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Gradient Well-Formedness in Optimality Theory
Bruce P. Hayes UCLA August 1997 Abstract A minor modification in the framework of Optimality Theory (Prince and Smolensky 1993) is suggested which enables it to model phenomena where consultant intuitions are gradient, falling somewhere between complete well- formedness and complete ill-formedness. The proposal consists of assigning to certain constraints bands of values along a reified continuum of constraint strictness. When a particular form can be generated only by assigning a constraint a strictness value within a designated “fringe” of the strictness band, the grammar generates the form marked with an intermediate degree of well- formedness. The proposal is tested against data involving light and dark /l/ in American English, using a set of gradient intuitions obtained from ten native speaker consultants. A rationale from language learning is then posited for why well- formedness intuitions are so frequently gradient.
Gradient Well-Formedness in Optimality Theory
Bruce P. Hayes UCLA August 1997 1 The Gradience Problem Virtually every generative linguist has had the following experience: a given linguistic entity (sentence, novel word, pronunciation) is presented to a native speaker and judged to be neither fully well-formed nor fully unacceptable. In such instances, consultants often say things like “I guess I could say that,” “It’s all right but not perfect,” “It’s pretty bad but not completely out,” and the like. Such judgments often get reified: the data are sorted into grammatical and ungrammatical categories, and an analysis is developed whereby the rules or principles generate all and only the grammatical outcomes. This procedure is controversial, as Schütze’s (1996) comprehensive review points out. Critics of generative grammar might take the existence of gradient well- formedness judgments as an indication that the entire enterprise is misconceived: that discrete “categories,” “rules,” and “constraints” are just illusions suffered by the linguist. In this eliminativist view, gradient well-formedness judgments constitute evidence that generative linguistics must be replaced by something very different, something much “fuzzier.” Other scholars, also reviewed by Schütze, have maintained that well-formedness really is categorical (surface appearances to the contrary), and that gradience is merely the result of performance factors that obscure the judgment process. However, while such factors certainly do exist, much of the patterning of gradient judgments is based on authentic structural aspects of the linguistic material being judged. This makes it unlikely that it could be described as mere performance (see Schütze 1996, 63-64; and below). A third possibility, the one advocated here, is to claim that gradient well-formedness judgments are on the whole authentic: abstracting away appropriately from performance factors, carefully elicited gradient judgments really do reflect the internalized knowledge of the native speaker. What has been lacking, in this view, is the right theoretical tools to model grammars that can generate outputs with varying degrees of well-formedness. My specific suggestion is that within Optimality Theory (Prince and Smolensky 1993), it is possible to devise such grammars. The modification in the theory that is needed is strikingly minor, and is quite independent of the choice of formal representations and constraints used in the grammar.
[É] pat [pÉt] [aƒ«] pal [paƒ«É] [¬ƒu] do [d¬ƒu] [uƒ«] fool [fuƒ«É] [oƒÉ] foe [foƒÉ] [o=É] foal [fo=ÉÉ] [É] put [pÉt] [Ƀ«] pull [pɃ«É] Error: Reference source not found [É] but [bÉt] [É=] dull [dÉ=É] [Ƀ«] saw [sɃ«] [É=] Saul [sÉ=É] [É] Pa [pÉ] [É=] all [É=É] [aƒÉ] tie [taƒÉ] [aɃ«] tile [taɃ«É] [aƒÉ] cow [kaƒÉ] [aɃ«] cowl [kaɃ«É] [ɃÉ] boy [bɃÉ] [ÉɃ«] boil [bÉɃ«É] The most careful phonetic study yet done of backness in English /l/ was carried out by Sproat and Fujimura (1993), who gathered X-ray microbeam data. An important claim that Sproat and Fujimura make is that there is no categorial distinction between light and dark /l/ in English, but only a phonetic continuum. This claim strikes me as controversial. In particular, the data Sproat and Fujimura gathered did not include the most crucial cases for demonstrating categories, namely those cited below under (10). Inspection of the data in their paper suggests, to me at least, that there are two analytical possibilities that remain tenable: (a) an outright phonetic continuum, as Sproat and Fujimura propose, or (b) two phonetic categories that are partially obscured by free variation and near-neutralizing lenition. It is the latter interpretation that will be adopted here, as it gives the most coherent account of the Paradigm Uniformity effects noted below. 2.2A Survey of Well-Formedness Judgments After exploring the pattern of /l/ allophony using just my own intuitions, I attempted to obtain higher quality data by conducting an organized survey of ten native speakers of American English.^3 All of my consultants were volunteers and were known to me; half were linguists and half were not. As subsequent statistical testing showed no essential differences between the two groups,^4 the results are pooled below. Each consultant was presented with 17 words, sometimes (^3) I discovered, somewhat late in the process, that there is a recent literature that provides valuable guidance to linguists conducting such surveys: Schütze (1996), Bard, Robertson, and Sorace (1996), and Cowart (1997). Much of what I have done here could have been done better by following the prescriptions of these works. All of the survey data may be downloaded from the author’s Web site, listed at the end of this article. (^4) Here are the result of a factorial ANOVA test. For well-formedness judgments, there was no significant main effect of the linguist/non-linguist difference (Fisher’s PLSD post-hoc test: p = .501), nor a significant interaction between type of word tested and linguist status (p = .891). For judgments of casualness, there was a small main effect (linguists tended to judge the forms overall as more casual, p = .019), but no significant interaction between word type and linguist status (p = .528).
placed in a particular sentence context to make their meaning clear. Each word contained an /l/, and was pronounced by the author in two ways, with light [l] and dark [É]. The consultants were asked to rate both pronunciations on an integer scale ranging from 1 to 7, with 1 designating “sounds just right, perfectly normal in my dialect of English” and 7 designating “sounds awful, I would never say it that way.” In addition, the consultants were invited, if it seemed appropriate, to check boxes labeled as follows: “ casual : to the extent it’s acceptable, it’s acceptable in casual speech only”; and “ formal : to the extent that it’s acceptable, it’s acceptable in formal, careful speech only.” On the whole, the consultants found the task somewhat difficult, and indeed the variance in their responses was rather high. The view taken here is that in any individual instance , the judgments were indeed subject to apparently random influences. However, when averaged over all the consultants, the results formed a quite coherent pattern.^5 I will report the results of the survey interspersed below amid a general, structurally-oriented description of the facts. 2.3Data Pattern In pretonic position (that is, immediately before a stressed vowel), it seems utterly obligatory to produce a light [l]. Representative examples, as I would pronounce them, are the following: ( 3 ) Pretonic: Obligatory Light [l] light [É l aƒÉt], Lee [É l iÉ], Lou [É l uÉ], aloud [«É l aÉd], balloon [b«É l uÉn], apply [«Ép l aÉ] This is likewise true for word-initial /l/ when the following vowel is stressless: ( 4 ) Word-Initial Pre-Atonic: Obligatory Light [l] Lamarck [ l «Émɨk] , Louanne [ l uÉÉn] If any of the forms of ( 5 ) or ( 6 ) is pronounced with dark [É] instead, the result sounds laughable, like a phonetic exercise. This is my own judgment, but it is clearly supported by the results of the survey, which included the words light and Louanne , ranked on the 1-7 scale. The numbers given are the mean of the judgment of all ten consultants; and the column labeled “s” gives the standard deviation. ( 7 ) Word with [l]: with [ É ]: mean s^ mean s light 1.30 0.48 6.10 1. Louanne 1.10 0.32 5.55 1. average for both words 1.20 0.41 5.83 1. (^5) Cowart (1997, Chap. 2) provides an interesting review and defense of the use of such data patterns in judgment experiments.
( 8 ) Preconsonantal: Obligatory Dark [ É ] fault [ÉfÉ=Ét], help [ÉhɃ«Ép], shelter [É ÉÉ ƒ«ÉtÉ] ( 9 ) Prepausal: Obligatory Dark [ É ] feel [Éfiƒ«É], whole [Ého=ÉÉ] Here, too, the substitution of the wrong allophone (light [l]) produces, I think, a comic effect; in this case, a rather cruel one of mocking a foreign speaker whose native language has only light [l]. The data from the 10 consultants is summarized below: ( 10 ) Word with [l]: with [ É ]: mean s^ mean s bell 6.60 0.97 1.20 0. help 6.60 0.97 1.05 0. average 6.60 0.94 1.12 0. The next environment to consider is intervocalic pre-atonic position. This environment, sometimes called “ambisyllabic,” yields special allophones for quite a few English consonants. For /l/ in the target dialect, it evokes free variation between light and dark: ( 11 ) Intervocalic Pre-Atonic: Free Variation Greeley [ÉgriÉ l i, Égriƒ«Éi] Bailey [ÉbeƒÉ l i, Ébeƒ«Éi] mellow [ÉmÉ l oÉ, ÉmɃ«ÉoÉ] Hayley [ÉheƒÉ l i, Éheƒ«Éi] Mailer [ÉmeƒÉ l É, Émeƒ«ÉÉ] The consultant survey examined four such words, and in all, found fair acceptability for both variants, the light one being slightly preferred: ( 12 ) Word with [l]: with [ É ]: mean s^ mean s (Norman) Mailer 2.00 1.33 2.00 1. Hayley (Mills) 1.55 0.96 3.05 1. (Horace) Greeley
(Mayor) Daley 2.25 1.48 2.80 1. average 1.90 1.26 2.64 1. The realization of intervocalic pre-atonic /l/ is also influenced by morphology. Suppose first that the /l/ is the first segment of a suffix. Here, the preference is rather strongly shifted to a light [l], and I will mark the dark [É] forms with a question mark:
( 13 ) Suffix-initial: light acceptable, dark “?” free-ly [ÉfriÉ l i], ?[Éfriƒ«Éi] dai-ly [ÉdeƒÉ l i], ?[Édeƒ«Éi] gray-ling [É ÉÉeƒÉ l ÉÉ], ?[ÉÉÉeƒ«ÉÉÉ] eye-let [ÉaƒÉ l «t], ?[ÉaɃ«É«t] The forms examined in the survey were as follows: ( 14 ) Word with [l]: with [ É ]: mean s^ mean s gray-ling^6 1.39 0.49 3.17 2. gai-ly 1.45 0.76 3.65 2. free-ly 1.85 1.25 3.20 1. average 1.57 0.87 3.34 2. Contrariwise, supposing that a vowel-initial suffix is added to a stem ending in /l/, the form with dark [É] is preferred, and the light [l] form deserves the “?”: ( 15 ) Stem-final before vowel-initial suffix: dark acceptable, light “?” (touchy-)feel-y [Éfiƒ«Éi], ?[ÉfiÉ l i] heal-ing [Éhiƒ«ÉÉÉÉ, ?[ÉhiÉ l ÉÉÉ mail-er ‘one who mails’ ÉÉmeƒ«ÉÉ ÉÉÉ?ÉÉmeƒÉ l ÉÉ Here are the forms tested with the consultants: ( 16 ) Word with [l]: with [ É ]: mean s^ mean s mail-er 2.80 2.20 2.00 1. hail-y 4.00 1.80 1.56 1. gale-y 3.39 2.42 2.28 1. ( touchy- ) feel-y 2.00 1.49 2.20 1. average 3.01 2.06 2.01 1. Such influences of morphology have been observed before in other dialects: see Wells (1982, 312-313 for vernacular London English, Simpson (1980) for Australian English, and Gimson (1970, 202) for Standard British (RP) in a limited (postatonic) environment. Stem-final /l/ can also become prevocalic when the stem precedes a vowel-initial word, as in mail it. The result here seems to be an exaggerated version of the preceding case: the /l/ “wants” quite strongly to be dark. This preference appeared in the single such form checked in the consultant survey: (^6) To assistance intuitions of morphological relatedness, this was elicited in the frame: “A grayling is a kind of trout with a gray color.” The words mail-er and hail-y were elicited with similar frames.
( 19 ) Word set average dif- significance ference score a. light, Louanne 4. p <. b. gray-ling, gai-ly, free-ly 1. p =. c. Mailer, Hayley, Greeley, Daley 0. p =. d. mail-er, hail-y, gale-y, feel-y -0. p =. e. mail it -3. p =. f. mail, help -5. It can be seen that all the results but one are highly significant statistically, and that the remaining one is near-significant. Keeping the near-significant outcome as a case where further checking should be done, I will assume for present purposes that all differences given here should be accounted for in an adequate analysis.^7 To keep the size of the problem under control, I will further reduce the numerical data of the survey to the traditional categories “ü”, “?”, “??”, and “*”. The categories assigned, with the survey numbers used to justify them, are given below: ( 22 ) as light as dark _ light, Louanne ü (1.20) * (5.83) gray-ling, gai-ly, free-ly ü (1.57)? (3.34) Mailer, Hayley, Greeley, Daley ü (1.90) ü (2.64) mail-er, hail-y, gale-y, feel-y? (3.01) ü (2.01) mail it ?? (4.40) ü (1.10) bell, help * (6.60) ü (1.12) In principle, one might analyze more finely, but given the uncertainties and high standard deviations, it seemed advisable to work with a fairly coarse well-formedness grid. 2.4The “Performance” Issue Before going on the to the analysis of these data, I wish first to address a crucial potential objection mentioned above. Suppose that linguistic well-formedness really is an all-or-nothing matter, but that the judgments we get are filtered through various performance mechanisms. It is the performance mechanisms, not the grammar itself, which results in the gradient intuitions. If (^7) Some further statistics: for non-adjacent categories on the scale of ( 20 ), all comparisons came out significant; p < .0001. Further, of the word-to-word comparisons within groups, only one came out significant, namely feel-y versus hail-y (p = .0137). This suggests that most of the relevant structural differences have probably been located. The individual consultants gave so few judgments that few subject-internal results reached significance, but the profiles of individual subjects tend to resemble ( 21 ).
this is so, then it is not legitimate to attempt to analyze the gradient data of ( 23 ); rather, we should be reducing them (somehow) to two categories and developing a model of the judgment process itself to account for the numbers observed. A problem with this view, as Schütze (1996, 64) has pointed out, is that patterns of gradient well-formedness often seem to be driven by the very same principles that govern absolute well- formedness. This holds true, for instance, for the phenomena under discussion here. Thus, for RP British English, Gimson (1970) and Wells (1982) report a data pattern that is reminiscent of what is described above, with gravitation of light and dark /l/ to pre-and post-vocalic positions and certain morphological effects similar to what we have seen. But there is also an important difference: RP does not allow dark [É] in words like free-ly or gray-ling at all.^8 This categorial prohibition is rather likely to be based on the same principles that govern the subtler intermediate judgment of the American speakers. I conclude that the proposed attribution of gradient well-formedness judgments to performance mechanisms would be uninsightful. Whatever “performance” mechanisms we adopted would look startlingly like the grammatical mechanisms that account for non-gradient judgments. For this reason, I will assume that the competence model itself should generate gradient judgments, and will now turn to the task of accounting for the data in ( 24 ). 3 Analysis 3.1Constraints Following traditional views in phonetics, we can plausibly attribute the variation in /l/ to conflicting principles based on articulation and perception. The loss or diminution of alveolar closure in dark [É] seems fairly plainly a case of lenition , a process widely thought to be grounded in the conservation of articulatory effort.^9 I state the relevant constraint as follows: ( 25 ) /l/ IS DARK This leaves open exactly what “darkness” is in English: roughly, it should be characterized as involving a lenited, delayed, or absent tongue blade closure. Often, in compensation, there is an especially backed tongue body position. A defect of the formulation in ( 26 ) is that it is categorial, not gradient. The expression of a constraint that would require darkness in /l/ in gradient fashion would require further theoretical development that goes beyond the scope of this article. I believe the central point at hand can be made, however, with the artificially categorized constraint given here. The other constraints on /l/ are perceptual in origin, and are more subtle in character. An important finding of Sproat and Fujimura’s (1993) X-ray microbeam study is that English dark [É] is temporally asymmetrical : it begins with a tongue body backing gesture and then in most (^8) Thanks to Peter Ladefoged, a native speaker, for confirming this judgment. (^9) See Kirchner (to appear) for extended discussion of constraints covering lenition.
( 33 ) PARADIGM UNIFORMITY
Morphologically derived forms may not deviate from their bases in Property X. Let us leave aside for a moment the issue of what Property X is in the present case. What is crucial is that in (say) touchy-feel-y , surface [Éfiƒ«Éi] possesses very much the same phonetic form as that which is observed in the base form feel [Éfiƒ«É]. This is not the case in the imperfect rival form ?[ÉfiÉli]. Similarly, in freely [Éf¨iÉli], the segments show very much the same phonetic quality that one observes in related forms like free [Éf¨iÉ] and barely [Ébɨli]; this is not so in the imperfect rival ?[Éf¨iƒ«Éi]. Imitation of base forms by derived forms is commonplace in phonology, and has in pre-OT approaches been analyzed with notions like cyclicity and word-internal boundaries (Chomsky and Halle 1968). It is not surprising that we should find them at work in /l/ allophony. Let us now try to specify the identity of Property X, the property that is being conserved across the paradigm. At first glance, it looks like X might be /l/ darkness itself: thus, the dark /l/ of feel [Éfiƒ«É] must be carried over into the derived form feel-y. However, for forms like freely with /l/-initial suffixes, this view is more dubious since the suffix -ly has no isolation form that could serve as the light [l] base. A more perspicuous analytic path would be to impose Paradigm Uniformity on the quality of the stem vowel , which as noted in ( 34 ), is always quite different before dark [É] than elsewhere. Under this view, the diphthongized vowel of feel ([Éf i ƒ«É]) is carried over into touchy-feel-y ([Éf i ƒ«Éi]), and the non-diphthongized vowel of free [Éf¨ i É] is carried over into freely ([Éf¨ i Éli]). For this to work, the system must include undominated constraints specifying the appropriate matchup of light and dark /l/ with the vowel allophones that go with them, as noted above in ( 35 ). This will exclude any candidates like *[Éf i ƒ« l i] or *[Éf i ÉÉi]. As the exact formulation of these constraints is not crucial, I will not attempt it here. Summing up, I will assume that in the present case, Paradigm Uniformity requires morphologically derived forms to possess the vowel quality of their bases, and that this indirectly regulates the distribution of light and dark /l/. There is one further elaboration needed for the Paradigm Uniformity phenomena seen here. Consider that both mail-er ([É, ?l]) and mail it [É, ??l] involve Paradigm Uniformity effects, with carry-over of the obligatory dark [É] of mail into larger morphosyntactic constructions. But the effect is stronger in the phrasal construction than in the suffixed form: specifically, light [l] gets a “??” (consultant average 4.40) in mail it but only a “?” (= 3.01) in mailer. Why should this be so? It is commonly observed that phonological alternation tends to be inhibited in relatively larger phonological domains. This typological observation has been translated into various
theoretical approaches in various ways; thus, for example, in one version of Lexical Phonology (Kiparsky 1985, 87), rules are held to be gradually “turned off” as one reaches later levels of the grammar. Similarly, hierarchies of boundaries (McCawley 1968) or “P-structure” (Selkirk
- are set up to permit less rule application (and thus less alternation) at higher levels. In the present approach, employing Optimality Theory and Paradigm Uniformity, an appropriate implementation of this idea would be to suppose that the Paradigm Uniformity constraints are a priori stricter for higher levels; for example, stricter in phrases than in words. For the case at hand, we can suppose that there are separate constraints of Paradigm Uniformity for phrasal versus morphological contexts, with the former ranked within UG as necessarily stricter than the latter. Thus: ( 36 ) PARADIGM UNIFORMITY(VOWEL QUALITY, PHRASAL) » ( 37 ) PARADIGM UNIFORMITY (VOWEL QUALITY, MORPHOLOGICAL) With this distinction in place, we now have the constraints that will be needed to derive the correct outcomes. The constraints are listed below with the abbreviations that will be used. ( 38 ) /l/ IS DARK /l/ IS DARK DARK [É] IS POSTVOCALIC [É] IS /V___ PREVOCALIC /l/ IS LIGHT PREVOCALIC:[l] PRETONIC /l/ IS LIGHT PRETONIC:[l] PARADIGM UNIFORMITY(VOWEL QUALITY, PHRASAL) PU(PHRASAL) PAR. UNIFORMITY (V QUALITY, MORPHOLOGICAL) PU(MORPHOL) What I have tried to argue in this section is that each constraint is principled , being grounded either in general concepts of phonetically driven phonology or in widely attested typological patterns of paradigmatic alternation. 3.2Generating One Set of Outcomes For purposes of presentation only, let us temporarily commit the methodological sin of overidealization, and generate an invariant set of outcomes, with no free variation and no gradient well-formedness. These reified outcomes may be schematized as follows: [l] in light (pretonic position), Louanne , (initial position), Greeley (medial pre-atonic) and freely (suffix- initial), and [É] in bell (prepausal), help (preconsonantal), feel-y (stem-final before suffix), and mail it (word-final before vowel-initial word). To generate these outcomes, it suffices to rank the two PARADIGM UNIFORMITY constraints over PREVOCALIC /l/ IS LIGHT, with the latter dominating /l/ IS DARK. The outcomes emerge as follows: ( 39 ) PRETON- IC:[l]
[É] IS /
V_
PU(PHRA-
SAL)
PU(MOR-
PHOL)
PREVO-
CALIC:[l] /l/ IS DARK a. light É [ l aƒÉt] * *[ÉaƒÉt] *! * * b. Louanne É [ l uÉæn] *
( 48 ) more strict less strict PRETONIC:[l] [É] IS /V_ PU(PHRASAL) PU(MORPHOL) PREVOCALIC:[l] /l/ IS DARK For the present grammar, which generates neither free variation nor gradience, such a presentation is trivial, but the idea will become more important as we proceed. 3.4 Accounting for Free Variation Moving toward a more accurate model, we can next account for the fact that monomorphemic forms with intervocalic pre-atonic /l/ (e.g. Greeley ) show free variation. A common approach to free variation in OT is to suppose that a subset of the constraints may be ranked freely: each variant outcome is obtained by fixing the free ranking in a particular way.^10 In the present case, let us assume that PREVOCALIC /l/ IS LIGHT and /l/ IS DARK are ranked freely. This means that all outputs derived under the tableau of ( 49 ), where PREVOCALIC /l/ IS LIGHT outranked /l/ IS DARK, will still be obtainable, but in addition we will obtain whatever outcomes derive from the opposite ranking, as shown below: (^10) An alternative is to let constraints actually be tied , so that violations of each count equally in candidate evaluation. The problem with this is that in realistically large grammars, it is likely that some constraint deep down within the hierarchy will discriminate between the free variants, wiping out the free variation.
( 50 ) PRETON-
IC:[l]
[É] IS /
V_
PU(PHRA-
SAL)
PU(MOR-
PHOL)
/l/ IS DARK
PREVO-
CALIC:[l] a. light É [ l aƒÉt] * *[ÉaƒÉt] *! * * b. Louanne É [ l uÉæn] * *[ÉuÉæn] *! * c. gray-ling É [Ég¨eƒÉ- l ÉÉ] * *[Ég¨eƒ«-ÉÉÉ] *! * d. Greeley É [g¨iƒ«Éi] * *[Ég¨ÉÉÉÉÉ *! e. mail-er É [meƒ«É-É] * *[meƒÉ l - É] *! * f. mail it É [Émeƒ«É Ét] * *[ÉmeƒÉ l Ét] *! * g. help É [ÉhɃ«Ép] *[ÉhÉ l p] *! As it happens, the only outcome that is altered under the new ranking is that for monomorphemic Greeley ( 51 d), which now comes out with a dark [É], since the lenitional constraint /l/ IS DARK outranks PREVOCALIC /l/ IS LIGHT. In all other instances, switching these two constraints makes no difference to the outcome: either a higher-ranking constraint has already decided the issue ( light , Louanne, gray-ling , feel-y ), or the loser has a superset of the violations of the winner ( help ), so that no reranking would ever make a difference. Here are some further ranking arguments. (a) It can be observed that the continued appearance of light [l] in ( 52 b) Louanne justifies the invariant ranking DARK [É] IS POSTVOCALIC » /l/ IS DARK, a ranking which could not be justified in the previous tableau. (b) Likewise, the continued appearance of light [l] in ( 53 b) gray-ling follows from the invariant ranking PU(MORPHOL) » /l/ IS DARK. 3.5More on the Strictness Scale We can depict variable rankings on the strictness scale by employing strictness bands : some constraints will vary in their strictness through a particular range. For the rankings that generate the tableaux of ( 54 ) and ( 55 ) it suffices to assign overlapping bands to the two bottommost constraints:
will vary accordingly. Thus, give ( 62 ), forms like Gree [l] ey will occur more frequently than forms like Gree [É] ey. The issue of modeling text frequencies is discussed further in section 5.2. 3.6Accounting for Gradient Well-Formedness We now have the theoretical apparatus at hand to treat actual gradient well-formedness, by adding one further amplification to the strictness-band idea. Let us suppose that, at least in the crucial cases, the range of a constraint is not firmly delimited. Formally, we can model this idea coarsely by positing fringes : at the edge of a constraint’s strictness band, we add special blocks labeled with traditional well-formedness diacritics such as “?” and “??”. Selection points may occur within a fringe, but only at the cost of the degree of ill-formedness indicated. For instance, the sample diagram in ( 63 ): ( 64 ) CONSTRAINT A: CONSTRAINT B: ??? CONSTRAINT C: can be interpreted as follows: (a) Ordinarily, Constraint B is outranked by constraints A and C. (b) However, it is somewhat possible for B to outrank C. This will occur if the selection point for B occurs quite close to the left edge of its “?” fringe, and that for C quite close to the right edge of its strictness band as a whole. Forms that can be generated only with this ranking are intuited to be mildly ill-formed (“?”). (c) It is only marginally possible for B to outrank A. This will occur if the selection point for B occurs close to the left edge of its “??” fringe, and that for A close to the right edge of its strictness band. Forms that can be generated only with this ranking are intuited to be considerably ill-formed, though not completely excluded (“??”). As for where the fringes come from: I conjecture that they arise as part of the acquisition process, in cases where the input data do not suffice to establish firmly what the upper or lower bounds of a constraint’s strictness band are. This is discussed further in section 4. How do we evaluate the well-formedness of a given linguistic form under the proposed model? I assume that in judging a given form, a consultant will normally assign it the highest rating possible under the grammar. Thus, suppose a given form emerges from the grammar in two ways: (a) with a “?” attached, using a choice of strictness values that employs a “?” fringe of one of the strictness bands; (b) perfectly, using a choice of strictness values that is drawn solely from the central (non-fringe) portions of the bands. This is illustrated below: ( 65 ) a. CONSTRAINT A: Ÿ CONSTRAINT B: ?? Ÿ? b. CONSTRAINT A: Ÿ CONSTRAINT B: ??? Ÿ
I assume that consultants normally avoid “perverse” parsings of the input like ( 66 a), which assign it some degree of ill-formedness, when there exist alternative selection points (( 67 b)) that generate the form as perfect. The proposal here is strongly reminiscent of Schütze’s (1996, 172, 189) view of the grammaticality judgment process. Schütze suggests that when consultants judge marginal forms, “constraints [can] be selectively relaxed when an initial parse fail[s]. Once a parse [is] eventually found this way, ... the nature and degree of constraint relaxation [is] reflected in their ungrammaticality ratings.” The difference here, following the general approach of OT, is that constraints per se are not relaxed, but rather their mutual rankings. 3.7Applying the Proposal to the /l/ Problem To test the proposal against data, let us first recall the cases that yielded intermediate well- formedness judgments in the consultant survey. · Forms like gray-ling tend to preserve the pure, uncoarticulated quality of the stem vowel ([eƒÉ] of gray [Ég¨eƒÉ]), rather than taking on the altered qualities that occur before dark [É]. Since the constraints (unstated here) that correlate vowel quality with /l/ darkness are undominated, this means that gray-ling prefers light [l]: [Ég¨eƒÉlÉÉ], ?[Ég¨eɃ«ÉÉÉ]. · Forms like mail-er tend to preserve the dark [É] and coarticulated vowel quality of their bases; thus [ÉmeɃ«ÉÉ] is preferred over ?[ÉmeƒÉlÉ], because of the base form mail [ÉmeɃ«É]. · Forms like mail it work exactly the same way, only more so; thus [ÉmeɃ«É Ét], ??[ÉmeƒÉl Ét]. The basic idea here is as follows. The two constraints which drive the appearance of light and dark /l/ in the crucial (intervocalic, pre-atonic) context are PREVOCALIC /l/ IS LIGHT and /l/ IS DARK. These two constraints are mutually opposed, one being based on perception, the other on articulation. They are ranked freely, as is demonstrated by monomorphemic forms like Greeley. But in suffixed forms, neither constraint is quite “strong enough” (in its central range) to override the PARADIGM UNIFORMITY constraints that enforce light and dark /l/ based on what appears in the isolation stem. More precisely, I posit that if one is to rank PREVOCALIC /l/ IS LIGHT over PARADIGM UNIFORMITY (VOWEL QUALITY, MORPHOLOGICAL), one must use the “?” fringes of PREVOCALIC /l/ IS LIGHT. This means that forms crucially derived with this ranking (specifically, mai [l]- er and similar cases) will receive a “?” under the analysis. Likewise, I posit that one must use the “?” fringe of /l/ IS DARK in order for it to outrank PARADIGM UNIFORMITY (VOWEL QUALITY, MORPHOLOGICAL). This means that forms crucially derived with this ranking (specifically, gray- [É] ing and similar cases) will also receive a “?”. Lastly, forms like ?? mai [l] it , with light [l], can be derived only if PREVOCALIC /l/ IS LIGHT is ranked above PARADIGM UNIFORMITY (VOWEL QUALITY, PHRASAL). It will be recalled that, by a general and well attested (but so far unexplained) principle of phonology, phrasal paradigm
