a. RTR/Hi >> RTR-Right High segments block rightward harmony.
b. RTR-Right >> RTR/Fr Front segments don’t block rightward harmony.
c. RTR/Fr >> RTR-Left Front segments block leftward harmony.
d. RTR-Left >> RTR/Hi High segments don’t block leftward harmony.
Following the chain from (a) to (d), we see that the rankings are circular, contradicting the fundamental premise that constraint ranking is a total ordering. Therefore, no grammar meeting all of () can exist in OT. To put the result more intuitively, the set of constraints impinging on rightward harmony is not a subset or superset of the set of constraints impinging on leftward harmony, so the subset criterion is not met, either way. The predicted impossibility of this hypothetical system shows that there is truly a restrictive claim here; the subset criterion sets an irreducible limit on how specific a constraint on a process can be in OT.
This argument shows that the definition of ranking, which is the central element of OT, has highly restrictive consequences for the character of process-specific constraint interactions. Related processes are ranked for a kind of robustness that may be seen from the subset relation among any constraints that limit their effect. In contrast, parametric rule-based theories make no such prediction. If arbitrary process-specific constraints are included as parameters in the processes themselves, as in (), then any process can be governed by any constraint, without regard to other processes coexisting in the grammar. Davis’s example of this type of process-specificity is hypothetical, while both of the real dialects he discusses meet the subset criterion (see sections 2 and 4). The inference, then, is that the OT model of process-specificity is not only more restrictive but also empirically correct.8 The reviewer’s comment confounds description with explanation. Properly speaking, an OT grammar is a ranking of universal constraints, like (), while a parametric rule-based grammar consists of (an ordering of) expressions like (). Process-specificity must meet the subset criterion in the OT grammar, but not in the parametric rule-based one. These are established results about the kinds of explanations the two theories do or do not provide. They are not touched by the observation that, descriptively, a multistratal implementation of OT may be able to simulate some kinds of process-specificity without the subset criterion. The parametric rule-based theory makes no such restrictive prediction, with or without multiple strata.
Two further remarks. First, it is by no means obvious that multi-stratal OT is even necessary; much of the prima facie evidence for it has been reanalyzed in monostratal terms by Benua (1995, forthcoming) and others. Second, when all the constraints of UG are considered, the differences in ranking between the two stratal grammars that are necessary to simulate process-specificity will very likely have unintended side-effects, making exact simulation of the rule-based analysis impossible.
At first glance, rightward RTR harmony in Northern Palestinian Arabic looks like it does not meet the subset criterion. (Leftward harmony is identical to Southern Palestinian and will not be discussed further here.) Two processes of rightward harmony are involved, with apparently disjoint conditions on applicability. (As in section 2, I cite the examples directly from Davis, who in this case bases his work on the important contributions of Younes 1982, 1993 and Herzallah 1990, which should be consulted for many additional details and insights.)
a. To following sequence of a and laryngeals ( , h) or pharyngeals ( , )
maSla aSa aaha
Ta nak Sa nak
Sa an Sahhab
b. Blocked by following high segment
Si a kaTTuu a
There is local rightward harmony onto the next vowel nucleus, including any intervening consonant, as long as no violations of RTR/Hi ( *[hi, RTR]) ensue. There is also unbounded rightward harmony onto a sequence of low segments, a class that in Palestinian includes the vowel a and the laryngeal and pharyngeal gutturals (McCarthy 1994). Observe from (b) that long-distance harmony, which targets only low segments, is supererogatorily blocked by high segments as well.
In Davis’s analysis, there are two separate rules of rightward harmony, each with its own target constraint included in the formulation. Local harmony applies first, and it includes among its parameters the constraint RTR/Hi. Long-distance harmony applies to the output of local harmony, and it parametrically includes the constraint RTR/Lower-VT (if [RTR], then Lower-VT), which requires the segment targeted by spreading to bear a Lower Vocal Tract node — i.e., it must be a pharyngeal segment (a low vowel or a guttural consonant).9 Given Node Generation, though, RTR/Lower-VT should be vacuous as a target condition on long-distance RTR spread. Since Node Generation always supplies Lower-VT as needed, how could this constraint ever block anything? In response, Davis (electronic communication, 4 February, 1996) has suggested that Node Generation applies in situations involving antagonistic target conditions (like RTR/Hi) but not sympathetic ones (like RTR/Lower-VT). This move does not seem to be independently motivated, though.
For simplicity, I adopt the null hypothesis, that specifications for RTR and Lower-VT are feature-geometrically independent, so a segment can be just RTR (S), just Lower-VT (), or both (). If the non-null assumption should turn out to be correct, however, then RTR/Lower-VT must be replaced. Two plausible alternatives are: a constraint defined as “if RTR, then primary pharyngeal,” which correctly limits the RTR class to the gutturals and a; or Dep(Lower-VT), which militates against “adding” Lower-VT to a segment (cf. McCarthy and Prince 1995).
Concerning Northern Palestinian, Davis asks (p. 495): “how would Optimality Theory account for the fact that the two different rules governing rightward spread of [RTR] ... are subject to two different target conditions?” If this characterization is correct — two different processes subject to two different constraints — then the constraints governing one process are not a subset of the constraints governing the other. At first glance, then, it appears that the subset criterion is not met in Northern Palestinian, because local rightward harmony is governed by one constraint, RTR/Hi, and long-distance rightward harmony is governed by a different constraint, RTR/Lower-VT. Since the subset criterion is an unavoidable consequence of constraint ranking, this result imperils the very foundations of OT.
The first glance, though, gives way on closer inspection. Long-distance rightward harmony can be governed by bothRTR/Hi and RTR/Lower-VT, as the subset criterion predicts. The situation becomes clearer once we get past the names of these constraints to their actual substance. RTR/Hi says “if RTR, then not high,” while RTR/Lower-VT says “if RTR, then Lower-VT”. Since the segments with a Lower-VT node (a and the gutturals) are a proper subset of the non-high segments, any segment that satisfies RTR/Lower-VT will also satisfy RTR/Hi. In (), I have made this same point in more familiar terms, so the syllogistic character of the argument is clear: