Principle o f Constraint Demotion:

For any constraint C assessing an uncancelled wirmer mark, if C is not dominated by a constraint assessing an uncancelled loser mark, demote C to immediately below the highest-ranked constraint assessing an uncancelled loser mark.

(Tesar and Smolensky 2000:36)

It orders that all the constraints violated by winners must be dominated by some constraints violated by losers, i.e. loser-marks > winnerrmarks:

loser-marks: ^loser (constraints violated by loser)

winner-marks: Cy^inner (constraints violated by wirmer).

So, RCD finds in (89) the highest-ranked *Cioser in the loser-marks in which is R e a liz e -M o r p h e m e . Next, (91) orders that for each *^w inner in the winner-marks if C loser does not dominate C winner in demote constraint € winner to the position immediately below that o f Closer creating a stratum if it does not already exist. So, the marks are checked to see if any o f the wiimer-marks DEP[voice], DEP[assoc.] and *[+voice, —son] are dominated by Realize-MORPHEME. Since none o f them are already

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dominated by the loser-marks in the current hierarchy all o f them are demoted immediately below Realize-MORPHEME creating a new stratum. The resulting hierarchy

looks like (92) after Step 1, an encounter with the datum origami.

(92) The constraint hierarchy (after step 1)

{OCP[+voice, -scm], REALIZE-MORPHEME, MAX[voice], MAX[assoc.], UNlFORMITY[voice]}

{D EP[voice], DEP[assoc.], *[+ v o ice, - s o n ] }

Note that within a stratum constraints are in ‘stratified partial order’. They are non-conflicting and therefore unrankable and unranked with respect to one another. This means that in a stratified hierarchy like {Cj, C3} > {Cg}, although the algorithm could

return a stratified partial order {Ci, C3} > {Cg}, the only crucial ranking could just be

{C i}>{C g} where the interaction between only Cj and Cg (and not C3 and Cg) is

observed in the language. In other words, the language may provide no evidence for a complete ranking.

In principle, learning should proceed by ‘demoting’ C y^rmer rather than ‘promoting’ C/oser- In this way, RCD is guaranteed to always find some hierarchy consistent with the given data. RCD is ‘recursive’ in the sense that it is repeated until no further demotions occur. In addition, reranking is allowed only if there is ‘positive evidence’ in the form o f a constraint violation on the optimal output.

• Step 2

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grammar via RCD. This section looks at only three o f them just to illustrate how further demotions are achieved. The full steps will be shown in the next section in order to simulate several learning scenarios used in constructing a hypothetical acquisition model o f rdk.

Now, suppose the learner with the ranking is exposed next to the datum

yaki-soba where rdk is blocked due to the OCP. There are several suboptimal output candidates, and we w ill consider only one o f them here: the OCP-violating [yakizoba]. This particular mark-data pair [yakizoba] -< [yakisoba] motivates a further reranking. The mark-data is constructed as in (93).

(93) Mark-data: [yakizoba] x [yakisoba] (step 2)

Mp[v] [v]

input suboptimal -< optimal loser-marks winrter-marks

/y a k i+ p + so b a / y aki-zoba -< yakisoba [v]p[v] [v] *OCP[+voice, -son ] *M AX[assoc:] *DEP[assoc.] *DEP[voice] * [+ v o ice, -s o n ] * [4-voice, -s o n ] ♦ R e a liz e - M orphem e ♦M A X [assocj ♦ [+ voice, -so n ]

The loser-mark *OCP[+voi, -son] is the highest-ranked in the current ranking % . Since Re a l iz e-Mo r p h e m e is not dominated by *OCP[+voice, -son] it is demoted to the stratum immediately below *OCP[+voice, -son]. The new ranking ^ € 2 is obtained.

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(94) The constraint hierarchy ^ 2 (after step 2)

{O C P [+ voice, - s o n ], M A X [voice], M AX [assoc.], UNIFORMITY[voice]}

{Re a l iz e-Mo r p h e m e}

{DEP[voice], DEP[assoc.], *[+voice, -son]}

This reranking fi-om (92) to % (94) underlines a very important idea about RCD:

m inimal demotion. Observe that REALIZE-MORPHEME is not demoted all the way down to the bottom o f the hierarchy to become dominated by all the constraints in the loser-marks. It is only demoted immediately below OCP[+voice, -son], creating a stratum o f its own immediately above (DEP[voice], DEP[assoc.], *[+voice, -son]}. The demotion is minimal. To illustrate the idea, consider the demotion o f G winner in hierarchy (a) below where two alternative rankings (b) and (c) can result:

(a)

>

(c)

When the constraints in loser-marks: Chser-\, ^loser-i, ^ioser-3 are in different strata as in (a), the demotion o f ^winner is always minimal in that it is only demoted immediately

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below the highest-ranking loser-mark Gioser-\, and the resulting hierarchy looks like (b), not (c).

• Step 3

The final demotion we consider takes place when the form tabi-bito is encountered. The optimal candidate in this step is the one which the two [voice] features are fused into one to obey the OCP. The following mark-data pair (95) can be constructed.

(95) Mark data: [tabi-hito] -< [tabi-bito] (step 3)

[V ] [ v ] p

input 1 suboptimal -< optimal loser-marks winner-marks

/tabi + P + hito/ 1 tabi-hito -< tabi-bito

1

Re a l iz e-Mo r p h e m e is the highest-ranking loser-mark, and it already dom inates all the constraints in the winner-marks except UNIFORMITY[voice]-G So, UNIFORMITY[voice] is dem oted im m ediately b elo w REALIZE-MORPHEME to share the lo w est stratum w ith DEP[voice] and the rest. This results in the n ew ranking in (96).

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(96) The constraint hierarchy % (after step 3)

{O C P [+ voice, - s o n ], M A X [voice], M A X [assocJ, UNIFORMITY[voice]-M}

{Re a l iz e-Mo r p h e m e}

{D E P[voice], DEP[assoc.], UNIFORMITY[voice]-Q *[+ v o ice, - s o n ]}

To complete the basic rdk ranking, we include in the hierarchy % the crucial ranking that gives rise to LL: {OCP[+voice, -son]} > {MAX[voice], MAX[assoc.]} (“Y stems must not contain more than one voiced obstruent”). As a matter o f fact, learning LL should be one o f the earliest steps a learner takes as it is the basic morpheme structure constraint in the Y morpheme class. This LL ranking is initiated by a mark-data pair like /buda/ (hypothetical) —► [buda] x [buta] (‘pig’) (see (102) for the mark-data). The learning process converges into the following hierarchy ^ 4 which is the target ranking

o f the adult rdk grarrunar.

(97) The constraint hierarchy the target rdk ranking

(O C P [+ voice, - s o n ], UNIFORMITY[voice]-M}

{MAX[voice], MAX[assoc.]}

>

{Re a l iz e-Mo r p h e m e}

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We have seen how RCD successfully accomplishes the task o f arriving at a stable target ranking by a set o f mark-data pairs, and how the key principles about RCD and assumptions in OT are necessary to make RCD workable. Our next task is to construct a hypothetical developing grammar model for the case o f rdk acquisition. In order to do this, we need to make a crucial adjustment to the initial state o f the grammar, which has been shown to be capable o f catering for certain empirical phenomena observed in phonological acquisition. It is the bias in the initial state, i.e. [Markedness constraints > Faithfulness constraints].