Disjunctive nonordering?

When I wrote that “[c]rucial nonordering of rules has probably also been explicitly discussed and has possibly also been rejected somewhere in the rule-ordering literature“, what I meant by “crucial nonordering of rules” was a situation in which two rules directly interact (i.e., they are in a potentially feeding or bleeding relationship with respect to at least some subset of forms) but are crucially unordered with respect to each other — perhaps leading to optionality, as crucial nonordering of constraints does in OT.

Bob Kennedy then asks:

Out of curiosity, would disjunctive rule-ordering be an example of non-ordering?

I think not, but I can sort of see how disjunctive ordering might be thought about in this context. This is the topic of this post.

Even though the order between disjunctively ordered rules is usually not extrinsically determined, disjunctive ordering is still crucial ordering — albeit a very special case thereof. Not only must one rule A precede the other rule B, it must be the case that if A applies, application of B is blocked.

But what determines disjunctive ordering? Everybody agrees that two disjunctively-ordered rules must be in a special formal relationship; specifically, the contexts of applicability of one (rule A) must properly include the contexts of applicability of the other (rule B).1 A typical way to put this is that A is the ‘special’ rule and B is the ‘general’ rule, and I will use this terminology here. Kiparsky (1973) maintains that the disjunctive order between special and general follows from the Elsewhere Condition (EC). Here is the revised version of the EC from Kiparsky (1982:136).2

The Elsewhere Condition

Rules A, B in the same component apply disjunctively to a form Φ if and only if
(i) The structural description of A (the special rule) includes the structural description of B (the general rule)
(ii) The result of applying A to Φ is distinct from applying B to Φ
In that case, A is applied first, and if it takes effect, then B is not applied.

Kiparsky held the view that only some cases of crucial rule ordering follow from principles like the EC — in his view, extrinsic ordering was still necessary. One of the extraordinary things about this position is how entirely unnecessary it seems to be, since the right interaction between special and general is easily expressible in terms of straight ordering. As Prince (1997) puts it:

This kind of effect, by which ‘special’ imposes itself on ‘general’ through ordinary rule-application, is predicted by ordering theories like SPE: there is no obvious need to re-predict it.

This point can be illustrated with the following two (hypothetical) rules.

Rule A: Pre-sonorant voicing

[–son] → [+voi] / __ C[+son]

Rule B: Pre-consonant devoicing

[–son] → [–voi] / __ C

These two rules are in the requisite inclusion relationship for the EC: the contexts of application of Rule A properly include the contexts of application of Rule B. The EC thus determines that Rule A precedes Rule B, and if Rule A applies, Rule B is blocked from applying. So, in a context where both rules are applicable (e.g., /apna/), Rule A applies (giving abna) and Rule B, even though applicable, is blocked from applying. With a form like /abna/, Rule A applies vacuously and this vacuous application is enough to block application of Rule B.3

Prince’s point is that the same result is possible with straight ordering, with Rule B preceding Rule A. In the case of /apna/, Rule B applies vacuously and Rule A then applies, giving abna. With /abna/, Rule B applies to give intermediate apna and Rule A applies to that result, giving abna. The outputs in both cases are the same as they are in the disjunctive ordering analysis.4

There are, of course, some differences between the straight ordering and disjunctive ordering analyses. One is that each requires a specifically different order between A and B. Disjunctive ordering requires that A precede B; if there is any evidence (e.g., via transitivity) that the opposite order holds, this analysis needs to be reworked. Likewise, straight ordering requires that B precede A, and any evidence to the contrary requires accomodation.5

Another difference is that the straight ordering analysis predicts that forms like /abna/ will, during the course of the derivation, become apna before settling back to abna. This means that some other rule could intervene between B and A, treating the underlying-and-surface [+voi] b as if it were [–voi] p during that fleeting point of the derivation. To the extent that such ‘super-opaque’ interactions do not occur, disjunctive ordering has an advantage over straight ordering (though one would then presumably want to carefully examine the extent to which similar super-opaque interactions occur with rules that are not in a proper inclusion relationship, and the extent to which such interactions are justified).

A final difference is that only one order (A before B) is possible with disjunctive ordering whereas both are in principle possible with straight ordering.6 Under the straight ordering view, however, A (special) before B (general) would result in B completely hiding the effects of A. But, again, some intervening rule could crucially depend on the result of A’s application in the super-opaque manner described above.

I think that these last two differences between disjunctive ordering and straight ordering clarify how disjunctive ordering could be thought of as a case of nonordering: the EC effectively disallows certain types of interactions among certain types of rules. This is not ‘crucial nonordering’ in the way I originally intended it — I’m still not exactly sure what would be — but it has that kind of smell.


1 I write “contexts of applicability” instead of “structural description” since the latter term is somewhat ambiguous in the relevant literature, depending in part on whether rules are written in the usual ‘A → B / C__D’ format or the notationally equivalent ‘CAD → CBD’ format. (See p. 9, fn. 7 of Koutsoudas et al. (1974) and p. 7 of McCarthy’s (1999) discussion of Halle & Idsardi (1997).) back

2 Kiparsky’s original EC required that rules A and B be independently adjacent in the ordering and that “the structural changes of the two rules are either identical or incompatible” (Kiparsky 1973:94, emphasis added). Both the rule-adjacency requirement and the identical-changes allowance have to do with the fact that the EC grew out of SPE‘s more restricted parenthesis notation. The rule-adjacency requirement seems to have been silently dropped in the subsequent literature on the EC (though I’d love to know about any work that specifically addresses this point). The identical-changes allowance was intended to accomodate the one sort of case in which the disjunctive application interpretation of the parenthesis notation is crucial: stress rules, which are now handled metrically. back

3 Even if vacuous application were not possible here, Halle (1995:28) has argued that “strings having the same form as the output of [Rule A] are prohibited from undergoing [Rule B]”. See also Halle & Idsardi (1997:345ff) and the discussion thereof in McCarthy (1999:7-8). back

4 This was in fact exactly the kind of special-general interaction predicted by the Proper Inclusion Precedence Principle (PIPP) of Koutsoudas et al. (1974). (Note that A is the general rule and B is the special rule here.)

Proper inclusion precedence: For any representation R, which meets the structural descriptions of each of two rules A and B, A takes applicational precedence over B with respect to R if and only if the structural description of A properly includes the structural description of B. (p. 8)

The PIPP thus states that general-before-special order is universal, and that there is no disjunctive blocking; the EC states that special-before-general order is universal, and that there is disjunctive blocking. But the real difference was one of theoretical outlook: Koutsodas et al. maintained that all rule ordering follows from principles like the PIPP. The fact that we all know about the EC (and who Kiparsky is) and that fewer of us know about the PIPP (or who Koutsodas et al. are) shows whose views prevailed. back

5 Unfortunately, in neither case can one really say that the counterevidence confirms the correctness of the opposing analysis; for example, the EC can be easily defeated, as Prince (1997) notes, by careful rule formulation. back

6 Though not if general-before-special order follows from the PIPP; see fn. 4 above. back

References cited

Halle, M. 1995. “A letter from Morris Halle: Comments on Luigi Burzio’s ‘The rise of optimality theory’.” Glot International 1:9/10, pp. 27-28.

Halle, M. and W. Idsardi. 1997. r, hypercorrection, and the Elsewhere Condition. In Derivations and Constraints in Phonology, I. Roca, ed., Oxford: Clarendon Press, pp. 331-348.

Kiparsky, P. 1973. “‘Elsewhere’ in Phonology.” In A Festschrift for Morris Halle, S. Anderson and P. Kiparsky, eds., pp. 93-106.

Kiparsky, P. 1982. “Lexical Phonology and Morphology.” In Linguistics in the Morning Calm, The Linguistics Society of Korea, ed., Hanshin Publishing Co.: Seoul, pp. 3-91.

Koutsoudas, A., G. Sanders, and C. Noll. 1974. The application of phonological rules. Language 50, 1-28. (Drafted 1971.)

McCarthy, J. 1999. “Appendix: A Note on Boston r and the Elsewhere Condition.” http://people.umass.edu/jjmccart/appendix.pdf.

Prince, A. 1997. “Elsewhere and Otherwise.” ROA-217, Rutgers Optimality Archive, http://roa.rutgers.edu/.

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