OT captures the synergistic character of constraint conjunction by providing tools for combining linguistic scales; see the literature just cited for discussion.
(ii) So far, we have only considered candidates where the underlying RTR segment is also RTR at the surface. But imagine a candidate derived from /xayyaaT/ with RTR detached from the final /T/ and re-attached to the initial /x/. This output would equally well satisfy RTR-Left, and it would do so without associating RTR to y, thereby sparing violation of RTR/Hi&Fr. Facts like this show the need for a high-ranking faithfulness constraint Stay-RTR, the symmetric counterpart of Stay-ATR. In particular, Stay-RTR crucially dominates RTR/Hi&Fr.
(iii) OT proposes to derive the properties of underlying structures from the same grammar that determines surface structures, so a full analysis of the phonology of RTR would have to define its role in the phonemic system. The reasoning behind this and the necessary analytic techniques can be found in the OT literature, including Prince and Smolensky 1993: Chapt. 9; McCarthy and Prince 1995: 279–281; Kirchner 1995; and Itô, Mester, and Padgett 1995. On this, cf. Stampe 1972.6 Assume that Palestinian has a class, X, of segments that never contrast in RTR. (Traditionally, X is said to be [–coronal].) In OT terms, that assumption motivates something like the following statement: the structural constraint *[RTR, X] crucially dominates the faithfulness constraint Stay-RTR. We have, however, previously established that Stay-RTR dominates RTR/Hi&Fr, which itself dominates RTR-Right. By transitivity of domination, then, *[RTR, X] must dominate RTR-Right — which means that the segments in the X class should be blockers of rightward RTR harmony. But the only actual blockers of rightward harmony are the high front segments, already given by RTR/Hi&Fr. Therefore, we have to conclude one of two things: (i) the class X is null, and in principle any segment can contrast in RTR; or (ii) the constraints or their rankings are wrongly understood.
In fact, the set X may indeed be null — the observations are somewhat delicate to interpret. Though the principal bearers of RTR contrast in Palestinian Arabic are the historical “emphatic” consonants, all of which are coronal obstruents, there is a small but stable body of words with contrastive RTR but no coronal obstruent: alla ‘Allah’, almaani ‘German’, lamba ‘lamp’, baaba ‘Pope’, yaaba ‘oh, my father!’, yamma ‘oh, my mother!’, mayyi ‘water’. This set includes native words and assimilated loans (witness the b for p in baaba, from Italian). The existence and stability of this class may indicate that the historical situation is no longer pertinent, and that there is no synchronically valid generalization about X.
If further empirical investigation should confirm the validity of X, however, then we must re-examine some of the constraints and ranking results. In particular, we should question the sub-hierarchy Stay-RTR >> RTR/Hi&Fr, which lies at the core of the presumptive ranking paradox. This sub-hierarchy derives from the assumption that harmony is based on alignment and that good alignment would be achieved just as well by moving (or deleting) RTR as by spreading it, were it not for the intervention of high-ranking Stay-RTR. But alternative conceptions of harmony are possible and may be desirable; for example, the view of harmony as a perceptual salience effect, mentioned in fn. 11, puts harmony securely into the faithfulness system: if RTR is present in the input, then it must be spread in the output. This view of harmony renders Stay-RTR irrelevant to determining the scope of spreading, and so it eliminates the ranking paradox.
It is worthwhile to reflect a bit on the schema for a process-specific constraint interaction (). Suppose top-ranked Mi is also subject to some specific limitation expressed by a constraint L. This means that L dominates Mi, by familiar reasoning. But constraint domination is a transitive relation. Since we already have Mi >> Mj, it follows that L dominates Mj. From these considerations, we obtain the following schema for process-specificity in OT, due to Alan Prince (p.c.):
() General Schema for Process Specificity
L >> Mi >> C >> Mj >> F
Any constraint that dominates Mi also dominates Mj, because constraint ranking is a strict order on the constraints of UG — it is an irreflexive, asymmetric, and transitive relation. Thus, as Prince observes, it is a general fact about OT that no constraint can be process-specific to just the Mi-related process in (); it must, in principle, be able to influence the Mj-related process as well. Whether or not this ability-in-principle is actually observable depends on details of the particular phenomena involved. Observations will be easiest to make when the two processes are similar, as in Palestinian Arabic.
Prince goes on to say that the general schema () motivates a subset criterion for process-specificity in OT: if Mi >> Mj >> F, then the set of constraints that can, in principle, impinge on Mi is a subset of the set of constraints that can, in principle, impinge on Mj. The subset relation can be improper, if C=Ø in (), and it can be trivial, if L=Ø. To put the matter differently, there is a sense in which the Mi-related process is more robust — or not less robust — than the Mj-related one.7 These are not special stipulations that OT makes about process-specificity. Rather, they derive from the most fundamental element of the theory, constraint ranking.
This result is of more than passing interest, for a couple of reasons. For one thing, a parametric rule-based theory, incorporating statements like (), makes no such claim about process-specificity. Since each process includes constraints as arbitrary parameters, there is no prediction about how constraints on two different processes in the same grammar will be related. In this respect, the parametric rule-based model is less restrictive than OT, in that it incorporates nothing like the subset criterion. Indeed, given the freedom of parameter setting that is intrinsic to the approach, it is impossible to see how the parametric model could even stipulate, much less derive, the subset criterion.
For another, the subset criterion bears directly on one of Davis’s challenges to OT (p. 495): “Relatedly, how would Optimality Theory analyze a possible dialect in which rightward spread of emphasis is subject to one grounded condition whereas leftward spread of emphasis is subject to a different grounded condition? If such a dialect were reported, it would be potentially problematic for an Optimality Theory account.” Indeed it would. If the constraints introduced in the previous section are rightly conceived, then the logic of the subset criterion predicts that no grammar could achieve the type of process-specificity described in this hypothetical case.
To put the issue in less abstract terms, let us examine a grammar for the hypothetical system Davis describes. Rightward harmony is limited by just one constraint (say, RTR/Hi) and leftward harmony is limited by another (say, RTR/Fr). Thus, all and only high segments block rightward harmony, while all and only front segments block leftward harmony. The rankings required are these: