Deriving Arabic verbal “templates” without templates

Much of the recent OT-based literature on Arabic root-and-pattern morphology has identified prosodic constraints as a main driver of the language’s verbal “templates”. I argue instead that the system is governed by non-prosodic (morpho)phonological constraints (in the spirit of McCarthy 1993). Following much recent work, this approach views Arabic’s root-and-pattern system as gardenvariety morpheme concatenation that is subject to unusual complications in the phonology and/or at the (morpho)syntax-phonology interface. This paper outlines an integrated analysis of the morphophonological properties of the Arabic verbal system without CV templates or prosodic constraints.


Introduction.
Arabic's root-and-pattern verbal morphology has long been described in terms of Consonant/Vowel (CV) "templates", which were analytically reified in McCarthy (1979McCarthy ( , 1981 and subsequent work (see, e.g., Faust 2015). Within the Optimality Theory (Prince & Smolensky [1993] 2004) literature, however, most researchers have pursued Generalized Template Theory (McCarthy & Prince 1995) analyses, whereby templatic effects are derived from independent principles. Many of these analyses have been based on the interaction between affixation and prosody (Ussishkin 2000, Tucker 2010, 2011, Kastner 2016. I argue instead that the Arabic verbal system is rather governed by the interaction between affixation and non-prosodic (morpho)phonological constraints, in the spirit of McCarthy (1993). Following much recent work (Tucker 2010, 2011, Wallace 2013, Kastner 2016, Kusmer 2019, this approach views Arabic's root-and-pattern system as garden-variety morpheme concatenation that is subject to unusual complications in the phonology and/or at the morphosyntax-phonology interface. In this paper, I outline an integrated analysis of the morphophonological properties of the Arabic verbal system, based on the types of constraints previewed in (1), that does not rely on CV templates or prosodic constraints.
(1) Constraint types a. Alignment constraints whose ranking follows dynamically from the morphosyntactic structure via the "Mirror Alignment Principle" (Zukoff to  2. Data preview. I make the following, largely traditional assumptions about the morphological composition of Arabic verbs: Roots consist of a string of underlying consonants (canonically 3); the "vocalic melodies" expone Aspect and Voice, and consist of a string of 1-3 underlying vowels; and the additional phonological content present in derived "Forms" expones v-domain morphemes (see Table 2). Subject agreement affixes are outermost: suffixal in the perfective, simultaneously prefixal and suffixal (thus circumfixal) in the imperfective. 1 The phonological shapes of the nine productive verb "Forms", in the four aspect/voice categories, are given in Table 1. The exponents of the v-domain morphemes are underlined. My morphological analysis of the various v-domain morphemes is given in Table 2. 2 (The precise morphosemantic characterization of the v-domain morphemes is not crucial.) nkatab-a nkutib-a y-ankatib-u y-unkatab-u VIII ktatab-a ktutib-a y-aktatib-u y-uktatab-u X staktab-a stuktib-a y-astaktib-u y-ustaktab-u  Ussishkin 2003, Tucker 2010 is that the ranking of alignment constraints is not fixed across derivations, but rather directly and dynamically tied to the morphosyntactic structure of individual derivations by means of the "Mirror Alignment Principle" (Zukoff to appear).
3.1. THE REFLEXIVE. Reflexive /t/ recurs across multiple Forms, but appears in different positions, as shown in Table 3 below. Recent accounts (Ussishkin 2003, Tucker 2010) have used alignment constraints like the ones in (2-3) to help derive the ordering alternation. However, an alignment-based analysis of the Reflexive requires an apparent ranking paradox (4), demonstrated in (5). (2) ALIGN-ROOT-L: Assign one violation * for each segment which intervenes in the output between the left edge of the exponent of Root and the left edge of the word.
(3) ALIGN-REFL-L: Assign one violation * for each segment which intervenes in the output between the left edge of the exponent of Reflexive and the left edge of the word. /tREFL, µ c CAUS , ktb, aAV, aAGR/ ALIGN-REFL-L ALIGN-ROOT-L a. takat c taba ** b.
ktat c taba *! Tucker (2010) circumvented this by indexing Form VIII to a special alignment constraint (basically: ALIGN-REFL VIII -L ALIGN-ROOT-L ALIGN-REFL-L). Similarly, McCarthy (1979McCarthy ( , 1981) posits a special methathesis rule for Form VIII. This successfully avoids the problem, but does not provide explanatory power. I propose a new solution based on a novel syntactic generalization (6). This can help account for the difference if we adopt the Mirror Alignment Principle (MAP) approach to linearization (Zukoff to appear), defined in (7).
(7) The Mirror Alignment Principle a. If a terminal node α asymmetrically c-commands a terminal node β, then the alignment constraint referencing α dominates the alignment constraint referencing β. 4 b. Shorthand: If α c-commands β → ALIGN-α ALIGN-β Compare the morphosyntactic structures of Form V (8a), the reflexive of the causative, and Form VIII (8b), the simple reflexive. In Form V, Refl asymmetrically c-commands Root, because it adjoins to the complex head containing Root and Caus. The MAP therefore generates the ranking ALIGN-REFL-L ALIGN-ROOT-L (9b), which produces a prefixal position for /t/ (5.ii). On the other hand, in Form VIII, Refl and Root symmetrically c-command one another, because Refl is the first head to adjoin to Root. The MAP thus asserts no ranking between ALIGN-REFL-L and ALIGN-ROOT-L, meaning that other factors will have to determine their relative ranking. While we have now identified a distinction in the alignment behavior between the two types of structures, the MAP itself doesn't directly explain why Reflexive /t/ is infixal in Form VIII. However, we can now observe one further generalization (10). This generalization holds not only for Form VIII ktataba (8b), but also for other combinations of heads (cf. Table 4 below). It holds of the relationship between Root and Causative in Form V takat c taba (8a) and Form II kat c taba. And it also holds of the parallel relationship between Root and Applicative in Form VI takaa v taba (11a) and Form III kaa v taba (11b).
(10) Root-alignment generalization: The (left edge of the) Root always surfaces further to the left than the first head it adjoins to.
We can understand the generalization in (10) in terms of alignment: in each of the relevant cases, the constraint ALIGN-ROOT-L outranks the left-oriented alignment constraint of the v-domain morpheme. Crucially, these are exactly the cases where the MAP does not establish a ranking, because the two heads stand in symmetric c-command. This suggests that there is a governing principle within the alignment system of Arabic that favors the high ranking of ALIGN-ROOT-L. I capture this with the "Default Ranking Statement" (DRS) in (12). For the infixal Reflexive in Form VIII ktataba (8b), the DRS in (12)  These two distinct rankings are the paradoxical rankings from (4) above which generate the contrasting prefixal vs. infixal behavior of Reflexive (Table 3). Unlike in Tucker's (2010) constraint indexation approach, we have found an explanation for the apparent paradox: the dynamic interaction of the MAP and Arabic's DRS as mediated by morphosyntactic structure.
3.2. SUMMARY OF STRUCTURES AND MAP RANKINGS. Using these same principles, we can analyze the full Form system with the structures and rankings in Table 4. Table 4. Morphosyntactic structure and alignment analysis of verbal Forms 3.3. ROOT AND ASPECT/VOICE. There is one place where naive assumptions about asymmetric c-command vis-`a-vis the MAP are not met: the interaction between Root and Aspect/Voice (i.e. the vocalic melodies). We would expect Aspect and Voice to asymmetrically c-command Root given their higher position on the clausal spine. However, an alignment-based ordering analysis requires that ALIGN-AV be dominated by ALIGN-ROOT. Tableau (14) shows the interaction from a Form I (basic form) perfective passive. Tableau (15) shows an additional case, the Form VII ("middle") perfective active, where the output is clearly not otherwise phonotactically optimizing. This ensures that it is alignment which is driving the derivation, rather than markedness considerations.
The consistent portmanteau exponence of Aspect and Voice points to a solution in the post-syntax. In Zukoff (to appear), I propose the structure in (16), which is derived through amalgamation (Harizanov & Gribanova 2019), followed by fusion (or perhaps contextual allomorphy). Wallace (2013; 4) assumes an equivalent structure. This structure generates the desired ranking. Because Aspect and Voice are displaced from the root of the complex head, they do not stand in any c-command relation with Root, and the MAP does not assert a ranking. This allows the DRS in (12) to generate the ranking ALIGN-ROOT-L ALIGN-AV-L. This interaction, and the resulting ranking, holds across all Forms. Nevertheless, conflict with higher-ranked constraints can generate outputs where (the left edge of) the AV morpheme surfaces further to the left than the Root.

A lexically-indexed phonotactic constraint.
Much of the original rationale for CV templates was the unpredictability of the CV-strings towards the left-edge of the various Forms. Embedded within the system proposed here, this unpredictability can be reduced to a single parameter (17), and its interaction with the other relevant constraints: some (consonantal) affixes must be immediately followed by a vowel (i.e. can't precede a consonant).
(17) *AFX i / C: Assign a violation * if a morpheme with the index i precedes a consonant in the output.
This is essentially a constraint against these morphemes surfacing in coda position. However, since initial clusters are only resolved post-lexically (no repair when following a vowel phrase-internally; epenthesis of [i] when following a consonant phrase-internally; epenthesis of [Pi] phrase-initially), this formulation circumvents syllabification problems. Regardless of the constraint's precise formulation, it is a lexically-indexed markedness constraint (following Pater 2009, a.o.), indexed to (i) Reflexive /t/, (ii) Causative /P/, and (iii) the imperfective agreement affixes (or at least the morphs that show up at the left edge: /y,t,P,n/). 5 This derives the absence of clusters in certain forms where alignment would otherwise predict them. Consider the Form IV (causative) perfective passive Puktiba. As shown in (18), if only alignment were in play (assuming the analysis in Table 4 above), we would incorrectly generate a left-edge cluster *[Pkutiba] (18i.a). Adding in *AFX i / C eliminates the clustering candidate and generates the desired result (18ii.b). This reverses the order of Root and AV relative to their preferred alignment, as a repair for *AFX i / C. In Forms without affixes indexed to *AFX i / C -e.g. Form VII (19) -alignment will be maximally satisfied, allowing for clusters to surface at the left edge. naktaba **! * c. knataba *! ** 4.1. *AFX i / C AND IMPERFECTIVE AGREEMENT. As can be seen in Table 5  . This strongly suggests that these vowels are not part of the agreement morpheme (as partially implied by templatic analyses like McCarthy 1981), but rather part of the AV morpheme (Brame 1970;70, Yip 1988;569). Therefore, just as with the v-domain morphemes, we can derive the requirement of a second-position vowel by indexing the imperfective agreement morphs to *AFX i / C.
Form Pf. Act. /a/ Pf. Pass /ui/ Impf. Act. (?) Impf. Pass. /ua/ I katab-a kutib-a y-aktub-u y-uktab-u II kat c tab-a kut c tib-a y-ukat c tib-u y-ukat c tab-u III kaa v tab-a kuu v tib-a y-ukaa v tib-u y-ukaa v tab-u IV Paktab-a Puktib-a y-u(Pa)ktib-u y-u(Pa)ktab-u V takat c tab-a tukut c tib-a y-atakat c tab-u y-utakat c tab-u VI takaa v tab-a tukuu v tib-a y-atakaa v tab-u y-utakaa v tab-u VII nkatab-a nkutib-a y-ankatib-u y-unkatab-u VIII ktatab-a ktutib-a y-aktatib-u y-uktatab-u X staktab-a stuktib-a y-astaktib-u y-ustaktab-u  (20). For now, assume that the agreement morphemes have left-oriented alignment constraints. (This will be revised below, in order to account for the behavior at the right edge.) The same interaction derives the more complex Forms in the same fashion.
(20) Form I Imperfective Passive yuktabu (*AFX i / C active for /y/) /ktb, uaAV, y i (-)uAGR/ *AFX i / C ALIGN-AGR-L ALIGN-ROOT-L ALIGN-AV-L a. ykutabu *! * ** b. yuktabu ** * c. kyutabu *! ** 4.2. *AFX i / C AND THE REFLEXIVE. Initial clustering is also found in Form VIII (reflexive). In this case, both alignment and *AFX i / C advocate for Reflexive /t/ to surface in pre-vocalic position (21a). 6 Nevertheless, we know Reflexive /t/ is indexed to *AFX i / C because of its behavior in Forms V & VI. In Form V (22), alignment dictates that Reflexive /t/ be leftmost, followed by the Root. This should generate a cluster (22a), but the AV vowel surfaces in second position instead (22b). This follows only if Reflexive /t/ is indexed to *AFX i / C.
kut c tutiba *!** ** * A candidate tukt c tiba would satisfy *AFX i / C and do better on alignment than (22b) -it would have one fewer violation of ALIGN-CAUS-L. This candidate is ruled out by phonotactics: either *CCC (see below) or a constraint forbidding geminates adjacent to consonants, both of which are surface true constraints in the language.
5. Explaining the vocalic melodies: INTEGRITY and *CCC. The interaction between alignment and *AFX i / C explains the behavior at the left edge of all the forms. The largest remaining piece of the puzzle is the position and number of the vowels of the AV vocalic melody in the various Forms. My jumping off point is the (somewhat novel) generalizations in (23), confirmed by Table 6. (See McCarthy 1981;400, Yip 1988; 565 for similar observations.) Form Pf. Act. /a/ Pf. Pass /ui/ Impf. Act. (?) Impf. Pass. /ua/ I katab-a kutib-a y-aktub-u y-uktab-u II kat c tab-a kut c tib-a y-ukat c tib-u y-ukat c tab-u III kaa v tab-a kuu v tib-a y-ukaa v tib-u y-ukaa v tab-u IV Paktab-a Puktib-a y-u(Pa)ktib-u y-u(Pa)ktab-u V takat c tab-a tukut c tib-a y-atakat c tab-u y-utakat c tab-u VI takaa v tab-a tukuu v tib-a y-atakaa v tab-u y-utakaa v tab-u VII nkatab-a nkutib-a y-ankatib-u y-unkatab-u VIII ktatab-a ktutib-a y-aktatib-u y-uktatab-u X staktab-a stuktib-a y-astaktib-u y-ustaktab-u b. Assuming the sonority scale a u i, whenever additional vowels are required in order to create well-formed structures, the most sonorous vowel splits.
These generalizations clearly hold in the Perfective Active, Perfective Passive, and Imperfective Passive, where the same combination of vowels in the same order appears across the different Forms. They hold also in the Imperfective Active, even though the set of vowels differs by Form. Note that this cannot be recast in directional terms (Yip 1988): in the Perfective Passive (/ui/) and Forms VII, VIII, and X in the Imperfective Active (/ai/), the lefthand vowel splits; but in the Imperfective Passive (/ua/), the rigthand vowel splits. This is problematic for directional autosegmental association accounts: in order to maintain left-to-right association, McCarthy (1981;401) had to stipulate a prior rule that associates /i/ to the right edge first.
We can use this phonological conditioning to generate the range of surface patterns from compact UR's. I implement this with the faithfulness constraint INTEGRITY (McCarthy & Prince 1995), relativized to individual vowel qualities, ranked (inversely) according to their sonority value (24). This approach yields three desiderata: (i) it correctly selects which vowel splits when splitting occurs; (ii) it correctly predicts that only one underlying vowel is ever split in a given form; and (iii) it predicts that splitting will be minimal (since more splitting incurs more violations), subject to the needs of higher-ranked constraints. The primary drivers of INTEGRITY violation are *AFX i / C and *CCC (25), modulated by alignment. One Form where splitting occurs is the Form X imperfective active yastaktibu, where there are two instances of [a] in the output. The order of the consonantal morphemes is determined purely by alignment ranking (cf . Table 4), as in (26). As long as INTEGRITY is ranked below these alignment constraints, it will always be preferable to split the AV vowels rather than reorder the consonantal morphemes as a repair for *AFX i / C. That is, a candidate like *syaktitbu, which satisfies *AFX i / C by swapping the order of the exponents, would excessively violate high-ranked alignment constraints (here, ALIGN-AGR-L and ALIGN-REFL-L).
(26) Ordering via alignment Holding the ordering of the consonantal morphemes constant, we can now see the interaction between *AFX i / C, *CCC, and INTEGRITY. Segments that are underlined in the output are exponents of morphemes indexed to *AFX i / C. Bolded vowels in the output are split vowels, incurring INTEGRITY violations.
(27) Form X Imperfective Active yastaktibu: motivating splitting /sCAUS, t i REFL , ktb, aiAV, y i (-)uAGR/ *AFX i / C *CCC INTEGRITY[a] a. ystkatibu *!* *!* b. ysatkitbu *!* c. yastiktbu *! d. yastaktibu * Perfectly adhering to alignment (27a) produces a long string of consonants at the beginning of the word, causing violations of both *AFX i / C and *CCC. The fact that this output is not selected shows that the alignment constraints must be dominated by (at least one of) these two markedness constraints. Shifting the AV vowels leftward can improve these problems, but it can't fix them completely. Placing the two vowels after every second consonant (27b) yields a *CCC-obeying output, 7 but doesn't alleviate the *AFX i / C violations. This confirms the ranking *AFX i / C INTEGRITY. As mentioned above, fixing the *AFX i / C violations by swapping the consonantal exponents (*syaktitbu) will worsen alignment. This confirms that the alignment constraints outrank INTEGRITY as well. Shifting all of the underlying vowels over towards the left without splitting (27c) can alleviate the *AFX i / C violations, but it creates a three-consonant cluster towards the right, fatally violating *CCC. This confirms the ranking *CCC INTEGRITY. Only by splitting the vowels (27d) can both markedness constraints be satisfied simultaneously.
Once splitting is motivated by *AFX i / C and *CCC, INTEGRITY does the rest, as shown in (28)  yasatakatibu **!* 6. Explaining the right edge: both-edge alignment. The last major piece of the puzzle is to account for the relative positions of consonants and vowels towards the right edge of the stem. Consider again the Form X imperfective active yastaktibu. Nothing about the current analysis distinguishes actual yastaktibu from alternative *yastakitbu. In both forms, left-alignment of all the morphemes is maximized, subject to its interaction with markedness and INTEGRITY, and both forms have the same number of codas and consonant clusters. The answer seems to lie in the longstanding generalization that all verbal stems (i.e. the material preceding the agreement suffixes) must end in a VC sequence (McCarthy 1979, McCarthy & Prince 1990. If something actively enforces this generalization, it will prefer yastaktibu over *yastakitbu. We could simply hardwire this into the analysis with some expanded version of the constraint FINAL-C (cf. McCarthy & Prince 1990, McCarthy 1993, 2005a, Kiparsky 2003, Farwaneh 2009, but this would not provide much explanatory value without further contextualization. We could alternatively appeal to paradigm uniformity using McCarthy's (2005b) "Optimal Paradigms" (OP) approach, which he shows can derive similar facts through paradigmatic overapplication. Since there are consonant-initial verbal agreement suffixes, and threeconsonant clusters are not allowed (*CCC), some inflected forms will not tolerate a VCC-final stem. These instead require a VC-final stem, and this is transferred through OP-correspondence (perhaps LINEARITY, or something relating to syllable weight) to the rest of the paradigm, resulting in consistently VC-final stems.
Regardless, the current alignment-based analysis presents a new explanation. First, we know that ALIGN-ROOT ALIGN-AV based on the behavior of the left edge of the stem.
Second, we know that the stem-final VC sequence is always composed of the last AV vowel followed by the last Root consonant. If these alignment constraints also regulate the right edge, then alignment derives the distribution. Furthermore, the right-side agreement morph always follows this VC sequence, just like the left-side agreement morph always precedes the Root and the AV morpheme at the left edge (cf., e.g., (20)). Thus, a right-oriented version of the alignment ranking needed for the left edge (29) generates the correct order in full. Considering just the right-edge alignment of these morphemes, the tableau in (30) shows how we derive a VC-final stem, followed by agreement of any shape. (Split vowels are bolded.) (29) Ranking (to be refined): ALIGN-AGR-R ALIGN-ROOT-R ALIGN-AV-R (30) Form X Imperfective Active yastaktibu: explaining the right edge ALIGN-ALIGN-ALIGN-INTEG /sCAUS, t i REFL , ktb, aiAV, y i (-)uAGR/ AGR-R ROOT-R AV-R a. yastaktiAVbRTuAGR * ** * b. yastakiAVtbRTuAGR * ***! * c. yastiAVktubRTuAGR * ***!** * d.
yastiAVktuAGRbRT *! **** Given that agreement must be rightmost (ruling out (30d)), there must be one violation of ALIGN-ROOT-R. This ensures the word-final sequence [bu]. Beyond that, the only constraint which cares about which segment comes next is ALIGN-AV-R, the next highest-ranked constraint. This ensures that the rightmost AV vowel will come next (30a). Having the Rootmedial /t/ surface next (30b) confers no benefit, nor does splitting the agreement affix and having it come next (30c).
As long as ALIGN-AV-R dominates the INTEGRITY constraints, this approach also explains why agreement suffixes don't split even when they provide the most sonorous (and thus most splittable) vowel: doing so would worsen AV-alignment. Consider the Form V perfective passive 3SG.MASC, with AV morph /ui/ and agreement morph /a/. The ranking INTEG[i] INTEG[u] INTEG[a] prefers splitting the agreement morph /a/ (31a), but this displaces the AV-final /i/ further left, incurring extra ALIGN-AV-R violations. To ensure that the AV-final /i/ is as far right as possible, the AV-initial /u/ gets split instead (31b). tukit c tiba ** *!
We now see that we need both left-alignment and right-alignment for the Root, the AV morpheme, and the (imperfective) agreement morphemes. This may have been obvious on its face for the imperfective agreement markers, which can (relatively straightforwardly) be categorized as circumfixes. 8 I propose that we implement this by enriching Generalized Alignment (McCarthy & Prince 1993;cf. Hyde 2012) to allow for alignment constraints that can select