Abstract
As codified by Baker’s (1985) “Mirror Principle” (MP), the linear order of morphemes within a word generally correlates with hierarchical syntactic structure. While Baker uses morphological ordering to demonstrate the inseparability of syntax and morphology, he simply assumes cyclic morphological concatenation as the formal means by which MP-compliance is enacted in the grammar.
This paper develops a new framework for morpheme ordering, the Mirror Alignment Principle (MAP), which derives the MP while avoiding some of the shortcomings of cyclic morphological concatenation. The MAP is a morphology-phonology interface algorithm that takes morphosyntactic c-command relations and dynamically generates a ranking of alignment constraints (McCarthy and Prince 1993) in the phonological component. All possible morpheme orders are considered and evaluated by an Optimality Theoretic (Prince and Smolensky [1993] 2004) phonological grammar, which selects the optimal surface order through constraint interaction. Even though morpheme order is computed in the phonology, the driving force behind this order is the syntax/morphology. This link between grammatical components generates MP-compliant morpheme orders.
This paper focuses on two case studies. First, it will show how the MAP is consistent with the complex interaction between MP-satisfaction and the “CARP template” in Bantu (Hyman 2003). Second, it will show that the MAP can explain intricate ordering alternations within Arabic’s root-and-pattern verbal system. This will demonstrate that MP-behavior can indeed be identified even in nonconcatenative morphological systems.
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Notes
Thanks to Gereon Müller for pointing this out to me. This adjustment would not be necessary if the MAP were calculated over the base-generated syntactic structure.
One other difference is that Potter uses opposite-edge alignment constraints, where the affix is the first argument of the constraint and the Root is the second argument, to derive the basically parametric difference between ordering in Apache and SiSwati. This is not something that is needed for the data examined in this paper, and thus is something which would be ideally eliminated from the theory on the grounds of parsimony, but this is an empirical question.
Note that these verb forms require “final vowel” suffixes, so the rightmost CARP element will never be absolute word-final. We can handle this by including a right-oriented alignment constraint for the final vowel morpheme that outranks the verbal extensions’ alignment constraints. This is totally consistent with the MAP, as the final vowel morphemes expone Tense/Aspect/Mood information (see, e.g., Nurse and Philippson 2006), which we would expect to be morphosyntactically higher than valence-changing heads. This interaction is further evidence that the alignment constraints must be evaluated gradiently.
Note that Banerjee’s (2019) syntactic analysis of Kinyarwanda is significantly more sophisticated than this tree suggests. The tree is meant for expositional purposes only.
Donca Steriade (p.c.) raises the following concern regarding this example: if we were to instead ascribe to uk- a translation ‘rise up,’ it is less clear that the suffixed derivatives truly have an idiomatic meaning at all. If this is correct, then it is less clear that this example constitutes evidence in favor of an underlying CARP-violating structure.
This approach bears some similarities to Hyman’s (2003) analysis, where a set of violable pairwise Mirror constraints compete with a unitary Template constraint that prefers the CARP order. However, since the MAP generates MP effects indirectly through the transmission of syntactic structure into the phonology, the MAP is not compatible with Hyman’s approach.
Thank you to Arto Anttila for suggesting this approach. See Zukoff (2017b) for discussion of alternative conceptions of this variation.
“Arabic” here refers to Classical Arabic and Modern Standard Arabic. They do not differ significantly on the points under discussion, and I will thus draw on scholarship of both varieties.
The following is a partial list of works which have sought to analyze the phonological properties—in concert with the morphosyntactic properties, in some cases—of Semitic nonconcatenative morphology: McCarthy (1979, 1981, 1993); Yip (1988); Guerssel and Lowenstamm (1990); McCarthy and Prince (1990a,b); Golston (1996); LeTourneau (1997); Gafos (1998, 2018); Ussishkin (2000a,b, 2003, 2005); Bat-El (2003, 2011); Lowenstamm (2005); Arbaoui (2010a,b); Tucker (2010, 2011); Wallace (2013); Faust (2015); Kastner (2016, 2019, 2020); Zukoff (2017a, 2021b); Kusmer (2019).
I follow much of the literature, both descriptive (e.g. Fischer 2002:98) and theoretical (e.g. McCarthy 1981:389), in identifying this morpheme as Reflexive. However, this morpheme does not consistently produce argument structure alternations typical of reflexives (Itamar Kastner, p.c.), so it is not completely clear if this is the right designation. All that is important for the current argumentation is that the /t/ morpheme that shows up in multiple Forms is the exponent of the same morphosyntactic terminal (whatever that happens to be) and is in the hierarchical relations with Root that I claim it to be.
Candidates where the Reflexive /t/ is immediately followed by the Root-initial /k/ are ruled out by a markedness constraint that is lexically-indexed to the Reflexive morpheme and several other verbal prefixes (Sect. 5.2). See Sect. 5 generally for explanation of additional phonological exigencies responsible for the non-minimal differences between the prefixal and infixal candidates, and consideration of additional candidates.
Note that cluster-initial forms like Form VIII and Form X are repaired by preposed epenthesis of [Pi] in phrase-initial position (i.e., phrase-initial clusters are not permitted, but word-initial clusters are). Epenthetic [ʔi] must be treated as being outside the domain of alignment, if present at this stage of evaluation at all. For this reason, I will omit them from word representations moving forward.
Notably, this root also has a Form V taʕallama ‘teach oneself, learn’ (Fischer 2002:99), which transparently adds reflexive semantics to the Form II meaning. This matches well with the proposed syntactic structures, as the Form II structure (50b) is contained within the Form V structure (44a).
Another odd fact about the /P/ exponent is that it is absent on the surface in the Imperfective (see Table 10). While, e.g., McCarthy (1979:243–244) schematizes the Form IV Imperfective Passive as
, the actual surface form is [yuktabu], with the /P/ and the following vowel “missing.” Citing Brame (1970:255), McCarthy assumes deletion by some mysterious later rule. Nevertheless, the [ʔ] in Form IV Perfectives cannot be (phrase-initial) epenthetic, because it is retained in post-consonantal position phrase-medially. How exactly to handle this whole complex of issues is an important question for future consideration.Arabic has only three vowels:
(with long variants which may or may not be phonemic). We might thus expect some overlap between Aspect/Voice UR’s even in the absence of shared exponents. Note also that the vocalic melody of Form I varies by root (e.g., McCarthy 1981:402–404; Guerssel and Lowenstamm 1990; Gafos 2018). This can probably be explained in terms of locality in allomorph selection given the absence of intervening heads in Form I. I leave the details for future study.This constraint is indexed to the /ʔ/ exponent of causative, but not the /\(\mu _{c}\)/ or /s/ exponents of causative. This indicates that the index is attached not to the “morpheme” (in the DM sense), but to the morph/exponent.
I have defined Integrity to assign violations to all pairs of corresponding output segments, so the number of violations will increase exponentially as splitting increases. This has no effect on the evaluation as long as we are operating with constraint ranking rather than weighting.
An alternative analysis based on McCarthy’s (2005) “Optimal Paradigms” approach, which McCarthy shows can derive similar facts through paradigmatic overapplication, may be available. However, since that technology is not needed for the other facts examined here, I will not consider it further.
Perfective agreement is aligned only to the right. Therefore, the direction of alignment must differ for the different agreement categories. Conceptually, we might relate this to the idea that the lexical index for
must apply to morphs not morphemes (see fn. 17). More thought about how this fits into the alignment system broadly is required.That on its own might not be sufficient, however, to explain the few cases like the Form VIII perfective passive ktutiba, shown in (i) below (cf. (58)), where Align-AV-E must rank even lower, below Align-Refl-L. This may motivate supplementing the default ranking to include the low ranking of Align-AV-E, as shown in (ii) below.
-
(i)
-
(ii)
Language-specific default ranking for Arabic (updated) (cf. (48))
Align-Root-E ≫ all the other alignment constraints ≫ Align-AV-E
-
(i)
Thank you to Ezer Rasin for pointing this out to me.
, the actual surface form is [yuktabu], with the /P/ and the following vowel “missing.” Citing Brame (
(with long variants which may or may not be phonemic). We might thus expect some overlap between Aspect/Voice UR’s even in the absence of shared exponents. Note also that the vocalic melody of Form I varies by root (e.g., McCarthy 
must apply to morphs not morphemes (see fn. 
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Acknowledgements
This paper has been in the works for a very long time. It has benefited immensely from input by too many people to count. I will here list (in alphabetical order) as many as I can remember right now, but certainly there are more that deserve my thanks. Thank you to Adam Albright, Nico Baier, Mark Baker, Eric Baković, Ryan Bennett, Chiara Bozzone, Kenyon Branan, David Goldstein, Chris Golston, Jelena Grofulovic, Heidi Harley, Larry Hyman, Laura Kalin, Itamar Kastner, Michael Kenstowicz, Gereon Müller, Neil Myler, David Pesetsky, Luise Popp, Ezer Rasin, Norvin Richards, Nik Rolle, Sharon Rose, Kevin Ryan, Ryan Sandell, Donca Steriade, Jochen Trommer, Matt Tucker, Martin Walkow, Tony Yates, Michelle Yuan, Eva Zimmermann, the members of the Leipzig Phonology Reading Group, the audiences at NELS 47 and LSA 2021, and audiences at MIT, Berkeley, UC San Diego, and CRISSP. I would also like to thank three anonymous NLLT reviewers, and Arto Anttila, the associate editor, for their very helpful feedback on this manuscript. The many mistakes and bad ideas that remain are entirely my fault.
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Zukoff, S. The Mirror Alignment Principle. Nat Lang Linguist Theory 41, 399–458 (2023). https://doi.org/10.1007/s11049-022-09537-2
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DOI: https://doi.org/10.1007/s11049-022-09537-2