Formal Phonology

ing away from all other features, in the underlying form[nasal] changes from+ to – synchronously with the change in [continuant]from – to +. This is described by a simple interval structure in whichthe nasal and the continuant interval systems are aligned according tothe timing tier, with no lag in either. IFS corresponds to a somewhatmore complex interval structure in which a positive (say 30%) phase ofthe [–nasal] interval is aligned with the beginning of the second timingunit. This yields an intermediate [–continuant, –nasal] interval in the ccrwhich, when reanalyzed as a full segment, corresponds to the intrusivestop. Clements (1987) argues that the proper way to view this phenomenonis retarded oral occlusion, rather than advanced velar opening. In thisanalysis, the [–continuant] spreads onto the following node, so that thedomain of the intrusive stop is carved out from the domain of the obstruentfollowing, rather than from the nasal preceding it. It is easy to see howthis analysis can be rephrased in terms of interval structures. Again[continuant] and [nasal] are aligned according to the timing tier, but thistime a positive (say 70%) phase of the [–continuant] is aligned with theend of the first timing unit. The (local) interpretation of a segment (root node) can now bedefined in a top-down recursive manner: 4. Synchronization149 (10.1) If the root node contains features corresponding to the inter-val structure and dominates class nodes of type,the interpretation function maps it onto an interval structure of type (10.2) If a class node does not contain any features, and dominates (class)nodes of type, the interpretation function maps it ontoan interval structure of type (10.3) A type node is mapped onto an n-valued interval system. Perhaps the most noteworthy feature of this definition is that it leaves theassignment of temporal structure free. This has the effect of leaving theinterpretation of segments time-free, i.e. containing no more informationthan the original representation contained, namely information about thefeatural composition of the segment. This means, among other things,that when we compute the interpretation of adjacent [m] and [s], someof the interval structures that will fit this representation will also fit therepresentation [mps]. The whole range of model structures will of coursedistinguish between these two, but there will be structures that are modelsof both, which is the intended effect. It is trivial to narrow down the above definition by requiring iden-tically 0 phases and lags for subordinate tiers, and regular (say 80msec)intervals for timing units – this will yield the interpretation presentedinformally in 2.4.4. But this would have the undesirable side effect ofcreating, among other things, a strict distinction between [ms] and [mps].Rather than insisting on some arbitrary phasepoint/lag structure, the for-malization presented above gets exactly as much out of the interpretationas we put in the representation. In order to give more content to theinterpretation, we will have to estimate the random variables that wereleft free here. As we shall see in chapter 5, this can be done by matchingtemporally fully specified interval structure tokens to interval structureswith parameterized random variables. 150Formal Phonology 4.3 The interpretation of large-scale structure In the previous section we have discussed the interpretation of singlesegments or a few adjacent segments. Here we turn to the large-scalestructural properties of speech, to phenomena that affect a large, in prin-ciple unbounded number of segments. Since it is well known that globaleffects, such as the gradual declination of F contours over larger do-mains, can be described as the cumulative result of local effects, suchas adjustment of pitch range across adjacent units (Liberman and Pierre-humbert 1984), the important distinction is not so much between smallerand larger domains, as between convex and non-convex ones. In theprevious section we restricted our attention to intervals (convex tempo-ral domains) – here we will investigate whether the use of non-convexdomains is also necessary for interpreting autosegmental representations. Let us first briefly survey the range of phenomena that can be callednon-convex. Reduplication rules (see 2.2.4 and 2.5.3 above) often pro-duce non-contiguous but otherwise homogeneous domains such as a re-peated vowel, but such examples can always be reanalyzed as being com-posed of two independent domains, each by itself convex. Echo phenom-ena, such as the “pundit’s pronunciation” discussed in 4.2 above, providebetter examples, but it is debatable whether they belong in (postlexical)phonology proper. The most important phonological cases come underthe heading of harmony systems. Vowel harmony was illustrated in 2.2.3above by the case of Hungarian , but harmony phenomena are in no wayrestricted to vowels – we find a wide range of harmony systems affectingconsonants in various ways, ranging from nasal harmony (e.g. Guarańı,see Poser 1982) to pharyngealization harmony (see Hoberman 1987). Although in rare cases all segment types are affected by the harmonyprocess (so that the domain created ends up being convex), typically we We should note here that vowel harmony is by no means restricted to Hungarian or toUralic. Many major language families from Indo-European to Niger-Kordofanian containat least some languages with vowel harmony such as Montañes Spanish (see McCarthy1984) or Akan (see Clements 1981). 4. Synchronization151 find two classes of segments: harmonizing and neutral. While harmo-nizing segments share the same value for a feature or sets of features,neutral segments will not share at least one of the values. Since theharmonizing segments (typically, vowels) and the neutral segments (typ-ically, consonants) appear interdigitated, harmony phenomena create alarge variety of non-convex domains. In this section, I will first overviewthe commonly used strategies for dealing with such domains: in 4.3.1underspecification, and in 4.3.2 the use of hidden variables, and arguethat both of these involve a non-monotonic element. The interpretationfunction is then defined in 4.3.3 so as to accommodate both of thesestrategies. 4.3.1 Underspecification Theories of underspecification come in several flavors (see Archangeliand Pulleyblank 1986, Steriade 1987) but the key idea is common to allvarieties. In addition to segments taking positive and negative values forfeatures, we also permit them to take no value at all – in such cases wecall the segment underspecified for the feature in question. So far wehave used such segments as archiphonemes, i.e. as a disjunction of thetwo fully specified segments that would be created by adding the positiveor the negative feature value. But this concept, what we might call two-sided underspecification, does not really capture the way underspecifiedsegments are actually used in phonology. One important usage, called trivial underspecification in Steriade1987, concerns the cases where a segment never acquires any value ofthe feature; Steriade’s example is labial segments, which arguably neverget specified for [anterior], since the tongue plays no role in the formationof labials. While this kind of justification for underspecification is notunappealing, from the perspective of the formalism developed in 4.1above such cases must be viewed as cases of 3-valued features. Touse Steriade’s example, [anterior] divides the set of segments into threeclasses: those in which the tongue forms a constriction after the soft 152Formal Phonology palate are [+anterior], those in which it forms a constriction at the softpalate are [–anterior], and those in which it plays no role are [0anterior].Trivial underspecification might turn out to be a useful tool in phonology,but most practicing phonologists tend to avoid three-valued features andwould reclassify the 0-valued segments as belonging to either the + orthe – class. Another important usage, in fact the one I take to be central for alltheories of underspecification, will be called one-sided underspecifica-tion. This means that the 0 feature value is treated as standing for only onevalue, a value that will be assigned by a later rule. In a typical harmonysystem, neutral segments will neither undergo nor block the spreading ofeither value of the harmonic feature – they are “transparent” in the sensethat harmony works as if these segments were not present at all. Some-what surprisingly, it is often the case that such neutral segments are, onthe surface, specified for a definite value for the harmonic feature. Giventhe No Crossing Constraint of autosegmental phonology, we would ex-pect such segments to block the spreading of the harmonic feature, but ina large class of cases they in fact do not block it. If we can maintain thatat the point in the derivation where harmony applies, neutral segmentsare underspecified for the harmonizing feature, this transparent behaviormakes sense. There is no association line to block the spreading and nofloating feature to complicate it. The intuitive picture behind this analysis is an extremely appealingone. The idea is that the domain is convex at the time when the harmonyrule applies, and this convex domain gets broken up only at a later,possibly very late stage of the derivation. But there is a price to be paidfor this idea – we are irrevocably committed to a procedural conception ofthe derivation, in which there can be earlier and later stages. To see thatthe commitment is in fact irrevocable, consider the harmonic spreading ofthe feature opposite to the surface specification of the neutral segments. In the case of [anterior], most phonologists would unhesitatingly put the labials inthe [+anterior] class, since the dominant constriction, though not formed by the tongue, isobviously in the anterior region. 4. Synchronization153 At the point where the harmony rule applies it spreads the wrong valueon the neutral segments, for if it did not, the domain would not in fact beconvex. Since the value at this stage is not what appears on the surface,there must be some later (default) rule that yields the correct surfacevalue. This is, by definition, a feature changing (i.e. nonmonotonic) rule. While the nonmonotonic element cannot be entirely eliminated, itcan be pushed into the derivational morphology by a judicious selec-tion of one-sided and two-sided underspecification. As Vágó (1976)shows, the same morphemes (case markers) can serve as suffixes and asstems in Hungarian. If we treat the suffixes as containing archiphonemes(two-sided underspecification), their harmonizing behavior in the inflec-tional morphology can be explained, but the feature specifications withwhich these morphemes surface as stems must be deleted to get thiseffect. However, such nonmonotonic effects are widespread in deriva-tional morphology at any rate, both in truncation (stray erasure) and incategory-changing suffixation. 4.3.2 Hidden variables The alternative approach, which I will call the hidden variable model,is based on an even more radical split between the surface value of afeature and the behavior of the segment. Rather than trying to bring the 0(underspecified) value into play, it employs a separate feature, the hiddenvariable, to encode behavior that contradicts the surface specification.Harmonic spread does not affect each segment equally. The ones thatget affected are distinguished from the ones that do not by the hiddenvariable. The idea here is that the domain is in fact not convex – rather,it is the harmonic projection (see 1.3 above) of the domain which isconvex. The hidden variable or, in phonological parlance, diacriticallyused feature, comes into play because the projection process itself cannotbe governed by the harmonic feature. There are segments, namely theneutral segments, which should not appear in the projection in spite of As pointed out by Kiparsky (pc), who attributes the idea to Harry van der Hulst. 154Formal Phonology the fact that they can carry the harmonic feature.Here the intuitive picture is no less appealing. The idea is that thedomain is not convex (i.e. not a contiguous substring) at any time in thederivation, but it is convex once a projection of the space is taken. Al-though the diacritic use of features has been rather forcefully condemned(see e.g. Kiparsky 1973), it still plays a crucial role in many analyses(for a recent example, see Hyman 1988). These contradictory tenden-cies can coexist only because it has not been widely recognized that theoperation of taking a projection introduces abstractness, as there is ma-terial deleted by the projection. The operation of deleting diacriticallyused features is of course generally recognized to be a non-monotonicoperation. This is not the place to sketch the historical developments thatled from Kiparsky’s (1973, originally 1968) Alternation Condition to thepresently accepted view that seeks to explain cases of obligatory neutral-ization in terms of strict cyclic effects (see Kenstowicz and Kisseberth1977, Ringen 1980, and in particular Kiparsky 1982). Suffice it to saythat clear cases of obligatory neutralization, such as discussed in Vágó1980 or Anderson 1981 remain, so that abstractness, though much betterunderstood, is not entirely eliminated from phonological representations.An important side-effect of autosegmentalization was that a largenumber of cases previously requiring diacritically used features are nowanalyzed in terms of floating features and other nonstandard configura-tions of features and association lines. To give an example, -aspiréstems in French are now analyzed with an initial empty consonant slot(Clements and Keyser 1983, Goldsmith 1990) rather than with a diacritic[+ -aspiré]. Here again the advances in phonological theory led to abetter understanding, but not to the elimination, of abstractness. Thefact that different underlying representations can lead to the same surfaceform remains. Since in such cases information present in the underlyingrepresentation is destroyed in the course of the derivation, again we mustconclude that phonology is non-monotonic. A similar conclusion is reached, primarily on the basis of arguments concerning phono-logical change, in Bromberger and Halle 1989. 4. Synchronization155 4.3.3 The interpretation function The above considerations suggest that our view of phonetic interpretationneeds to be refined in two important respects. First, condition (7.2) mustbe abandoned. Underspecification means that not every feature takesa definite value at all times. To capture this fact, -valued intervalsystems must be replaced by -valued ones, in which the extra (0th)value corresponds to time periods for which the feature in question isunderspecified . Second, we must permit the interpretation function tobe nonmonotonic to the extent that certain features (corresponding to thehidden variables) become “masked” in certain intervals. For example,the echo vowel following the visarga (see 4.2 above) is best understoodby assuming that the oral features characterizing the preceding vowelare retained until after the echo, but are, in effect, masked during theaspiration. The same masking analysis is suggested by the Öhman 1967model of vowel to vowel coarticulation (see also Keating 1988).Therefore the global interpretation function is extended to contain aset of interval systems encoding hidden variables. The mapping betweenphonetic representations and the waveform will depend not only on theovert features but on the hidden ones as well. With this addition, globalinterpretation can be based on local interpretation the following way.Given an autosegmental representation and an interval structure , the(global) interpretation function maps on iff: (11.1) For every root node in , has a part that is the interpretation ofthat node (segment) as defined in (10) above. (11.2) Each non-zero valued interval for every overt feature in is li-censed by a segment in or by a hidden feature, in an order-preservingmanner. (11.3) Contour features are mapped on adjacent level-valued intervals,with possibly 0-valued intervals in between. Whether a MINDUR condition on such intervals is reasonable remains to be seen. 156Formal Phonology These requirements capture the intuitive idea that the interpretation of arepresentation is the concatenation, possibly with 0-valued intervals inbetween, of the interpretations of the segment-size parts of the repre-sentation. (11.3) means that whenever a single unit, such as a vowel,is associated with a series of features on a single tier, such as a HLHmelody, the interpretation is a set of intervals (in the example, H, L, andH) which can, but need not, be separated by shorter intervals on whichthe feature is underspecified. The dual situation, in which a single featureis spread over several segments, does not require a special provision, asit is handled by the same synchronization mechanism that was motivatedby microsynchrony in 4.2 above. With this last definition, the task of formalizing autosegmental phonol-ogy is completed. We inspectedwhat phonologists do and explicated theirpractice in a more rigorous framework built from “logicomathematical”primitives. This framework enables us to turn autosegmental phono-logical descriptions of natural languages into rigorously defined, thoughnot necessarily very effective, algorithms. Even more importantly, thisframework will guide our efforts in chapter 5 to introduce a new, linguis-tically motivated architecture for Markov modeling of speech.