INALTERABILITY IN CV BRUCE HAYES University ofCalifornia, Los Angeles Geminate and long frequently resist the application of rules that would a-priori be expected to apply to them; Le., they are frequently 'inalterable'. This article argues that, by invoking the theory ofCV Phonology, it is often possible to predict which phonological rules are unable to affect long segments. The prediction follov's from rather minimal assumptions about how rules apply to forms. * A long tradition of phonological research has shown that geminate conso­ nants and long vowels behave exceptionally. Within generative phonology, the work of Kenstowicz 1970, Pyle 1970, Fidelholtz 1971, Guerssel 1977, 1978, Leben 1980, Steriade 1982, and others has uncovered at least three exceptional properties of these long segments: (1) a. AMBIGUITY: Long segments act in some contexts as if they were two segments, in others as if they were one. b. INTEGRITY: Insofar as they constitute two segments, long segments cannot be split by rules of epenthesis. c. INALTERABILITY: Long segments often resist the application of rules that a-priori would be expected to apply to them. The theory ofCV Phonology, as applied to length (cf. Leben 1980, McCarthy 1981a, Steriade 1982, Clements & Keyser 1983), has provided convincing the­ oretical accounts of the first two properties mentioned above, Ambiguity and Integrity. However, the problem of Inalterability has, in my opinion, not yet been adequately dealt with. Consider a specific instance, to be discussed in greater detail below. In Per­ sian (cf. Cowan & Yarmohammadi 1978), a rule I will call lvi-Weakening con­ verts Ivl to Iwl whenever it occurs in, roughly speaking, syllable-final position (2a). Unexpectedly, lvi-Weakening fails to affect syllable-final Ivl whenever it forms the first half of a geminate, as 2b shows: (2) a. Inov-ru:zl ~ nowru:z 'New Year' (lit. 'new day') (cf. novi:n 'new kind') Ijrevl ~ jc£w (~ jow) 'barley' (cf. jc£vi:n 'made of barley') b. c£vvc£l 'first' morovvc£l 'generosity' qolovv 'exaggeration' In this instance, the long segment Ivvl is clearly inalterable. Now, it is certainly

* I would like to thank Diana Archangeli, G. N. Clements, B. Elan Dresher, Wilson Gray, Morris Halle, Patricia Keating, Phil LeSourd, Joseph Malone, John McCarthy, Brian McHugh, David Odden, Russell Schuh, Donca Steriade, and Charles Ulrich, among others, for their very helpful advice and comments on the research reported here. None of them should be held responsible for shortcomings. An early version of this article was presented as Hayes 1984. 321 322 , VOLUME 62, NUMBER 2 (1986) possible to write a version of lvi-Weakening that respects Inalterability by appropriately complicating the structural description. However, as I will show below, the phenomenon is quite widespread; this suggests that it would be wrong to write Inalterability into individual rules. Rather, we should seek a general principle that predicts cases of Inalterability automatically. To locate such a principle is not trivial, because not all rules respect Inal­ terability. An example of a rule that does not may be found in Feinstein's 1979 phonological analysis of Sinhala, an Indo-European language of Sri Lanka. He proposes a rule of Cluster Simplification, which freely applies to geminates: (3) Sinhala Cluster Simplification C ~ 0I C_-]Sy) kand.da ~ kanda 'hill-sG.DEF' Thus an adequate account ofInalterability should be able to predict which rules cannot affect long segments and which rules can. Ideally, the principle that makes this prediction should not be an arbitrary stipulation, but should follow naturally from general principles. This article is an attempt to provide such an account. The exposition is organized as follows. I begin with a review of CV Pho­ nology, showing how the properties of Ambiguity and Integrity are conse­ quences of it. In §2, I propose a CV account of Inalterability, and defend it with examples from a number of . In §3, I discuss alternative pro­ posals; the results are summarized in §4. 1. CV PHONOLOGY is an outgrowth of autosegmental phonology, as devel­ oped in Goldsmith 1976 and other works. The basic tenet of CV Phonology is that the property of syllabicity is represented on a separate autosegmental tier from the strictly segmental features. The tier specifying syllabicity, or 'CV tier', is linked to that specifying the remaining features, or 'melodic tier', with association lines in standard autosegmental fashion. As is normal in autoseg­ mental phonology, the theory allows for one-to-many and many-to-one asso­ ciations. Some of these principles are illustrated in Figure 1 by a CV repre­ sentation of the English word junior, phonetically [Ju:ny~].

c VV C C V ~ V I I I + cons +cons -cons + cons -cons +cons -son -son +son +son +son +son -cont +cont +cont -cont +cont +cont -nas -nas -nas +nas -nas -nas +ant -ant + high +ant + high -ant +cor +cor +back +cor -back +cor -dist +dist +rnd -dist -rnd -dist CVVCCV I I I d. z Vu n i r FIGURE 1.

In particular, observe that the symbols i and u suffice for both glides and INALTERABILITY IN CV PHONOLOGY 323 vowels, with the CV tier determining which they stand for. Many-to-one as­ sociations between tiers may be found in , short , and pre­ nasalized stops; one-to-many associations occur in long vowels and geminate consonants. The literature is now replete with evidence supporting the CV view of pho­ nological structure. McCarthy 1979, 1981b originally motivated the independent existence of the two tiers by showing that, in Semitic languages, may be defined on either one. Later work has shown the applicability of the CV framework in solving problems in reduplication (Marantz 1982); compen­ satory lengthening (Steriade 1982, Clements Mssa,b); secret language games (Yip 1982, Odden MS); global rule application (Clements & Keyser 1983); phon­ otactics (Prince 1984); and speech error analysis (Sternberger 1984). A number of general principles governing CV representation are generally or partially agreed upon in the literature. Three ofthem will be important below: THE OBLIGATORY CONTOUR PRINCIPLE (Leben 1973, McCarthy 1986), devised originally by Leben 1973 for tonal phonology, forbids sequences of identical segments where a single multiply-linked segment could replace them. Hence a long must be represented as 4a, not 4b: (4) a. VV b. VV V II a a a I assume that the Obligatory Contour Principle is a statement of markedness, assigning greater value to the structure of 4a. This structure is thus selected by the language learner in the absence ofevidence to the contrary. By the same token, languages sometimes contain rules of 'melodic degemination', con­ verting input structures like 4b to 4a. That 4a should be more highly valued is plausible, given that it represents the same phonetic substance as 4b less redundantly. PROHIBITION ON CROSSING ASSOCIATION LINES. Configurations like 5 are uni­ versally ill-formed, and rules are blocked when such configurations would be derived: (5) *C V

aX t ASSIMILATION AS SPREADING. Halle & Vergnaud 1980, as well as others, argue that total assimilation rules do not actually change a segment into something more like its neighbor, but rather involve spreading of the trigger segment's melody onto the target segment's CV position, in the same fashion that tonal autosegments spread. Thus a rule assimilating ItI totally to Ikl carries out the following operation: (6) CC ~ CC II V t k k To show some of the effects of these principles, I will first discuss how they 324 LANGUAGE, VOLUME 62, NUMBER 2 (1986) solve the problems of Ambiguity and Integrity. The results obtained in these areas will be directly relevant to my proposal concerning Inalterability. 1 1.1. AMBIGUITY. The phonological framework of SPE (Chomsky & Halle 1968) provides two ways of describing long segments: they can be single seg­ ments bearing the feature value [+long], or they can be sequences of two short segments bearing identical feature specifications. Generative phonologists working in the post-SPE period rapidly found that neither description could account for the way phonological rules treat long segments (see Kenstowicz 1970, Pyle 1970, Fidelholtz 1971, Sampson 1973, Barkal 1974, Malone 1976, 1978). For some rules, only the sequence description allowed for an adequate account; but other rules required that long segments be counted as units, ne­ cessitating the feature description. Kenstowicz 1970 tentatively suggested let­ ting long segments start out as sequences, applying all rules that demand this representation-then converting the sequences to [+long] units, and applying the rules that demand the feature representation. However, this proposal proved to be untenable: Fidelholtz showed that the independently needed rule­ orderings of Micmac are inconsistent with it; and Kenstowicz 1970 demolished his own scheme by pointing out a rule of Lithuanian that demands both rep­ resentations at the same time. Although the post-SPE research failed to solve the problem of Ambiguity, it did identify the difficulties much more precisely. In addition, Kenstowicz 1970 uncovered a generalization that will be important here: for the most part, the rules that demanded a sequence representation were 'prosodic rules', which affect , , and length itself. The rules requiring the feature [+long] were mostly rules affecting segment quality. However, as Fidelholtz pointed out, nothing in the theoretical framework of the time provided any formal ac­ count of the intuitive distinction between prosodic and qualitative rules. Consider now how Ambiguity can be dealt with in CV phonology. The theory represents most long segments as single melodic segments linked to two C or V positions, in accordance with the Obligatory Contour Principle: (7) a. VV b. CC V aV t

1 Two further issues within CV Phonology are not strictly relevant to the proposal I will make below. I mention them here for rigor's sake: (a) In some versions of CV Phonology, the symbols C and V are replaced by the single unit X, with consonants distinguished from vowels by virtue of their location within a hierarchical syllable structure: vowels are X's included within the syllable Nucleus, while consonants are extranuclear X's (cf. Kaye & Lowenstamm MS, Prince 1984, Levin 1982). As far as I can tell, everything I say below can be expressed equally well in either version ofthe theory. I use C's and V's for expository simplicity. (b) The CV representations originally posited by McCarthy 1979, 1981b for morphology involve placing each melodic on a separate tier. As Steriade (l03-7) points out, these multi­ tiered representations sometimes lead to problems when put to phonological use; phonology ap­ parently requires a single tier for all melodic segments. McCarthy 1986, citing unpublished work by R. Gutmann Younes, suggests a straightforward procedure that collapses multi-tiered morpho­ logical representations into just two tiers before the phonological rules apply. I assume that this procedure is correct, and that all the phonological rules described here apply to its output. INALTERABILITY IN CV PHONOLOGY 325

These representations largely solve the problems uncovered in earlier research: the long segments form single units on the tier responsible for representing quality, and two-segment sequences on that responsible for representing quantity. Consider two examples, which appear to be quite typical. In Rausa (Klin­ genheben 1928), diphthongs and long vowels may not occur in closed syllables. When such configurations arise through morphological combination, they are resolved by shortening long vowels and deleting the second halves of diphthongs: (8) a. a:-n-ka ~ cfanka 'your son' son-of-2m.sg. b. kai-n-ka ~ kafLka 'your (m.sg.) head' head-of-2m.sg. c. kyau-n-fuska: ~ kyanfuska: 'beauty of face' beauty-of-face This situation clearly requires that long vowels be represented as sequences; if they were represented as [+ long], then the shortening of long vowels could not be collapsed with the structurally similar simplification of diphthongs. CV Phonology can account for the facts straightforwardly. To shorten long vowels, the rule must delete a V position: (9) Hausa Shortening V ~ fJ I V--C]syl a. CVVC.CV ~ CVC.CV I \J IIIIIIII cf an ka cfan ka b. CVVC.CV ~ CV C.CV ~ CVC.CV IIIIIIIIIIIIIIII kainka kainka kanka In 9b, kafLka, the melodic segment Iii is stranded by vowel deletion; such stranded segments are deleted by convention (McCarthy 1981b:382, 399). Consider now a purely qualitative rule. In Lithuanian (Kenstowicz 1970), the vowels Ie e:1 are backed to 10 0:1 before the vowel lui and the glide Iw/. Such a rule must treat long vowels as units; otherwise it would convert leeul, for example, to *[eou] rather than [oou]. In CV phonology, the rule is expressed on the melodic tier, where vowel quality is represented:

(10) Lit[h;a;;:;JB:~i::aCk] / __ [~~;~~] g + hIgh Such a rule can affect both long and short vowels: (11) a. VVV ~ VVV b. VV ~ VV V I V IIIII eu ou eu ou (= [o:u]) (= [au]) The significance of these examples is that neither the feature representation 326 LANGUAGE, VOLUME 62, NUMBER 2 (1986) nor the sequence representation of length can alone account for both cases. The Hausa example requires the sequence representation in order to capture the parallel behavior of long vowels and diphthongs; the Lithuanian example requires the feature representation to generalize over long and short vowels. CV Phonology makes both representations available, and correctly predicts which one will be relevant from whether the rule affects quantity or quality. It will be seen shortly that Kenstowicz's generalization about quantity and quality also plays an important role in Inalterability. 1.2. INTEGRITY. In languages with both long segments and rules of epen­ thesis, it has been consistently found that epenthetic segments cannot be in­ serted between the halves of long segments. Abu-Salim 1980 describes an interesting case from Palestinian Arabic. Omitting some irrelevant details, epenthesis in this language works as follows: (12) Palestinian Epenthesis ~ ~ ,I C__C {~} (applies iteratively, right-to-Ieft) i Here are some examples: (13) a. l?akV ~ ?akil 'food' b. I?akl-kuml ~ ?akilkum 'your food' c. Ijisr kbiirl ~ jisrikbiir 'a big bridge' bridge big d. II-?akl I-mniil)1 ~ l?akllimniih ~ l?akillimniih DEF-food DEF-good 'the good food' The statement of Epenthesis under 12 is inadequate in one respect: it fails to state that the rule is blocked when it would insert Iii in the middle of a geminate: (14) a. ?imm (* ?imim) 'mother' b. sitt-na (*sititna) 'our grandmother' Steriade, following a suggestion by Jonathan Kaye, argues that this effect re­ sults automatically from principles of CV Phonology. Observe that an epen­ thesis rule must insert both a V position and the melody associated with it. If long segments normally have the structure given in 15, with multiple associ­ ation, then it is impossible to split them without violating the universal con­ straint against crossing association lines: (15) a. CVCC ~ *CVCVC b. CVCC ~ *CVCVC IIV IIX! II\} 11\;1 ?im ?iim ?im?i mi Thus the theory automatically predicts that Epenthesis should not be able to split geminates. Some further facts support this analysis. Note that the structure for geminates under 15 would be expected to arise only within morphemes, where the Oblig­ atory Contour Principle enforces it. Where a geminate arises through mor­ pheme concatenation, each morpheme must provide a melodic segment from INALTERABILITY IN CV PHONOLOGY 327 its lexical entry, giving the structure under 16a. For convenience I will refer to these accidental geminates as FAKE, while the doubly-linked variety found within morphemes will be called TRUE geminates: (16) a. Fake geminates b. True geminates C + C CC II V t t t Unlike true geminates, fake geminates should be freely splittable by epenthesis, since no association lines would cross. As Abu-Salim points out, this is indeed true in Palestinian Arabic: (17) a. IC V C-CI ~ CVCVC 'I entered' IIIIIIIII fut-t fut i t enter-1sg. b. ICVCVC CCVVC/~ CVCVCVCCVVC 'big fish' IIIIIII V IIIIIIIII V I samak kbi r samakikbi r fish big One additional fact provides even stronger support for the theory: a hetero­ morphemic geminate WILL resist epenthesis, provided it derives from a rule of total assimilation. This again follows from standard assumptions. In CV Pho­ nology, total assimilation is expressed as the autosegmental spreading of the melody to an adjacent C slot, creating a true geminate as the output. This is illustrated in Figure 2 with the Palestinian rule that assimilates the definite article II/ to coronal segments.

c-cvcvc c-ccvvc 'the small boy' I 11I11 I II VI l-wa I ad 1- z)' i r (underlying form) DEF-boy DEF-small CCVCVC CCCVVC IV-Assimilation II IIII \j I VI I wa I adz)' i r BLOCKED Epenthesis (first iteration) ccvcvc vcccvvc Epenthesis (second iteration) I11111 I. ~ I YI lwalad I z)' I r FIGURE 2.

Here the Izzl that results from II/-Assimilation forms a true geminate. This blocks Epenthesis on its first iteration, producing [lwaladizz-yi:r] instead of the expected [lwaladziz-yi:r]. The predictions of CV theory concerning Integrity extend to other languages and rule types. Thus epenthesis is also unable to split true geminates in Berber (Saib 1976, Guerssel 1977, 1978), Moroccan Arabic (Guerssel 1978), Amharic (McCarthy 1986), and Tiberian Hebrew (McCarthy 1986). Metathesis rules (e.g. of the form CCV ~ CVC) are clearly also subject to the predictions of the 328 LANGUAGE, VOLUME 62, NUMBER 2 (1986) theory; cases in which metathesis fails to split geminates may be found in Berber (Guerssel 1978), Tunisian Arabic (Kenstowicz & Pyle 1973), and Clas­ sical Arabic (McCarthy 1981b:398-9). Finally, CV theory predicts that epen­ thesis rules which insert consonants to break up vowel clusters should not be able to split up long vowels. This is indeed true in Kfhehe (Bantu, Tanzania; Odden & Odden 1985) and in Sinhala (Feinstein 1979). 2. INALTERABILITY. The summary above suggests that the phenomenon of Integrity follows from independently motivated principles of CV Phonology: (a) the Obligatory Contour Principle, (b) the ban on crossing association lines, and (c) the statement of assimilation as spreading. Together, these determine the geminates subject to Integrity: monomorphemic geminates, and hetero­ morphemic geminates derived by assimilation. Obviously, this set would not be a natural class a-priori. The predictions of CV Phonology concerning In­ tegrity thus constitute a rare instance of a successful (albeit elementary) 'theo­ rem' in phonology.2 I will now consider whether the same kind of theorem can be derived for the phenomenon of Inalterability. 2.1. THE ROLE OF CV THEORY. To start, I will show that merely adopting CV representations does not, of itself, solve the Inalterability problem; but it does provide a different perspective. To demonstrate this, I will discuss in greater detail the Persian rule of lvi-Weakening mentioned earlier. In Modern Persian, [w] is a distributional variant of underlying Iv/: roughly speaking, [w] occurs when it follows a short vowel and is not syllable-initial (cf. Cowan & Yarmohammadi). An additional rule of lre/-Backing takes lrel to 101 whenever it precedes Iw/. The rules oflvi-Weakening and lre/-Backing result in alternations like these: (18) a. mi:-rCEV-CEm 'I am going' PRES-go-l sg. b. bo-row « Ibo-rrev!) 'go!' IMP-go

2 A caveat: These results appear to hold only for 'local' autosegmentallinkings, such as those found in geminate consonants and long vowels. Autosegmental phonologists have also posited long-distance linkings, extending over several syllables, to handle phenomena such as tonal spread­ ing and vowel harmony. Such linkings sometimes fail to respect Integrity; cf. examples from Hun­ garian in Clements 1976 and from Pasiego Spanish in McCarthy 1984. Moreover, long-distance linkings suffer from a serious Ambiguity problem of their own. For example, a sequence of high­ pitched syllables is sometimes best analysed as a single, multiply-linked high tone, and sometimes as a sequence of high tones. This can happen even in a single language; thus in Shona (Odden 1980, 1984), a high-toned sequence must be analysed as a series of high tones for the verbal mor­ phology; as a single, multiply-linked high tone for the nominal morphology; and again as a tone sequence for the phrasal phonology. Given that long-distance linking leads to problems in Ambiguity and Integrity, it is not surprising that it should yield counter-examples to my proposal below concerning Inalterability. The Venda rules of Pre-Penult Simplification and Final Simplification (Cassimjee 1983) are two particularly compelling cases; both arise because of long-distance linking. It is clear that distinguishing the behavior of long-distance vs. local linking is a major problem which goes beyond the scope of this article. In what follows, the discussion will therefore be confined to local linking. INALTERABILITY IN CV PHONOLOGY 329

(19) a. nov-i:n 'new kind' neW-SUFF b. now-ru:z « Inov-ru:zl) 'New Year' new-day (20) a. mi:-dCEv-i:d 'you are running' PREs-run-2pl. b. pa:-dow « Ipa:-drevl) 'gofer' foot-run(ner) The lvi-Weakening rule is also supported simply by the surface complementary distribution of [v] and [w]: (21) a. pa:ltow 'overcoat' mow 'vine' cetowr 'how' dowre 'era' b. vCEli: 'but' voju:d 'existence' kesvCEr 'country' omi:dva:r 'hopeful' ga:v 'bull' hi:vdCEh 'seventeen' jozv 'except' SCErv 'cypress' As the data make clear, lvi-Weakening should be stated as applying to a Ivl that occurs in the same syllable as a preceding short vowel. I state the rule as follows, using Kahn's 1976 formalism for syllable membership: (22) Persian lvi-Weakening IT A VC II v~wl[] The rule says: 'Convert Ivl to Iwl when its associated C position shares the same syllable with a short vowel.' The rule applies to underlying Isenrevl as in Figure 3. cvcvc-vccv cv-cvcvc IIIIII II I II IIIII sence v -ce n d e be-sencev listen- er 'listener' IMP-listen 'listen!' CVCVCVC lvi-Weakening IIIIIII besencew cvcvcvc Ire I-Backing IIIIIII besenow

FIGURE 3.

We now can consider how lvi-Weakening might be expected to affect a true geminate Ivvl in CV theory. Plausibly, the derivation would be as follows: (23) VCC ~ VCC I V I V CE v CE w 330 LANGUAGE, VOLUME 62, NUMBER 2 (1986)

Since Ivl is linked to a C position following a short vowel, it should undergo the rule. This is the wrong result, since Ivvl is in fact inalterable; cf. numerous examples like CEVVCEl 'first', morovvCEt 'generosity', qolovv 'exaggeration'. Note that derivations similar to 23 actually occur for Lithuanian Backing, as in 10-11. It is not immediately clear why Persian lvi-Weakening should behave differently. The point of this is that CV Phonology does not by itself solve the Inalter­ ability problem; it merely makes different wrong predictions: phonological rules will wrongly affect entire geminates, rather than halves of geminates. But with a minor revision, CV theory CAN account for Inalterability, correctly distin­ guishing the Persian and Lithuanian cases. I will now show how this can be done.

2.2. AN ACCOUNT OF INALTERABILITY. A survey of the cases known to me reveals the following generalization: roughly speaking, the rules subject to In­ alterability are those which mention both the CV tier and the melodic tier (cf. Rule 22); but those rules which escape Inalterability are formulated onjust one tier (cf. Hausa Shortening, Rule 9; Sinhala Cluster Simplification, Rule 3; and Lithuanian Backing, Rule 10). While the correlation is not perfect, I believe it forms the basis of an adequate account. To make this account rigorous, it is necessary to make explicit the criteria by which one may determine when a rule must mention a particular tier. My criteria are as follows: (a) Any rule mentioning distinctive features other than [syllabic] must ob­ viously mention the melodic tier; e.g., a rule that refers to the natural class of glides and vowels must mention the melodic tier in order to include [- consonantal]. (b) Any rule that appeals to the class of consonants or to the class of vowels must mention the CV tier, where syllabicity is represented. (c) Any rule that refers to position within the syllable (e.g. 'syllable-initial') must refer to the CV tier. Here I follow Clements & Keyser in assuming that it is the CV tier which is incorporated into syllables. This is a plausible as­ sumption, given that elements of the melodic tier are often spread over more than one syllable, which would result in improper bracketings if the melodic tier were syllabified. These three criteria normally suffice to identify the tiers that a rule must mention. Thus Persian lvi-Weakening (22) must mention the melodic tier to identify lvi, and the CV tier to ensure that the Ivl is tautosyllabic with the preceding vowel. The next step is to show that the proposed dependence of Inalterability on the number of tiers mentioned is not to be stipulated, but follows naturally from independent principles. What is special about two-tier rules, I would argue, is not that they mention two tiers, but that they include association lines in their structural descriptions. Such rules are ambiguous in a way that has not yet been clearly resolved. To clarify this ambiguity, I will refer to the schematic example 24, below. Suppose that some phonological rule P contains in its structural description autosegments a and (3, linked by an association line, as in 24a. Suppose further INALTERABILITY IN CV PHONOLOGY 331 a representation R, which contains the autosegments A and B. A is an auto­ segment analysable by a (e.g., if a is [+coronal], A could be the melodic autosegment It/); and B is an autosegment analysable by f3. The crucial question is: What association lines should be present in representation R in order for rule P to apply to it? Two logical possibilities exist. (a) First, we might suppose that P is applicable to R if A is linked AT LEAST to B, where A and B may also be linked to other autosegments. Under this interpretation, P may apply to any of the candidates for R under 24c: (24) a. Rule P contains ex. I f3 b. A 'is an' a. B 'is a' f3. c. Possibilities for Representation R (i) x A x (ii) x A (iii) x A x (iv) x A III If\ IV \t\ xBx xBx xB Bx This interpretation was tacitly adhered to in the derivation of 23. (b) The other possible interpretation is that rule P applies to R only if A is UNIQUELY linked to B, and vice versa. If this is true, P would apply only to representation 24c(i). These two interpretations seem about equally plausible a-priori; only data can determine the right choice. I will show here that, if the second option is taken, then the Inalterability problem is solved directly. For clarity, I will give a name to my interpretation of association lines: (25) LINKING CONSTRAINT. Association lines in structural descriptions are interpreted as exhaustive. This formulation is intended to cover structural descriptions in which an auto­ segment is multiply-linked: an autosegment bearing n linkages in a structural description must be matched to an autosegment bearing exactly n linkages in the actual form, as seems natural. Note that the Linking Constraint will be relevant only if the ex and f3 in the structural description actually have association lines attached to them. If an autosegment appears in a structural description with no lines attached, this should be interpreted as allowing any number of association lines, including zero. Thus a bare autosegment in a structural description does not mean that it is necessarily 'floating'. Rather, I assume (following standard practice) that a 'necessarily floating' autosegment must be marked as such by circling it. The meaning of the Linking Constraint is summarized below, where ex is an auto­ segment appearing in a rule: (26) a. ex = ex linked to any number of autosegments. b. @ = ex linked to no autosegments. c. ex = ex linked to exactly one autosegment. I d. ex = ex linked to exactly two autosegments (etc.) A 332 LANGUAGE, VOLUME 62, NUMBER 2 (1986)

To see how all this works, let us return to Persian lvi-Weakening. For the reasons already mentioned, the rule must mention both the CV tier and the melodic tier, together with an association line linking C and the focus: (27) Persian lvi-Weakening (repeated from 22) (T A VC II v~wl[] Given this formulation, lvi-Weakening cannot apply to a true geminate Ivvl, because the associations of the [v] melody exceed those permitted by the Link­ ing Constraint (see 28a). Similarly, the rule cannot apply following a long vowel, because the associations of that vowel's melody would again exceed those specified in the rule, as in 28b: (28) a. VCC b. VVC IV VI re v a v These are the correct outcomes. Consider next what happens in the case ofa one-tier rule. Here the structural description contains no association lines, and it is matched up to a form solely on the basis of the autosegments it contains. As an example, recall Lithuanian Backing, which converts Ie e:1 to 10 0:1 before lui and Iw/. The only way to generalize over lu wi is to state the rule on the melodic tier, using the feature combination [- cons, + back, + high]. Since the rule is stated on just one tier, it contains no association lines, and the Linking Constraint allows it to apply freely to long and short vowels: (29) Lithuanian Backing (repeated from 10)

=~?n~J ~ [+ back] I __ [~~;~~l [ g +h~hj a. VVV ~ VVV b. VV ~ VV IIIIII eu ou eu ou The discussion thus far has dealt only with true geminate structures. Since fake geminates have a different configuration of association lines, one might expect them to behave differently with respect to Inalterability: each half of a fake geminate should behave like a normal single . This can be tested in Persian, since one can create a fake geminate Ivvl by attaching a productive lvi-initial suffix to a lvi-final stem. As can be seen below, such a Ivvl does not respect Inalterability: (30) a. C VVC-C V C-C VVC ~ cvvccvccvvc I V IIIII V I I V IIIII V I pi s rrev va r pi srowva r ahead-go(er)-like ([pi: srowva:r]) 'having the qualities of a leader' INALTERABILITY IN CV PHONOLOGY 333

b. pCErtov-vCEr ~ pCErtowvCEr ray-ful 'shiny' c. pa:-dCEv-va:r ~ pa:dowva:r foot-run(ner)-like 'having the qualities of a gofer' It can be seen that, in a fake geminate, the first Ivl can undergo Weakening without running afoul of the Linking Constraint. This observation (which will be replicated below in a number of languages) is important, because it argues against a purely phonetic account of Inaltera­ bility. One might imagine that the two halves of a geminate 'reinforce' each other, thus resisting any externally applied phonological process. The contrast between the behavior of true and fake geminates argues against this phonetic explanation, since the two types express the same phonetic substance. It is the difference in their phonological structure that causes the difference in their behavior. 3 To summarize the predictions of the theory: phonological rules that include association lines in their structural descriptions should respect Inalterability for true geminates, but not for fake ones. Rules that mention only one of the two tiers, and thus lack association lines, will ignore Inalterability. These pre­ dictions are verified in the Persian and Lithuanian rules discussed so far. In the following sections, I will show that the predicted generalization also holds for other phonological rules.

2.3. RULES SHOWING INALTERABILITY include the following. 2.31. KLINGENHEBEN'S LAW IN RAUSA states that syllable-final have become , by the following pattern: (31) labials ~ Iwl sabroo ~ sawroo 'mosquito' alveolars ~ IfI biyad ~ biyaf 'five' velars ~ Iwl batagyee -~ batawyee 'twin' This rule failed to affect geminates; thus VttV remained the same, and became neither VffV nor VftV. The geminates existed in Rausa prior to Klingenheben's Law,4 so that the inapplicability ofthe law to them is unlikely to be explainable on historical grounds. But under the T-Jinking Constraint, the blockage of the rule is to be expected in any event. To identify both syllable-final position and the class of obstruents, the rule must be stated on two tiers (some irrelevant details are ignored here):

3 For completeness, it should be noted that the Persian data above are from a formal style of speech that preserves an earlier stage ofthe language. In colloquial style, lvi-Weakening has entered the lexical phonology (cf. Kiparsky 1982, Mohanan 1982), resulting in a more complex surface distribution of [v] and [w]. These facts do not crucially affect the argument above. 4 This claim is supported by the existence of many demonstrably ancient words in Rausa that contain geminates, as well as by the treatment of Arabic loans (Greenberg 1947). At least some of the Arabic loans in Rausa antedate Klingenheben's Law; but of the numerous words borrowed by Rausa that have geminates in Arabic, none was ever affected by the low. 334 LANGUAGE, VOLUME 62, NUMBER 2 (1986)

(32) Klingenheben's Law C]syl I [- cont] ~ [+ son] I Under our assumptions, the rule as stated cannot analyse geminate consonants either in whole or in part. 2.32. BERBER GLIDE VOCALIZATION, in the dialect of Ait Segrouchen (Guers­ sel 1977, 1978), changes the glides Iy wi to syllabic Ii ul when they cannot otherwise be incorporated into a syllable. Thus in Figure 4, representations like (b), which are intermediate forms derived by a rule of Construct Deletion (Guerssel 1977:272), are rendered syllabifiable by vocalizing the glide.

'FEM-SG-hare-sG' 'FEM-SG-slope-sG' (a) t-a-wtul-t t-a-ysar-t underlying forms (b) twtult tysart Construct Deletion (c) tutult tisart Glide Vocalization FIGURE 4.

In CV Phonology, glide vocalization rules necessarily refer to two tiers: the melodic tier to distinguish glides from other consonants, and the CV tier to carry out the structural change C ~ V. Here is the rule for Berber: (33) Berber Glide Vocalization c~v/{;} _C I [ -cons] I express the rule linearly for explicitness; in a theory of syllabic phonology, the rule could simply say: 'Convert unsyllabified C to V if it is linked to [- cons].' In any event, Glide Vocalization must include an association line in its structural description, and thus should be blocked by the Linking Constraint from applying to geminate glides. Guerssel shows that this is so with data including Figure 5.

CVCCCV 'strangle me' CVCCCVC 'take a picture for him' II \J II II ~ III z{} yf i [z~yyfi] [~~wwras] *[z~yifi] *[~~wuras] FIGURE 5.

The analysis is confirmed in that Glide Vocalization respects the distinction between true and fake geminates. Figure 6 shows that a fake geminate Iwwl permits Glide Vocalization, just as the Linking Constraint would predict. Furthermore, when a glide derives from total assimilation, and is therefore a true geminate, the Linking Constraint correctly predicts that it will be inal­ terable. In Figure 7 (example from Guerssel 1978), the morpheme In-I is a genitive marker that assimilates totally to a following . INALTERABILITY IN CV PHONOLOGY 335

C-V-CCVC 'hare' (Guerssel 1978:235) I I IIII w-a-wt u I CCCVC Construct Deletion IIIII wwtul VCCVC Glide Vocalization IIIII uwtul FIGURE 6.

C-CCVC 'of a male' I II II n-wt {}m CCCVC In/-Assimilation \J III wt ~m BLOCKED Glide Vocalization [wwt~m] other rules FIGURE 7. These facts again show that it is the linking structure of geminates that de­ termines whether rules may apply to them. 2.33. GLIDE VOCALIZATION. According to Brame 1970, syllable-final glides in Classical Arabic are vocalized when preceded by a vowel of identical quality. For example, underlying /yu-wqaf-u/ 'he gets arrested' surfaces as [yuuqafu]. Like all rules of glide vocalization, this rule must be stated on two tiers: (34) C ~ V/V- ]syl II [:b~~~] [:~~;~ ] Expressed in this way, the rule should not be able to analyse geminate glides. Indeed, it does not apply to them; cf. xuwwifa 'he has been scared'. The condition [aback] [aback] that appears in Rule 34 is suspicious; it is plausible that, in a well worked out theory of CV Phonology, it will be possible to avoid the use of Greek-letter variables. The alternative is easy to state: a rule having the effect of the Obligatory Contour Principle must apply first, merging the melodic representations of the vowel and the following glide. Glide Vocalization can then be stated as follows: (35) C ~ V/V- ]syl V [] This rule cannot apply to xuwwifa any more than 34 can, since the two links associated with [] cannot be matched up to the three links in the input form: (36) CVCCV CV I \V III x u if a 336 LANGUAGE, VOLUME 62, NUMBER 2 (1986)

2.34. SPIRANTIZATION IN TIORINYA. The implications of CV theory for Inal­ terability were first pointed out in independent work by Schein 1981 and Ken­ stowicz 1982 on the Spirantization rule of Tigrinya, a South Semitic language spoken in Eritrea. In this language, the velar stops [k g k'] become when they follow a vowel: (37) a. kA lbi 'dog-so' ?axaUb « /?akalibl) 'dog-PL' b. gAn?i 'pitch-so' ?ayani? «/ ?agani?1) 'pitch-PL' c. k'AbArA 'to bury' yi-x'Abbir « /yi-k'Abbirl) 'he buries' In CV theory, the Tigrinya Spirantization rule must be two-tiered: it mentions the CV tier to identify postvocalic position, and the melodic tier to identify the velar stops. I write the rule as follows: (38) Tigrinya Spirantization v C I -son ] ~ [ + cont] / [ + back Since the rule contains an association line,S it should not be able to apply to true geminate /kkl. This is indeed the case, as shown in 39a. Fake geminates can be tested by concatenating /kI-final and /kI-initial morphemes. As 39b shows, the first /ki of these clusters can spirantize, as the Linking Constraint predicts. Finally, geminate /kk/ from total assimilation is correctly predicted by the theory to be inalterable, as in 39c: (39) a. Blockage in /kk/ fAkkArA (*fAxxArA) 'he boasted' VCC V k b. Spirantization in /k + kI /mirak-ka/ ~ miraxka 'calf-2sg.MAsC. ' VC+C~ VC+C IIII k k x k

5 Note that this is necessarily so. A rule of the following form­

(a) [-son]+back ~ [+cont] / V_ -would be ill-defined, as linear precedence is defined only on single tiers. To see why, consider the commonly invoked device of autosegmental mapping-which presupposes that, at some levels of the derivation, the temporal alignment of tiers is not defined at all. Steriade & Schein (MS) point out that it is possible to develop an abbreviatory convention whereby (a) is interpreted as having the same meaning as Rule 38. However, the inventory of abbreviatory conventions available to phonological theory is an empirical issue. Our goal is not to save as much ink as possible, but to delimit the class of possible rules and predict their properties. Insofar as Tigrinya Spirantization and similar rules respect Inalterability, I take this as indirect evidence that we should not adopt a convention of the sort proposed by Steriade & Schein. INALTERABILITY IN CV PHONOLOGY 337

c. Blockage in Ik + kl from Assimilation lyi-t-kAfAtl ~ yikkAfAt 'open-PASSIVE-JUSSIVE' VC+C~ VCC (Kenstowicz 1982: 198) II \vi t k k Again, the facts show that it is the linking structure of long segments that determines Inalterability. 6 2.35. TIBERIAN HEBREW SPIRANTIZATION. In Tiberian Hebrew, the stops Ip t k b d gl became spirants postvocalically, except (as we now expect) in gemination. As the facts and arguments are essentially the same as in Tigrinya, I will forego a specific analysis here (see Malone 1976, Leben 1980, and McCarthy 1981a for details). A messy corner of the Hebrew facts is that heteromorphemic geminates also resist spirantization; McCarthy 1981a cites karat-tf 'I cut', where -tf is a suffix. Following McCarthy, I assume that Hebrew (like Classical Arabic) has a rule with the effect of the Obligatory Contour Principle, which applies before Spi­ rantization and bleeds it in the case of heteromorphemic geminates. 2.36. GLIDE FORMATION IN SANSKRIT. All of the cases of Inalterability noted so far involve the Inalterability ofgeminate consonants. Cases can also be found of Inalterability in long vowels. For example, in Sanskrit the vowels Ii u fl become glides Iy w rl when they precede a vowel. This gliding rule must be two-tiered-referring to the melodic tier to exclude application to la!, and to the CV tier to carry out the change V ~ C. The rule can be formalized as follows: (40) Sanskrit Glide Formation V~C __ V I [-low] A consequence of this formulation is that, in long Ii: u:/, the first half of the long vowel will not devocalize before the second half, producing *[yi], *[wu]. Such an application would violate the Linking Constraint: (41) VV ~ *C V V V i i This is not a meaningless prediction, given that [yi wu] are possible sequences in Sanskrit-deriving from the concatenation of the diphthongs lay awl with IiI and lui respectively. 2.37. GLIDE FORMATION IN MICMAC. Fidelholtz describes a rule of Micmac (Algonquian, Eastern Canada) whereby the vowel lui becomes a glide when word-final, as in la+u#1 ~ [aw#]. The rule resembles Sanskrit Glide For-

6 The discussion of this section holds for the Tigrinya dialect described in Pam 1973. In the dialect described by Leslau 1941, Spirantization applies obligatorily after vowels and optionally after glides as well. Spirantization after glides is problematic, since it can be stated as a one-tier rule with the environment [- cons] _0 See Steriade & Schein MS for a plausible account of these facts that preserves the predictions of the Linking Constraint. 338 LANGUAGE, VOLUME 62, NUMBER 2 (1986) mation in that the second half of a long lu:1 does not undergo it. This follows straightforwardly from the way in which Micmac Glide Formation must be stated: (42) V ~ C I V_ # I u In general, the Linking Constraint predicts that rules of glide formation will not have the effect of diphthongizing long vowels, which is surely the normal result. But in a version of CV theory without the Linking Constraint (Le. a theory in which association lines are interpreted non-exhaustively), special stipulations would have to be added to most rules of glide formation to keep them from applying to Ii: u:/. 2.38. NASALIZATION IN WESTERN MUSKOGEAN. Munro & Ulrich MS, and Ul­ rich 1986, point out an interesting case of Inalterability in the Western Mus­ kogean languages Choctaw and Chickasaw (Oklahoma). The basic content of what follows is taken from their work; I have added a specific analysis in the framework advocated here. Chickasaw and Choctaw have both nasal and oral vowels. Nasal vowels are not underlying segments, but derive from V +N sequences in preconsonantal position. The Nasalization rule results in alternations like the following, from Choctaw: (43) a. im-oka? 'his water' poss-water lim-tali?1 ~ f.·tali? 'his rock' poss-rock b. on-apa-h 'eat on' Loc-eat-VERB 10n-basli-hI ~ o.·baslih 'cut on' LOC-cut-VERB Observe that the vowel created by the merger of V + N is always long. I assume that this rule should be expressed as a mutual assimilation: the vowel takes on the nasality of the , while the nasal takes on the place and manner of articulation of the vowel. Both parts of the rule are necessary, since vowels are not generally nasalized before nasals in these lan­ guages. The mutual assimilation can be expressed formally if we assume that the melodic tier can be split into multiple sub-tiers, including one for nasality and one for the placelmanner features. (For discussion of multiple sub-tiers, see Goldsmith 1979, Clements Msb, Hayes 1986.) The rule would appear as follows: (44) Western Muskogean Nasalization [- nasal] [ + nasal] ~ [+ nasal] Nasal tier II ~ VCC ~ VC C CV tier II ~ [] [] [] ~ Place/manner tier INALTERABILITY IN ev PHONOLOGY 339

The formalism means 'Spread the nasality of a nasal consonant onto the pre­ ceding vowel, and the place and manner features of the vowel onto the C-slot of the nasal.' Nasalization would derive Choctaw f:tali? from lim-tali?1 as in Figure 8. IBI denotes the placelmanner features of Im/.

-n +n -n -n -n -n-n +n - n - n - n - n - n Nasal tier IIIIIII /'1 IIIII vee V eve ~ veeveve ev tier IIIIIII V IIIII B t a I ? t a I ? Place/manner (lim-tali?/) ([i:tali?]) tier FIGURE 8.

Note that the length of the nasalized vowel is a consequence of expressing the rule as mutual assimilation; the new vowel encompasses both CV units of the former V + N sequence. Since the Nasalization rule must mention association lines in its structural description, it should respect Inalterability. The data confirm this extensively. First, morpheme-internal geminates, which contain doubly-linked elements on both melodic tiers, do not participate in Nasalizaton; cf. hommah 'be red', hannah 'want'. Second, fake geminate nasals undergo Nasalization of their 'first halves' only; cf. o:nallih from lon-na!!ihl 'shoot on'. Finally, if a geminate nasal is heteromorphemic but derives from total assimilation, it is immune to Nasalization; cf. fammih 'he whips him', from Ifam-li-h/; in which the initial III of the active suffix -li has assimilated completely to the final Iml of the stem Ifam/. Derivations for each of the three classes of examples are shown in Figure 9.

/homma-h/ /on-naUi-h/ /fam-li-h/ be.red-VERB LOC- shoot-VERB whip-ACT-VERB vee vee vee Underlying forms l\j III III o m o n n a m I vee Assimilation IV of /1/ to /m! a m -n +n -n +n +n -n +n Creation of 1/\ III 1/\ multiple tiers vee vee vee IV III IV (B, D = oral o B oDD a B features of m, n) BLOCKED +n +n BLOCKED Nasalization ~ veeI V I o D [hommah] [6:naUih] [fammih] Output

FIGURE 9.

This account describes the facts of Choctaw. In Chickasaw, the data are the 340 LANGUAGE, VOLUME 62, NUMBER 2 (1986) same except for an interesting complication: if a Chickasaw V +N sequence precedes an oral stop, the nasal is assimilated to the stop and the vowel remains oral. Thus Chickasaw derives intali? 'his rock' from /im-tali?/, where Choctaw would derive f:tali? If the consonant following the nasal is not a stop, Chick­ asaw derives a long nasalized vowel, just as in Choctaw. The Chickasaw facts can be directly predicted by the Linking Constraint, assuming the following autosegmental formulation of the Nasal Assimilation rule: (45) Chickasaw Nasal Assimilation [+nas] [ +nas] Nasal tier I I CC ~ CC CV tier II ~ [] [=~~~t] g l=~~~t] Pl~~~manner This rule says: 'Spread the place/manner features of a stop onto a preceding nasal.' The rule in effect creates 'partial geminates'; i.e. doubly-linked struc­ tures on the place/manner tier. Since the rule of Nasalization requires a singly­ linked nasal in its structural description, it will be unable to apply to nasals that have been assimilated to a following stop; see Figure 10.

/im-tali?/ pass-rock 4his rock' VCC Underlying form III i m t -n +n -n Creation of III multiple tiers VCC III B t -n +n -n Nasal Assimilation III VCC I~ t (= [intD BLOCKED BY Nasalization LINKING CONSTRAINT FIGURE 10.

The analysis thus accounts for why Nasal Assimilation and Nasalization should apply in complementary environments-the first before stops, the sec­ ond before other consonants. Nasal Assimilation bleeds Nasalization by cre­ ating doubly-linked autosegments, which invoke the Linking Constraint. The example suggests that the Linking Constraint is valid for multiple melodic tiers as well as for intact melodies. 2.39. GLOTTAL FORMATION IN TOBA BATAK. In this Austronesian language of Sumatra, the voiceless stops /p t k/ surface as glottal stops whenever they precede a consonant. The relevant rule, which I call Glottal Formation, results INALTERABILITY IN CV PHONOLOGY 341 in numerous alternations as it applies across word boundaries; cf. haLak 'per­ son', haLa? batak 'Batak person'. Glottal Formation must be expressed on two tiers in order to identify both the class of stops and preconsonantal position: (46) Toba Batak Glottal Formation CC - son ] ~? I _1_ (applies across word [- cont boundaries) Since the rule contains an association line, we would expect it not to apply to true geminates. This is confirmed by the data of47a. Fake geminates, however, should undergo the rule, as in 47b: (47) a. True geminates rupput (*ru?put) 'grass' gotti (*go ?ti) 'follower' nakka (*na?ka) 'jackfruit' b. Fake geminates Ilap piI)goll ~ La? piygoL 'wipe off an ear' wipe-off ear ladat-tal ~ ada?ta 'our custom' custom-lpl. Ihalak korea! ~ haLa? korea 'Korean person' person Korea Toba Batak also has several assimilation rules that can create true geminates. For example, Inl is completely assimilated to any following consonant, as in baoa a[pp]eddek from Ibaoa an peddekl 'The man is short.' In addition, Ihl is assimilated to any preceding , as in marisa[pp]ita from Imarisap hital 'Let us smoke.' In both cases, the geminates resulting from complete assim­ ilation are inalterable, as the Linking Constraint predicts. (For arguments against the alternative hypothesis that Glottal Formation is ordered before the assimilation rules, see Hayes 1986.) These facts do not exhaust the Inalterability phenomena of Toba Batak, which extend as well to linkings created by partial assimilation. For a full account, see Hayes 1986.

2.4. RULES APPLYING ON ONLY ONE TIER. We have seen that at least ten pho­ nological rules must mention association lines in their structural descriptions, and respect Inalterability. The other side of the story is to show that, in rules which mention just one tier, and therefore lack association lines, Inalterability is not found. 2.41. RULES APPLYING ONLY TO THE CV TIER. One type of single-tier rule ap­ plies to consonants or vowels without regard to their quality, and thus would mention only the CV tier. For example, the Cluster Simplification rule of Sin­ hala mentioned above (cf. Feinstein) applies to any kind ofconsonant, and thus only needs to refer to the CV tier: (48) Sinhala Cluster Simplification (repeated from 3) C ~ 0 I C--]syl 342 LANGUAGE, VOLUME 62, NUMBER 2 (1986)

As the Linking Constraint predicts, Cluster Simplification applies freely to the halves of long segments. The inputs to the rule include most of the logical possibilities for linking structures. In the derivations of Figure 11, some of the geminates are derived by a rule that totally assimilates glides to preceding consonants.

(a) 'hill- (b) 'to get' (c) 'madman- (d) 'well-PL' SG-DEF' SG-DEF' CYCC.C-y CVC-C.CV CVCC.C-V CVCC Underlying forms I III II III VI II ~ II IIII (syllabified) ka nd u a gan n a pi sua lind CYCC.CV CVCC.CV Glide Assimilation III \j I II \V I kan d a pi s a CVC.CV CYC.CV CVC.CV CYC Cluster III II III II IIVI II I Simplification kan da gan na pi s a lind CVC Loss of stranded III segments lin FIGURE 11.

As can be seen, the syllable-final consonant in these examples is deleted, no matter how it is linked. Note that in (d), the Idl melodic segment stranded by Cluster Simplification remains unpronounced, by the convention noted under Rule 9 for Hausa. Rules that delete vowel positions regardless of their quality should also es­ cape Inalterability. We have already seen an example of this sort in Rausa. Micmac (cf. Fidelholtz) also has a 'quality-free' vowel deletion rule: (49) Micmac Apocope V~0/-# a. CVCVV~ CVCV 'bow-sa' III V IIII tapi tapi b. VCCVCV ~ VCCVC ~ VCCVC 'other-sa' IIIIIIIIIIIIIIII ikt iki ikt iki ikt ik In 49a, this rule deletes the second half of the final li:/, avoiding the effects of the Linking Constraint. There is additional support from Micmac for the idea that quality-free vowel deletion rules apply only on the CV tier. If the word-final vowel is short lui, the melodic segment that is stranded by Apocope is linked to a preceding Ikl by a special rule, producing a sequence which Fidelholtz transcribes as Ikw/: (50) CVCVCV ~ CVCVC ~ eve V c IIIIIIIIIIIIIII f\ pukuku pukuku pukuku = [pukukw] 'eye-sG' In Fidelholtz's linear analysis, this sequence derives from a rule that applies before Apocope, converting short lui to a glide in the environment k__#. INALTERABILITY IN CV PHONOLOGY 343

The CV analysis is preferable because it explains why this 'glide formation' applies in the same environment as Apocope, and why only SHORT lui undergoes it. Kenstowicz's 1970 account of Lithuanian phonology includes four separate rules that shorten long vowels and diphthongs in various environments. In all four cases, the rules are indifferent to the quality of the vowels involved; they can be stated in CV Phonology as rules that delete V positions on the CV tier. Since they are one-tier-only rules, the Linking Constraint correctly predicts that they will not involve Inalterability, and will thus freely delete the second halves of long vowels (for details, see Kenstowicz 80-85). 2.42. RULES APPLYING ONLY TO THE MELODIC TIER. Just as the purely quan­ titative rules applying only to the CV tier should escape Inalterability, so should the purely qualitative rules of the melodic tier. Lithuanian Backing (Rule 10) is an example: since its focus and environment are defined melodically, it can freely apply to long segments. Here are three further examples. Clements (MS a) analyses the phonology of Luganda, a Bantu language of East Africa, within a CV framework. Here Ik g/ are optionally palatalized to [c j] whenever they precede either the vowel Iii or the glide Iy/. In order to capture the natural class of high front [- cons] segments, one must explicitly avoid reference to the CV tier in the rule: (51) Luganda Palatalization

t - back - cons -son [][] =~~~ ~ + CO~ / __ + high + strld - back -cor Luganda allows for geminate stops Ikk gg/. As Clements shows, these are linked to the sequence VC, not CC, though this is not important to the present argu­ ment. Since Palatalization is optimally formulated NOT to mention the CV tier, it should be able to palatalize these geminates as well. This is in fact the case: (52) VCVVCV ~ VCVVCV III V IIII V I o lug 0 I u J i 'door' In West Greenlandic Eskimo (Rischel 1974), the vowels Ii i: u u:1 have low­ ered [e e: 0 0:] when word-final. The rule is qualitative in nature, and thus is optimally expressed on the melodic tier: (53) West Greenlandic Lowering [-cons] ~ [-high] 1__ # As a one-tier rule, Lowering is free of the Linking Constraint; it lowers both long and short vowels. There is no question ofRule 53's applying to word-final Iy wi, since these segments are lacking in West Greenlandic. In Yagua (Peba-Yaguan, Peru; Powlison 1962), la a:1 are raised to Ie e:1 re­ spectively in the environment y__Cy. The Cy cluster is apparently always derived by a rule of Metathesis from underlying lyCI. Though this is not cru­ cial, I assume that C in Cy is co-articulated with the glide, and is thus 344 LANGUAGE, VOLUME 62, NUMBER 2 (1986)

[ + high, - back]. The Raising rule can then be stated as follows: (54) Yagua la/-Raising

[ ~ ~~~s ] ~ [ =~a~k ]/[ ~ ~~~ ] -- [ ~ ~~~ ] Although other formulations are possible, it is clear that Raising is a purely qualitative rule, and should be stated exclusively on the melodic tier. It thus avoids the Linking Constraint, applying freely to long and short Ia/. 2.5. THE PREDICTIONS OF THE LINKING CONSTRAINT. To review: I have posited a number of criteria for whether a phonological rule must mention both the melodic and the CV tiers, and thus include association lines in its structural description. Ifa rule satisfies these criteria, the Linking Constraint (25) predicts that it will not apply to configurations containing more association lines than the rule specifies. As I have just shown, this theory predicts, for a large number of rules, whether Inalterability will be respected. I now attempt to evaluate the Linking Constraint further by clarifying the nature of its predictions. 2.51. A NON-PREDICTION. I wish to emphasize that the theory proposed here specifies only a SUFFICIENT condition for Inalterability. It does not claim that, whenever a rule is blocked from applying to long segments, we will necessarily find that the rule must be formulated to contain association lines on independent grounds. In fact, it is unlikely that a necessary condition for Inalterability will be found, and I will show here why this is so. Any theory that claims to have found a necessary condition for Inalterability runs up against the many rules that apply only to short segments of a certain quality. For example, in Lithuanian (Kenstowicz 1970), short 101 is lowered context-freely to Ia/, although long 10:1 remains. It is simple to write this rule in the theory I have proposed: (55) lo/-Lowering v I [~ ~~:~ ]~ [~ ~~:nd ]/_- The association line that lo/-Lowering mentions must be analysed exhaustively; hence the rule cannot analyse the doubly-linked structure of a long 10:/. But note that the only reason the linked V position need appear in the rule is to invoke Inalterability; no independent basis exists for predicting the Inaltera­ bility effect. A similar example is found in Berber (Saib 1976, Guerssel 1978), in which the stops Ip t k b d gl become spirants in all contexts except gemination; Le., only 'short stops' undergo the rule. Again, Inalterability must be stipulated by adding a singly-linked C to the rule environment. Although examples like the two just cited demolish the prospect of a theory that predicts all cases of Inalterability, they offer a consoling aspect: at least the Linking Constraint provides a way of expressing rules that apply only to short segments in a reasonably compact way. For example, if we were to do INALTERABILITY IN CV PHONOLOGY 345 without the Linking Constraint, the /o/-Lowering rule would have to be ex­ pressed as follows, where an association line terminated by an x indicates 'no association': (56) v -V- +backJ ~ [+IOW ] /- [ - high ~ - round Given that 'short segments only' rules are fairly common and natural, it would seem undesirable to have a theory which must express them with rules as complex as 56. A few other rules have been proposed in the literature which require that Inalterability be stipulated, but which are not simply 'short segments only' rules. Thus Harris 1982 provides an elegant account of Spanish Spirantization in which the rule essentially says: 'Spirantize a voiced stop provided it is not multiply-linked.' The rule unifies the various complex conditions on Spiran­ tization into a single, simple generalization. However, there is no reason to mention the linkages ofthe melodic autosegment in the rule other than to invoke Inalterability. Tuller's 1984 analysis of plural formulation in Hausa similarly includes association lines in a rule solely to invoke Inalterability. However, in general it appears that such cases are rare in comparison with those where Inalterability results from an independently motivated structural description. 2.52. SOME ADDITIONAL PREDICTIONS OF THE LINKING CONSTRAINT. Like any theory, the Linking Constraint should be evaluated not only on whether it predicts the existing data, but also on what it predicts not to exist. It makes substantive claims about what phonological rules can and cannot do-claims that are valid for the examples I have seen. In the phonological framework of SPE, or in a CV framework that lacks the Linking Constraint, it is very easy to write rules which, under my theory, are not linguistically significant gen­ eralizations. For example, if one assumes an SPE theory, with long segments interpreted as sequences, it is straightforward to write a fictional version of Klingenheben's Law (cf. 32 above), with the effects shown: (57) Klingenheben's Law II C ~ [ + son] / --]syl a. takta ~ tawta b. takka ~ *tawka Under a version of CV Phonology in which association lines are interpreted non-exhaustively, it is again easy to write a rule with the following effects: (58) Klingenheben's Law III C]syl I [- son] ~ [ + son] / __ a. CVCCV ~ CVCCV b. CVCCV ~ *CVCCV IIIIIIIIII II \J III \J I takta tawta ta ka ta wa 346 LANGUAGE, VOLUME 62, NUMBER 2 (1986)

Neither Klingenheben's Law II nor III can be expressed as single generali­ zations under the Linking Constraint. To the extent that we fail to find pho­ nological rules of this sort-in particular, rules modifying segmental quality, conditioned by syllable position, and affecting long segments-the Linking Constraint is empirically confirmed. Several other rule types could in principle falsify the Linking Constraint. These include: (a) rules affecting segment quality, triggered by adjacent V or C; (b) rules converting vowels of a given quality to glides; and (c) any rule of glide vocalization. To the extent that such rules fail to affect doubly-linked long segments, the Linking Constraint is supported. Finally, consider a rule type not yet discussed: two-tier rules that actually do alter only half of a long segment. Such rules are a logical possibility under the theory presented here, provided the following condition is met: They must apply ONLY to long segments, so that the multiple linkings will be mentioned in the structural description and not violate the Linking Constraint. One example of this sort is found in Attic and other Ancient Greek dialects (see Steriade): geminate Issl was simplified to lsi. The rule can be expressed as follows: (59) Iss/-Degemination C~gl _C

Vs Note that the association lines in the rule will match one-to-one with those of a geminate Issl, so the rule will not run afoul of the Linking Constraint. The double link in the rule is needed regardless of the Linking Constraint, simply to characterize the kind of segment to which the rule applies. The relevance ofthese cases is that the Linking Constraint makes predictions about what processes may occur together in a single rule. As an example, compare Rule 59 with a rule that simply deletes lsi before another consonant: (60) lsi-Deletion C-df/TC

s Like Iss/-Degemination, lsi-Deletion is a possible phonological rule, having actually occurred in the history of French (de Chene & Anderson 1979). Now in a theory with no Linking Constraint, Rules 59-60 are collapsible; indeed, the second expresses the structural change of the first. In contrast, the Linking Constraint requires them to be expressed separately: since the linkings of the lsi melodic segment must be interpreted exhaustively, neither rule can do the work ofthe other. Note that we can often find independent evidence to indicate whether two rules should be collapsed:"'-e.g. similar history, shared ordering, shared optionality, and shared exceptions. Thus, if cases where we must col­ lapse rules like 59-60 are missing (and I believe they are), we have indirect support for the Linking Constraint. The above prediction can be restated in a different way: the only two-tier INALTERABILITY IN CV PHONOLOGY 347 rules that affect long segments will be those that apply ONLY to long segments, and not to phonetically similar non-identical clusters. In fact, this property holds for all the rules with which I am familiar that are two-tiered and affect halves of long segments. Examples from the literature are (a) Icelandic Pre­ aspiration, which converts Ipp tt kkl to Ihp ht hkl, but leaves non-identical stop sequences alone (see Thrainsson 1978 for a formal account); (b) a rule of Weak­ ening in Maxakalf (Brazil; Gudschinsky et al. 1970), which converts the first half of a geminate obstruent into a homorganic glide; (c) a rule ofDe-aspiration in Ancient Greek, which removes aspiration from the first half of a geminate stop (Steriade, 39-40); and (d) a rule degeminating the laryngeal and pharyngeal glides of Tiberian Hebrew (Rappaport 1981, Kaye & Lowenstamm MS). The result ofthis discussion is that the Linking Constraint predicts a narrower class of rules expressing linguistically significant generalizations than other theories. The rules I have seen are all encompassed within this narrower span. 3. EARLIER RESEARCH ON INALTERABILITY. The notion that Inalterability is predictable from general principles was first suggested by Guerssel 1977, 1978. His principles, which covered Integrity as well, were stated within a linear phonological framework. Steriade 1982 was the first to formulate Integrity and Inalterability constraints within the framework of CV Phonology. She showed that most of the explan­ atory burden in these areas could be carried by independently needed postulates of CV theory; thus the entire set of Inalterability principles would not have to be stipulated, as Guerssel had done. In addition, Steriade adduced strong em­ pirical evidence favoring the CV approach to Inalterability over the linear one. Steriade & Schein 1984 propose a different CV theory ofInalterability, which I will now discuss. Their theory distinguishes more accurately than the theory of Steriade 1982 between rules that respect Inalterability and those which do not. The theory is based on the following principle: (61) A structure-dependent rule will fail to affect the contents of a seg­ mental matrix unless all skeleton slots [i.e. segments on the CV tier-BH] associated to it meet the structural description. (265) A rule is defined as 'structure-dependent' if it requires access to syllable struc­ ture or to the CV tier. Here is an example of how this principle would handle an instance of Inalterability. Persian lvi-Weakening, restated below, would be unable to affect true geminate Ivvl because the second C-slot of the geminate does not 'meet the structural description' of the rule; i.e., it does not imme­ diately follow a short vowel: (62) a. Persian lvi-Weakening b. V CC IT l\j A v V C II v~wl[] By itself, Principle 61 would disallow rules that apply only on the melodic tier. For example, Lithuanian Backing (Rule 10) could not apply to long leel 348 LANGUAGE, VOLUME 62, NUMBER 2 (1986) because the first V-segment linked to the lei melody would not directly precede the vowel or glide that triggers the rule. To avoid this difficulty, Steriade & Schein 1984 add a further principle which renders the CV tier 'invisible' in certain cases: (63) In the application of a rule, skeletal information is accessible just in case the structural description ofthe rule makes reference to the skel­ eton [= CV tier-BH] or to syllabic structure. (286) Since Lithuanian Backing does not refer either to the CV tier or to syllabic structure, it escapes the effects of Steriade & Schein's Inalterability condition. Together, Principles 61 and 63 make predictions fairly similar to those made by the Linking Constraint. I will now discuss two reasons for preferring my proposal. First, I believe that the Linking Constraint is a considerably simpler answer to the Inalterability problem than what Steriade & Schein propose. It is a likely candidate for a general principle of phonological theory, in that it establishes how autosegmental rules apply to forms-a question that must be resolved in any event. Under the Linking Constraint, it is a natural consequence of the theory that 'melody-only' rules should escape Inalterability. In contrast, Ste­ riade & Schein must directly stipulate this. Second, the Linking Constraint is broader in scope, in that it covers rules affecting the CV tier as well as the melodic tier. It thus correctly predicts Inalterability in cases like Glide Vocalization in Berber and Classical Arabic, or Glide Formation in Sanskrit and Micmac (cf. §§2.32, 2.33, 2.36, 2.37). As can be seen by inspecting these rules, Steriade & Schein's principles fail to predict Inalterability in these cases. Steriade & Schein 1984 attempt to remedy the problem by making syllabicity a property of both the CV and melodic tiers. However, a-priori this seems an undesirable redundancy. Steriade & Schein consider it an advantage of their proposal that it predicts that mismatches of association lines in the context, rather than the focus, of a rule will not block rule application. Thus they observe that a rule of IA/­ Rounding in Tigrinya, which rounds IAI to I'JI before a tautosyllabic Iw/, is not blocked when the Iwl forms part ofa true geminate; cf. s.Jwwige from ISAwwigel 'call-PERFEcT-3sg.MAsc'. This would appear to violate the Linking Constraint. However, as Steriade & Schein (MS) point out, the full range of facts is quite complex: the rule actually can affect IAI to the right as well as to the left of I wi, and applies optionally even when the tautosyllabicity condition is not met. Further, in its mirror-image mode, the rule is subject to a strange restriction: assimilation in one direction precludes assimilation in the other. This latter fact strongly suggests Inalterability; the extra association line created by one it­ eration of the rule would block the second iteration. No fully adequate analysis of all the facts yet exists, but the murkiness of the data suggests that they cannot stand as a clear counter-example to the Linking Constraint. I am aware of one example that suggests that the Linking Constraint does hold for segments appearing in the context of the rule. Gray 1985 notes that Old Rumanian lal was raised to shwa in the context __me, where C is any consonant other than a nasal. Later the rule generalized, making all vowels INALTERABILITY IN CV PHONOLOGY 349

[+high] in the same context. The rule can be expressed straightforwardly under the assumption of a separate [nasal] tier (cf. §2.38): (64) Rumanian Raising [ + nas] Nasal tier I v C CV tier I a ~ a / __ Place/manner tier (Later: structural change becomes [] ~ [ + high].) A nasal cluster would block the rule, since the [ +nas] autosegment would be doubly linked and unable to match up with the singly-linked autosegment in the structural description. It should be noted, however, that this rule too has its complications (cf. Gray), and clearly cannot alone decide the issue of contextual Inalterability. 7 4. CONCLUSIONS. The theory I have presented can be thought of as an am­ plification of Kenstowicz's 1970 typology of how phonological rules refer to length. He contended that rules can be roughly divided into two kinds: quality rules, which treat long segments as units; and quantity rules, which treat long segments as sequences. CV Phonology provides an explicit formal implemen­ tation of Kenstowicz's suggestion, thus overcoming Fidelholtz's objection that Kenstowicz's claim had no theoretical expression. In addition, the theory I have proposed here suggests that there is a third category of rules, which refer both to quantity (in our terms, to positions on the CV tier) and to quality (to melodic segments). It is this third category that respects Inalterability. The existence of 'quantity/quality' rules, and the fact that such rules show a very special property, provides a further argument that CV Phonology is the correct formal expression of Kenstowicz's original idea. The other part of my proposal, which is clearly more speculative, was to try to derive the Inalterability of quantity/quality rules more or less as a theorem. The assumption that was required, i.e. the Linking Constraint, seems a plau­ sible candidate for a universal principle, simply because it is primitive in char­ acter and involves no arbitrary stipulations. To my knowledge, it is the most general solution available that fits the data.

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7 Since the appearance of Steriade & Schein 1984 and the original presentation of the present paper as Hayes 1984, Steriade & Schein MS have developed yet another theory of Inalterability, which appears in some respects to be a synthesis of the two earlier proposals. Although their proposal is of great interest, it is not clear to what extent the new theory overcomes the objections made above to the older one. 350 LANGUAGE, VOLUME 62, NUMBER 2 (1986)

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