Shifting Interactions and Countershifting Opacity: A Note on Opacity in Harmonic Serialism

McCarthy (2008) and Elfner (2016) have shown that Harmonic Serialism (HS; McCarthy 2000, 2016), a serial variant of Optimality Theory (OT; Prince and Smolensky 2004), can generate certain opaque interactions between stress and vowel deletion or epenthesis that seem to pose a challenge to Parallel OT.¹ At the same time, McCarthy (2000, 2007) has argued that HS is unable to generate canonical cases of counterfeeding and counterbleeding opacity.² Given our current understanding of opacity, this is a mystery: the opaque interactions discussed by McCarthy and Elfner are not of any familiar type (counterfeeding, counterbleeding, or any other type in Baković 2007, 2011), and it remains unclear whether they are isolated cases or instantiations of a yet unknown class of opaque interactions.

In this squib, I will argue that there is indeed a generalization regarding a class of opaque interactions that HS can generate, and that at least the stress-epenthesis interactions discussed by Elfner, as well as additional opaque interactions discussed here, are special cases of this general class. The new generalization, given in (1), will rely on terminology regarding pairwise process interactions that includes the new terms shifting and countershifting.

A process

is said to shift a process if does not feed or bleed but still affects ’s application by making it apply in a different way. Countershifting is the opaque counterfactual inverse of shifting. The term countershifting will be shown to fill a basic gap in the traditional taxonomy of opaque process interactions into counterfeeding and counterbleeding, a gap already identified by Kiparsky (2015).

The new generalization in (1) will be developed in a few steps. In section 2, I will introduce the new terms shifting and countershifting. In section 3, I will compare the ability of HS to generate a simple case of countershifting with its inability to generate a canonical case of counterbleeding. I will explain why the difference between shifting and bleeding is responsible for this expressive difference. In section 4, I will illustrate the generality of countershifting opacity using several attested examples of countershifting from morphophonology. In addition, I will present a proof-of-concept HS analysis of a case of countershifting opacity involving reduplication. In section 5, I will summarize my conclusions.

As noted by Kiparsky (2015:15), the traditional taxonomy of pairwise process interactions into (counter)feeding and (counter)bleeding is incomplete, as it ignores attested interactions where a process

neither feeds nor bleeds another process but still affects ’s application. The derivation table in (2) illustrates.

In (2), a process of APOCOPE deletes a word-final vowel and is followed by a process STRESS that assigns stress to the penultimate syllable. This interaction of APOCOPE and STRESS is not a feeding interaction, because APOCOPE does not create any additional inputs to STRESS. Neither is it a bleeding interaction, because APOCOPE eliminates no potential inputs to STRESS. Instead, STRESS applies regardless of the application of APOCOPE, but APOCOPE still affects it by making it apply to a different syllable. Interactions of this nature that cannot be described using the notions “feeding” or “bleeding” have been discussed in Zwicky 1987 and Baković and Blumenfeld 2020, where they are referred to as transfusions (a term Zwicky (1987) attributes to an unpublished paper by Donald Churma).³ Here, I will refer to interactions as in (2) using the term shifting, because APOCOPE can be thought of as shifting the locus of application of STRESS.

Derivation table (3) shows the reverse ordering of the two processes.

Here, APOCOPE applies after STRESS and makes STRESS opaque: even though STRESS targets the penultimate syllable, stress falls on the final syllable on the surface. Following the same reasoning regarding feeding and bleeding as before, this opacity is not a case of counterfeeding or counterbleeding (neither is it an opacity of any other type identified in Baković 2007, 2011); I will refer to it as countershifting.⁴

It will be useful to give more precise working definitions of shifting and countershifting to make it easier to identify and label new interactions of this type.⁵ In the following definitions, I use φ to denote a phonological representation, which will typically be the input to the derivation, and X(φ) to denote the result of applying the process X to the representation φ. A proposed working definition of shifting is given in (4).

According to this definition, an interaction between a process

and a later process is considered a shifting interaction if it meets the following conditions. First, the earlier process applies nonvacuously to the input (4a). Second, the later process would have applied nonvacuously to the input had it applied first (4b). This condition excludes the possibility that the interaction is a feeding interaction, because otherwise the context for would have been created by rather than being present in the input. The next condition is that still applies nonvacuously after the application of (4c). Given this condition, this is not a bleeding interaction, because otherwise would have removed the context for , preventing from applying. Finally, the order of application of and matters, so the two interact. Taken together, we can interpret these conditions as follows: can apply either before or after , and nevertheless the early (nonvacuous) application of results in a nonvacuous interaction. The interaction in (2) meets these conditions, assuming that is POCOPE and is STRESS: APOCOPE applies nonvacuously to the input, STRESS can apply nonvacuously to the input or after APOCOPE, and applying both in the opposite order would have yielded the different output [CVCC].

We can define countershifting as the opaque counterfactual inverse of shifting, as in (5). The interaction in (3) meets this definition, assuming that

is STRESS and is APOCOPE, since we have just seen that APOCOPE would have shifted STRESS had it applied first. This working definition of countershifting will be used in the discussion of HS, to which I turn next.⁶

HS (McCarthy 2000, 2016) is a serial version of OT. Like Parallel OT, an HS grammar includes one set of ranked, violable constraints. Unlike in Parallel OT, computation is serial. GEN, which generates output candidates, is limited to changing the input by at most one atomic change at a time (epenthesis, deletion, feature change, etc.). At each step of the derivation, EVAL selects the most harmonic candidate as the output, which then serves as the input for the next step. GEN and EVAL loop until convergence.

In HS, the constraint ranking determines the order of operations. As an example, consider a hypothetical language with the following two processes: palatalization of /k/ before /i/ and high vowel deletion in a nonfinal open syllable. Assume an HS-based grammar where the markedness constraint that triggers palatalization is *ki and the constraint that triggers high vowel deletion in nonfinal open syllables is *iCV (the constraints in this section are taken from McCarthy’s (2007) discussion of Bedouin Hijazi Arabic, which will be reviewed below). Consider the hypothetical underlying representation (UR) /kirmila/, to which the two processes apply without interacting, yielding the output [k^jirm.la]. If *ki outranks *iCV, palatalization would apply first. In the first step of the HS derivation, given in (6), there would be at least three output candidates: the faithful candidate (6a), the candidate in which palatalization applies (6b), and the candidate in which deletion applies (6c) (since GEN cannot make more than one change at every step, there is no candidate in which both processes apply; syllabification is assumed not to count as an additional process). Since candidate (6b) is the only candidate that does not violate the highest-ranking *ki, palatalization is the only process that applies in Step I.

The output of Step I, [k^jir.mi.la], serves as the input to Step II (by assumption, the constraint ranking does not change between steps). Now that *ki has been resolved, constraint evaluation can attend to the next constraint in the ranking, *iCV, which triggers the deletion of the second /i/, yielding the output [k^jirm.la] as shown in (7).

As all markedness constraints have been resolved, the faithful candidate will win in Step III (not shown here), and [k^jirm.la] is the final output. It is easy to verify that an alternative constraint ranking, where *iCV outranks *ki, would have produced the same output, but with the reverse order of application of the two noninteracting processes.

Despite the serial nature of HS, McCarthy (2000, 2007) has shown that HS cannot generate canonical cases of counterbleeding and counterfeeding opacity. Understanding the failure of HS on counterbleeding will make it easier to see why it succeeds on countershifting. Therefore, in the next section I review McCarthy’s (2007) demonstration of why HS fails on counterbleeding in Bedouin Hijazi Arabic and characterize the reason for the failure.

In Bedouin Hijazi Arabic (Al-Mozainy 1981, McCarthy 2007), palatalization (k → k^j before i) is counterbled by syncope (i →

in nonfinal open syllables), two processes we have seen in the previous section. The result is mappings like /ħaːkim-in/ → [ħaːk^jm-in], where palatalization is opaque, as it applies even though its context for application is no longer present on the surface. As McCarthy notes, the challenge for HS is to apply palatalization before syncope. The tableau for Step I of the derivation of /ħaːkim-in/ is given in (8).

Here, *ki outranks *iCV, a ranking needed to try to make palatalization apply before syncope. The ranking of *iCV over MAX is needed to trigger syncope, and the ranking of *ki over IDENT[back] is needed to trigger palatalization. In this tableau, candidate (8a) is obtained by applying palatalization to the UR, and candidate (8b) is obtained by applying syncope before palatalization. The problem for HS, since syncope destroys the context for palatalization, is that applying syncope to the UR in the first step of the derivation satisfies the markedness constraint triggering syncope (= *iCV) and the markedness constraint triggering palatalization (= *ki). The result is that candidate (8b), in which syncope has applied first, is incorrectly chosen as the winner. The shaded cell in the tableau highlights the absence of a violation that causes the failure.

The reasoning that leads to a problem for HS is general and goes beyond this particular case of counterbleeding. In canonical counterbleeding interactions, a process

applies before a process that destroys ’s context for application. Since removes the context for , applying first would satisfy the markedness constraints that trigger both processes. This results in the application of to the UR, which, by destroying the context for , incorrectly blocks ’s application. The failure, then, is directly related to the following property of counterbleeding:

This property is not shared by countershifting, where

((φ)) ≠ (φ), due to condition (4c) in the inverse definition of shifting. In the next section, we will see that if the opaque interaction is one of countershifting rather than counterbleeding, the problem indeed disappears.

Consider again the schematic countershifting interaction between STRESS and APOCOPE from section 2, and the mapping /CVCVCV/ → [CVC

C] that results in final stress on the surface. To best highlight the difference between countershifting and counterbleeding, I will first assume that stress assignment is triggered by a cover markedness constraint STRESS!, which penalizes a surface representation unless its final two syllables comprise a trochaic foot (the constraint STRESS! will be decomposed into more familiar constraints below, after the comparison with counterbleeding). Apocope is triggered by the constraint *V#. Similarly to the counterbleeding case, the tableau in (10) has two candidates: candidate (10a), in which the first process (here, STRESS) has applied, and candidate (b), in which the second process (here, APOCOPE) has applied. Differently from the counterbleeding case, here candidate (b) receives a fatal violation (shaded) from the highest-ranking markedness constraint, and candidate (a)—the correct candidate in Step I—wins.

Why does countershifting behave differently from counterbleeding? Given the shifting component of countershifting, APOCOPE would not destroy the context for STRESS if applied first; rather, it would shift it (see, in particular, condition (4c) in the definition of shifting). And shifting means that STRESS could still apply to [CVCVC] even if APOCOPE had applied first. In terms of constraint satisfaction, the ability of STRESS to apply to [CVCVC] translates into the shaded violation of the constraint STRESS!. As a result of this violation. Step I of the derivation succeeds and STRESS correctly applies before APOCOPE.

As was the case with counterbleeding, this reasoning is general and goes beyond this particular case of countershifting. In countershifting interactions, a process

applies before a process that can shift ’s context for application. Since shifts the context for but does not remove it, could apply even after the application of , so applying first would not satisfy the markedness constraint that triggers . This results in the correct application of to the UR, thus avoiding the problem for counterbleeding in Step I of the derivation. The generality of this reasoning will be further illustrated in section 4, which shows that the same logic applies in an analysis of a different case of countershifting involving reduplication rather than stress. The result is the Countershifting Generalization in (1).

The derivation is not yet complete. After [CV(C

CV)] has been selected as the output of Step I, the grammar must ensure that APOCOPE applies in Step II, despite making penultimate stress non-surface-true. Given the logic of OT, the challenge in Step II is easy to address, since penultimate-stress assignment can be interpreted as a violable preference. Penultimate stress will be the default, but final stress will be tolerated in order to satisfy a higher-ranked restriction against word-final vowels. More concretely, we can decompose STRESS! along the lines of McCarthy’s (2008) analysis of stress-syncope opacity. In particular, STRESS! can be decomposed into a constraint like HAVEFOOT!, which requires any foot structure,⁷ as well as various constraints regarding properties of this structure, such as ALIGNR, which requires a foot to be aligned to the right edge of the prosodic word; TROCHEE (omitted from the tableaux below for reasons of space), which requires a foot to be trochaic; and FTBIN, which requires a foot to be binary. The violable preference for penultimate stress can be represented by ranking FTBIN below *V#. Tableau (11) repeats Step I with the new set of constraints, and tableau (12) shows that Step II yields the desired output [CV(CC)]. In Step III, shown in (13), the derivation will converge on [CV(CC)] (candidate (13a)) despite its violation of the markedness constraint FTBIN. On the assumption that GEN does not have a stress-shifting operation, candidates like (13b) cannot be generated. Stress can only move as a result of a combination of two operations: foot removal and foot (re)assignment (Elfner 2016:8). Since foot removal (candidate (13c)) would incur a violation of the highest-ranked HAVEFOOT!, there is no way to shift stress to the penultimate position to satisfy FTBIN, and the correct candidate with final stress wins.

Note that Step I, in which the opaque process applied, was successful directly due to the countershifting status of the interaction. However, I have not provided a general characterization of the success of HS in Step II and Step III, which relied on a specific decomposition of the markedness constraint responsible for stress. This leaves open the possibility that these steps might behave differently in other countershifting interactions. For example, in section 4 we will see an analysis of countershifting opacity involving reduplication in which Steps II and III are completely trivial once the opaque process has applied in Step I, and no decomposition of the markedness constraint is needed. Since it is also conceivable that HS would fail on Step II or III in currently unknown countershifting interactions, (1) is given as a narrow statement about the application of the opaque process rather than as a general statement about the success of HS on complete countershifting interactions.

According to McCarthy (2000:13), HS can account for counterbleeding opacity in a limited set of cases with special properties. In this section, I present McCarthy’s example of such cases and note that it is meaningfully different from countershifting.

McCarthy’s example is a hypothetical interaction, suggested by Alan Prince, where a process of postvocalic spirantization applies while a later deletion process removes its triggering vowel. What allows HS to succeed on this interaction is a decomposition of deletion into a two-step process involving first the deletion of the segment’s featural content (reduction) and then the deletion of its autosegmental V slot (ә-syncope), as shown in (14).

Here, postvocalic spirantization is triggered by any vowel, featureless or not. This interaction is not a canonical counterbleeding interaction in the sense that the later process (ә-syncope) that has the potential to bleed an earlier process (spirantization) cannot apply to the input without the help of a third process (reduction). Neither is this a countershifting interaction, because no process has the potential to shift any other.

On the assumption that full deletion is not a GEN operation, the deletion process that can bleed postvocalic spirantization cannot apply in Step I and simultaneously satisfy the markedness constraints that trigger both processes, here *Vb (for spirantization), REDUCE (reduction), and *ә (empty-vowel deletion). The effect of this restriction on GEN is highlighted in tableau (15), where the otherwise generable candidate (15b), which would have satisfied all markedness constraints, is struck out. The correct candidate (15a) is selected in Step I and the problem discussed in section 3.2 for counterbleeding is avoided (see McCarthy 2000:13–16 for the full story). The HS analysis of a different counterbleeding interaction in Torres-Tamarit 2016 uses a similar strategy.

This example illustrates that the reported success of HS on some counterbleeding interactions relies on a decomposition of the two interacting processes rather than on similarities between the interaction and countershifting, further supporting the distinction between countershifting and counterbleeding.

Countershifting opacity can arise with persistent processes that apply no matter what, even if their original context is modified. As we have seen, this includes stress, which in many languages necessarily applies in every word. Other relevant processes include reduplication in morphophonology, which can obligatorily realize reduplicative morphemes, and agreement-type processes like nasal-place assimilation (though I have yet to find an attested case involving the latter).⁸ Here is a short list of attested countershifting interactions.

Elfner (2016) presents HS analyses of multiple languages with opaque stress-epenthesis interactions. In Dakota (Shaw 1985), for example, stress falls on the second syllable of the word, unless the second vowel is epenthetic, in which case stress is initial (16a). In Syrian Arabic (Kiparsky 2015), stress is assigned to the final syllable if and only if it is superheavy. On the surface, however, stress also falls on a heavy syllable derived from an underlying superheavy syllable through degemination (16b). In Alsea (Buckley 2008), which will be analyzed below, a reduplication process that copies the initial C(C)V portion of the stem becomes opaque through syncope, which deletes the stem’s vowel (16c).

If the Countershifting Generalization is correct, we expect HS to be able to correctly apply the opaque processes in all of these cases, even when they seem quite different from the stress-apocope interaction analyzed in section 3. Elfner (2016) has already shown this to be true for stress-epenthesis interactions. In the next section, I will illustrate this using opaque reduplication in Alsea (16c).⁹

In this section, I provide a proof-of-concept analysis of countershifting involving reduplication in Alsea (formerly spoken in central Oregon, USA). My goal is to illustrate that once an interaction is identified as countershifting, an HS analysis is readily available using the logic of section 3, even when stress is not involved.

According to Buckley’s (2008) description of reduplication patterns in Alsea, one type of reduplication involves a prefix that copies the following C(C)V syllable-portion from the stem. A process of syncope deletes the stem’s vowel in certain morphosyntactic environments independently of reduplication (c

^wt-ay-x ‘began to fight’ vs. c^wat-iyu ‘fighting’; cx^wt-t ‘push him!’ vs. cix^wt-an- ‘pushed him’). Reduplication is made opaque by syncope. The two examples in (17a) illustrate the regular application of reduplication in an environment where syncope does not apply. In (17b–d), a CV syllable is reduplicated, even though the copied vowel of the stem is deleted by syncope (the syncopated vowel can be seen in the nonreduplicated basic forms).

These alternations suggest an ordering of reduplication before syncope and a countershifting interaction. Applying syncope first would not have fed or bled reduplication. Rather, it would have caused reduplication to copy different phonological material: presumably, for example, applying syncope first to ‘always laughing’ in (17c) would have resulted in the mapping /RED-ciq^w-i/ → [cq^wi-cq^w-i]. Similar countershifting interactions in the related language Klamath have been discussed in Barker 1964, Clements and Keyser 1983, McCarthy and Prince 1995, and Zoll 2002.

Assuming a templatic theory of reduplication in HS along the lines of McCarthy, Kimper, and Mullin’s (2012), and following the reasoning of the HS analysis of countershifting in section 3, a proof-of-concept HS analysis of the Alsea interaction will work as follows. Abstracting away from the details of McCarthy, Kimper, and Mullin’s theory, reduplication will be triggered by the syllabic template [CV] , which needs to be filled by a (potentially complex) onset and a vowel. The constraint that requires filling the template will be FILLTEMPLATE!. The copying operation that fills templates violates the faithfulness constraint *COPY. Syncope will be triggered by the simplified *V_STEM . In Step I, the copying candidate (18a) is correctly selected. Given the countershifting nature of the interaction, candidate (18b) fatally violates the constraint that triggers reduplication. In Step II, nothing special needs to be said and the correct output candidate (19b) wins. Since all markedness constraints are satisfied, the derivation will converge in Step III (not shown).

This squib makes two contributions. The first, which is not theoretically significant in and of itself, is the introduction of the new terms shifting and countershifting. While shifting interactions have already been identified in the literature (under the name transfusions; Zwicky 1987), the term countershifting fills a gap in the traditional taxonomy of pairwise process interactions. The second contribution is the observation that some opaque interactions that can be generated by HS are not isolated cases but rather special cases of a general class of opaque interactions: the class of countershifting opacity. The identification of countershifting opacity, together with the logic concerning the ability of HS to deal with countershifting interactions in general, constitutes progress in our evaluation of HS as a theory of opacity. This result raises questions that I have not been able to address in the scope of this squib, such as: Can HS generate any countershifting interaction or is it limited to interactions with certain properties? What is the broader typology of countershifting, and what is the range of processes that can participate in countershifting interactions? Hopefully, further research into countershifting will reveal the answers to these questions.

For helpful feedback and discussion, I am grateful to Daniel Asherov, Roni Katzir, Gereon Müller, Jochen Trommer, Eva Zimmerman, the audience at the Leipzig Opacity Symposium (held on 29–30 May 2020), an anonymous LI reviewer, and especially Eric Baković, whose suggestions have significantly improved the quality of this squib.