On the treatment of super-heavy syllables in Arabic Dialects: an Optimality Theoretic approach to historical typology HASSAN BOKHARI

This study provides a historical typological Optimality Theoretic analysis of the treatment of potential super-heavy syllables in six Arabic varieties: Hijazi, Egyptian, Emirati, Kuwaiti, Algerian, and Palestinian. The analysis in this study uses the same violable OT constraints for all languages, and the differences between the grammars are represented by the order in which the constraints are ranked relative to one another. The similarities and differences between these varieties are examined from the point of view of one approach to historical OT (Cho 1998), which states that individual pairs of constraints may be ranked or unranked in relation to one another, one operation at a time, meaning that switching the order of two constraints takes two steps historically. According to Cho (1998, 45), “each step of a sound change should be viewed as a change in the ranking of constraints.” Cho’s approach in detecting the historical typological differences between varieties by counting the steps of constraint reranking is compatible with a common approach to historical linguistics. Specifically, Wichmann et al. (2010) provide a quantitative method for determining the geographic homeland of a group of related languages, which takes into account a simple linguistic-difference metric and the geographic distance between the languages. Using constraint reranking in place of Wichmann et al.’s linguistic-difference metric to calculate the homeland of Arabic dialects results in an area around Hijaz as the homeland of Arabic dialects, since Hijazi, Egyptian and Emirati dialects form a cluster of geographically close, but linguistically diverse dialects.


Introduction
This paper considers the typology of how Arabic dialects deal with the potential generation of super-heavy syllables word-internally. Superheavy syllables are syllables with at least three timing slots in the rhyme, that I take to the question of how syllable weight can be dealt with in Arabic involves the interaction between markedness and faithfulness constraints. For example, the word /bint-na/ surfaces with epenthesis as [ˈbintana] in Hijazi Arabic because *σμμμ (a markedness constraint which prohibits syllables from surfacing with three moras) outranks DEP-V (a faithfulness constraint that prohibits forms from surfacing with a vowel that was not present in the underlying representation). If these two constraints were ranked in the opposite order, then /bint-na/ would surface faithfully as [ˈbintna]. One tenet of classical Optimality Theory is that all languages use the same set of universal constraints, and grammars may only differ in terms of their ranking of the constraints. While a constraint may not be deleted, it may be so low-ranked that it is not active in a language -i.e., it has no real impact on the grammar; conversely, a constraint that is not active in one language may be active in another language simply due to the fact that it is highly ranked, or even undominated, and not because that language's grammar has an additional constraint.
Work in historical OT assumes that when a language's phonology changes, what is happening is the constraints are being reranked, since according to OT, constraints cannot be deleted or added. There are different theories as to how, why, and in what way this happens. For example, one approach assumes that constraints are normally 'demoted,' meaning they lose their domination relationship over another constraint. Another approach (Cho 1998) assumes that individual pairs of constraints may be ranked or unranked in relation to one another, one operation at a time, which means that switching the order of two constraints takes two steps historically. Parallel OT contrasts with rulebased historical phonology, where a list of sound changes is simply described. 2 One advantage of the OT approach is that it can explain the relationship between different sound changes in a language that would normally not be relatable. Other issues in historical OT relate to lexiconoptimization, i.e., the fact that the lexicon is restructured in OT as needed to produce input forms that most efficiently derive the current output form. Some previous work also argues that reranking happens when the evidence for a particular ranking is not very robust in a language. This may be the case for super-heavy syllables in modern Arabic dialects, since Classical Arabic did not have good evidence for how to treat wordinternal super-heavy syllables. This problem is described in more depth later in this paper. Bermúdez-Otero (2006) raises some important questions related to historical approaches in OT. The main issue that Bermúdez-Otero (2006, 498) raises is that markedness may simply be a side effect of a series of sound changes, which are caused by simple restrictions on phonetic mechanisms. The sound changes, in turn, are caused by speakers "misparsing … phonological structures that pose articulatory, acoustic, or auditory difficulties", reminiscent of Haspelmath's (2006) claim that phonological markedness is in fact usually just a way of talking about phonetic difficulty. 3 An example of this is contextual voicing neutralization, where many languages devoice codas, but preserve a voicing contrast in onsets. The explanation provided for languages like this relies on the fact that voicing is harder to perceive in coda position than in onset position, so that if voicing is neutralized in one context, it will be in the coda, and not the onset. The normal expression of this as a markedness constraint is said to be problematic because the 'markedness' of voicing in the coda is simply due to perceptual difficulty.
In Cho's (1998, 45) OT approach, "each step of a sound change should be viewed as a change in the ranking of constraints." This approach means that "both synchronic variation and change are based on the same phonological principles" (Cho 1998, 45). According to this approach, there are only two types of change that can occur: creating a ranking between two unranked constraints, or undoing a ranking between two ranked constraints. Hence, a reversal in ranking between two constraints has to happen in two steps, not one.
As an example of this, Cho (1998) examines r-deletion in English, including linking-r and intrusive-r. Linking-r is the preservation of /r/ between vowels in certain dialects of English where coda /r/ is normally deleted; for example, the /r/ in "Homer arrived" is preserved in dialects with linking /r/ even though the same /r/ is deleted in "Homer left". Intrusive-r. is the insertion of a non-underlying /r/ between a short low vowel and a following vowel in a subset of the dialects where linking-r occurs; for example, an /r/ is inserted between "Wanda" and "arrived" in "Wanda arrived" in dialects with intrusive-r.. For Cho's (1998) analysis, there are three constraints, as defined in (1).
(1) CODA CONSTRAINT -prohibits the occurrence of /r/ in a syllable coda FINAL-C -prohibits a short vowel at the end of a prosodic word FAITHFULNESS -the output should match the input Cho (1998) tracks five stages in the development of different dialects of English. The first stage is the most conservative, and corresponds to most North American dialects, with no deletion or insertion of /r/. The second stage is a transition between the first and third stage, with optional deletion of coda /r/, and hence consistent use of linking-r. The third stage is attested in formal Received Pronunciation (RP), with consistent deletion of coda /r/ and use of linking-r. The fourth stage is a transitional stage between the third and fifth stages, which is like stage 3, but also has optional use of intrusive-r, and is attested in parts of England. Stage 5, which is also attested in many parts of England, has consistent /r/ deletion and use of linking-r, as well as consistent insertion and use of intrusive-r.
Stage 1 is characterized by FAITHFULNESS outranking the CODA CONSTRAINT, which in turn outranks FINAL-C. In this stage, since FAITHFULNESS is ranked most highly, any /r/ in the input is preserved in the output, and no insertion or deletion can occur. The second stage is characterized by the 'undoing' of the ranking between FAITHFULNESS and the CODA CONSTRAINT. This means that the speaker has the option of pronouncing the /r/ or deleting the /r/ in the coda of forms like "Homer left". Stage 3 makes deletion mandatory in this environment by creating a new ranking in which CODA CONSTRAINT now outranks FAITHFULNESS (which in turn outranks FINAL-C). In stage 4 the ranking between FAITHFULNESS and FINAL-C is undone. Because of this, there is no clear winner between "Wanda arrived" without r-insertion and with rinsertion, leading to optional insertion. Stage 5 makes insertion mandatory by creating a new ranking in which FINAL-C outranks FAITHFULNESS. Throughout these stages, the FAITHFULNESS constraint 'works its way down' the constraint ranking. Stages 2 and 4 demonstrate variation with constraints unranked relative to each other, and also serve as intermediate stages historically. Each subsequent stage corresponds to the level of innovation in a given dialect. Bermúdez-Otero's (2006) treatment of intrusive-r is that it is a case of reanalysis. He argues that the status of /r/ as an epenthetic consonant is not predicated by markedness, since /r/ is extremely marked and epenthetic consonants should be unmarked. Instead, the phonological rule that resulted in linking-r was inverted to create the intrusive-r rule. Rule inversion is argued to be a type of reanalysis, and reanalysis is not subject to markedness laws "because it is not driven by phonetics, but by cognitive principles governing the relationship between phonology, morphology, and the lexicon" (Bermúdez-Otero 2006, 499;also see Vennemann 1972).
The present study will analyze how word-internal super-heavy syllables are dealt with in Arabic dialects using an approach similar to that of Cho (1998).

Methodology
This study makes use of data elicited from six speakers, each speaking a variety of one of the following six Arabic dialects: Saudi, 4 Egyptian, Emirati, Kuwaiti, Algerian, and Palestinian. Data were presented to the participants in the form of written English words, and each participant was asked to pronounce each word in their native dialect of Arabic. The forms were presented in English and not in Arabic orthography, in order to avoid an orthographic effect, where the speakers might use a more Modern Standard Arabic-like pronunciation. The reason for such an effect is that all the participants are highly educated in Arabic, and so know Modern Standard Arabic (MSA) well; also, since modern Arabic dialects are rarely written, written Arabic is assumed to be a representation of MSA. Lastly, the academic and formal nature of the elicitation procedure could induce the participants to automatically produce MSA.
The pronunciations were recorded using a digital audio recorder, and transcribed carefully. These transcriptions constitute the primary body of data used in this study. Before starting each recording session, a test session was conducted with each participant to make sure that they understood the task. In the case of the Algerian speaker, several stems that were problematic in her dialect were identified during this session, and replaced with more appropriate stems with the same target syllable structures.
The stimuli were composed to target specific phonological structures. Three noun stems representing different types of potentially super-heavy syllable were chosen (CVVC, CVCC, and CVCː), as well as two stems which end with regular heavy syllables, which can never be superheavy (CVCVC and CVCVV). The words used for all of the dialects except Algerian were /naːr/ 'fire', /bint/ 'daughter, girl', /Ɂumː/ 'mother', /ʤamal/ 'camel', /samaː/ 'sky'. These are all very well entrenched parts of the basic lexicon of each dialect, and so should be resistant to borrowing, and hence have cognates in each dialect (Zenner et al. 2014). All of these words had cognates in all of the dialects, except for /Ɂumː/ in Algerian Arabic, which was replaced with /ʤɨdː/ 'grandfather', which has the same prosodic structure and can also be considered to be well entrenched.
Three forms of each word were elicited: the base form of the noun, with no additional morphology; the first person plural possessive form, with the consonant-initial suffix /-na/ 'our'; and the first person singular possessive form, with the vowel-initial suffix /-i/ 'my'. In Algerian Arabic, there is a different set of possessive suffixes for inanimate nouns, so the inanimate noun /naːr/ 'fire' was replaced with /χɐːl/ 'maternal uncle'. No animate nouns were found at the time of original elicitation to replace the stems with non-potentially super-heavy syllables, so the possessive forms of these stems were elicited with the knowledge that they may end up being problematic.

Participants
All participants are at least bilingual -i.e., they know their native dialect of Arabic and are L2 speakers of English. They are also all between the ages of 20 and 35. Below, each participant is referred to by the name of their dialect, and some further information is given about the specific dialect they speak and their educational background. While only one speaker was consulted for each dialect, each dialect is assumed to be uniform in regard to how it deals with potential superheavy syllables. Despite the gender distribution, the range of educational backgrounds, differences in experience with linguistics, level of knowledge of MSA, and knowledge of other languages, only the variable of dialect is relevant to this study. These other variables may influence the speakers' production of potential super-heavy syllables, but since they are not the focus of this study, they will not be addressed further.
The Hijazi, Emirati, and Kuwaiti speakers all represent Arabian dialects of modern Arabic, the Egyptian speaker is the only representtative of Egyptian Arabic, the Rural Palestinian speaker is the only representative of Levantine Arabic, and the Algerian speaker is the only representative of Maghrebi Arabic. This covers four of the five modern dialect areas described by Bassiouney (2009).

Data
The data for Hijazi Arabic, along with a basic moraic analysis, is presented in (2).
(2) Hijazi All three stems with potentially super-heavy syllables (when a consonant-initial suffix is added), undergo epenthesis. This allows the final consonant in each stem to resyllabify as the onset to the syllable whose nucleus is the epenthetic vowel, avoiding any potentially superheavy syllables. In addition, the long vowel in /samaː/ shortens wordfinally.
The data for Egyptian Arabic, along with a basic moraic analysis, is presented in (3).
knowledge of MSA, and knowledge of other languages, only the variable of dialect is relevant to this study. These other variables may influence the speakers' production of potential super-heavy syllables, but since they are not the focus of this study, they will not be addressed further.
The Hijazi, Emirati, and Kuwaiti speakers all represent Arabian dialects of modern Arabic, the Egyptian speaker is the only representative of Egyptian Arabic, the Rural Palestinian speaker is the only representative of Levantine Arabic, and the Algerian speaker is the only representative of Maghrebi Arabic. This covers four of the five modern dialect areas described by Bassiouney (2009).

Data
The data for Hijazi Arabic, along with a basic moraic analysis, is presented in (2).
(2) Hijazi gloss UR SR /-naː/ 'our' /-i/ 'my' All three stems with potentially super-heavy syllables, when a consonant-initial suffix is added, undergo epenthesis. This allows the final consonant in each stem to resyllabify as the onset to the syllable whose nucleus is the epenthetic vowel, avoiding any potentially superheavy syllables. In addition, the long vowel in /samaː/ shortens wordfinally.
(3) Egyptian The three stems with potentially super-heavy syllables exhibit differing behaviors. The vowel in the stem /naːr/ shortens when a consonant-initial suffix is added, i.e., in the form [ˈnar.na], avoiding a potential super-heavy syllable. In forms of the stems /bint/ and /Ɂumː/ with a consonant initial suffix, a vowel is epenthesized after the last consonant of the stem, allowing it to resyllabify, avoiding any potential super-heavy syllables. It is noteworthy that the epenthetic vowel is stressed in the Egyptian data, unlike in other dialects where epenthesis occurs, though this study will not explore the differing stress systems of Arabic dialects. Like in most of the other dialects, the long vowel in /samaː/ is shortened word-finally.
The data for Emirati Arabic, along with a basic moraic analysis, is presented in (4).

Hassan Bokhari 10
(3) Egyptian The three stems with potentially super-heavy syllables exhibit differing behaviors. The vowel in the stem /naːr/ shortens when a consonant-initial suffix is added, i.e., in the form [ˈnar.na], avoiding a potential super-heavy syllable. In forms of the stems /bint/ and /Ɂumː/ with a consonant initial suffix, a vowel is epenthesized after the last consonant of the stem, allowing it to resyllabify, avoiding any potential super-heavy syllables. It is noteworthy that the epenthetic vowel is stressed in the Egyptian data, unlike in other dialects where epenthesis occurs, though this study will not explore the differing stress systems of Arabic dialects. Like in most of the other dialects, the long vowel in /samaː/ is shortened word-finally.
The data for Emirati Arabic, along with a basic moraic analysis, is presented in 4.
(4) Emirati Like the Egyptian data, the treatment of potential super-heavy syllables differs depending on the prosodic shape. The form of /naːr/ with a consonant-initial suffix does not undergo epenthesis, but the forms of /bint/ and /Ɂumː/ do undergo epenthesis with a consonantinitial suffix.
The data for Kuwaiti Arabic, along with a basic moraic analysis, is presented in (5).

Historical OT Typology of Internal Super-heavy syllables in Arabic Dialects
Like the Egyptian data, the treatment of potential super-heavy syllables differs depending on the prosodic shape. The form of /naːr/ with a consonant-initial suffix does not undergo epenthesis, but the forms of /bint/ and /Ɂumː/ with a consonant-initial suffix do undergo epenthesis.
The data for Kuwaiti Arabic, along with a basic moraic analysis, is presented in (5).

(5) Kuwaiti
In Kuwaiti Arabic, there is no epenthesis or vowel shortening, even in forms with consonant-initial suffixes, which create potential super-heavy syllables, including situations where there are two consonants in the coda, and in situations where a long vowel precedes a coda consonant. In the form [ʤɪ.ˈmɛl.na], the coda consonant receives a mora, but in [ˈnɑːr.na], the coda consonant does not receive a mora, since this would create a trimoraic syllable.
The data for Rural Palestinian Arabic, along with a basic moraic analysis, is given in (6).

Hassan Bokhari 12
gloss In Kuwaiti Arabic, there is no epenthesis or vowel shortening, even in forms with consonant-initial suffixes, which create potential superheavy syllables, including situations where there are two consonants in the coda, and in situations where a long vowel precedes a coda consonant. In the form [ʤɪ.ˈmɛl.na], the coda consonant receives a mora, but in [ˈnɑːr.na], the coda consonant does not receive a mora, since this would create a trimoraic syllable.
The data for Rural Palestinian Arabic, along with a basic moraic analysis, is presented in (6). The data for Algerian Arabic, along with a basic moraic analysis, is presented in (7).

13
Historical OT Typology of Internal Super-heavy syllables in Arabic Dialects This Rural Palestinian dialect of Arabic exhibits the same patterns as Kuwaiti Arabic, in terms of faithfulness in the presence of a consonantinitial suffix.
The data for Algerian Arabic, along with a basic moraic analysis, is presented in (7).
(7) Algerian The Algerian data are similar to the Palestinian and Kuwaiti data in terms of faithfulness in the presence of consonant-initial suffixes. Since the word 'camel' is considered inanimate in Algerian Arabic (and so does not take the same possessive morpheme as the other stems), and is furthermore mono-syllabic (so it doesn't show a stress shift like in other Arabic dialects), the word [mu.ˈʕal.lim] 'teacher' was examined in addition. The first-person plural possessive form of this word is [mu.ʕal.ˈlim.na], showing both that there is no epenthesis, and that stress shifts in order to remain on the penultimate syllable as in other Arabic dialects.
The transcriptions made for this research include close transcriptions of the vowels. It is worth noting that the quality of epenthetic vowels differs in the three dialects with epenthesis: [a] in Hijazi, [i] in Egyptian, and [ɨ] in Emirati. The question of what vowel is epenthesized is not the focus of this study, and so will remain unaddressed. This topic is an interesting one to consider in future research, but will not be discussed further in this paper (see Broselow 1976, Abu-Mansour 1991, Farwaneh 2009.
As this paper is about historical phonology, use of Classical Arabic or MSA data might be considered ideal for determining what the original treatment of potential super-heavy syllables may have been. However, underlying word-internal super-heavy syllables are at best rare in these The Algerian data are similar to the Palestinian and Kuwaiti data in terms of faithfulness in the presence of consonant-initial suffixes. Since the word 'camel' is considered inanimate in Algerian Arabic (and so does not take the same possessive morpheme as the other stems), and is furthermore mono-syllabic (so it doesn't show a stress shift like in other Arabic dialects), the word [mu.ˈʕal.lim] 'teacher' was examined in addition. The first-person plural possessive form of this word is [mu.ʕal.ˈlim.na], showing both that there is no epenthesis, and that stress shifts to stay on the penultimate syllable as in other Arabic dialects.
The transcriptions made for this research include close transcriptions of the vowels. It is worth noting that the quality of epenthetic vowels differs in the three dialects with epenthesis: [a] in Hijazi, [i] in Egyptian, and [ɨ] in Emirati. The question of what vowel is epenthesized is not the focus of this study, and so will remain unaddressed. This topic is an interesting one to consider in future research, but will not be discussed further in this paper (see Broselow 1976;Abu-Mansour 1991;Farwaneh 2009).
As this paper is about historical phonology, use of Classical Arabic or MSA data might be considered ideal for determining what the original treatment of potential super-heavy syllables may have been. However, underlying word-internal super-heavy syllables are at best rare in these two varieties. Forms like /naːr-na/ did not exist, and instead a case morpheme always needed to intervene between the noun and the possessive suffix, e.g. /naːr-u-na/ 'fire-NOM-our'. This allowed a potentially super-heavy syllable to resyllabify, surfacing as e.g.
[ˈnaː.ru.na]. 5 Because no faithful forms of this sort would ever produce a super-heavy syllable in Classical Arabic, there are no data on which to argue for the relative rankings of various constraints. Basically, the classical data are not comparable to the modern dialectal data. However, this fact suggests that the loss of case morphology historically may have given rise to the very set of problems that this paper investigates in the modern Arabic dialects. Gruber-Miller (1990) presents several potential reasons why essentially all modern dialects of Arabic have lost case morphology, including final short vowel loss, and stress shift. However, these phonological reasons do not explain why the case suffixes were not preserved before possessive suffixes. Either way, their loss may have motivated the need in some dialects for an epenthetic vowel before consonant-initial suffixes, at least in situations following different types of potential super-heavy syllables.

Analysis
This study utilizes the optimality-theoretic framework in order to explain the change from a certain Arabic dialect to another using constraints that will be defined in the following subsection.

The Constraints
The analysis of the various dialects to come below makes use of the set of universal constraints given in (8). c) WEIGHT-BY-POSITION (WBP) -A coda consonant must be moraic. Assign a constraint violation for any coda consonant that is not moraic (Kager 1999, 147). d) *CCC -No three consonants in a row. Assign a violation when three consonants appear in a row. This phonological condition was originally proposed by Kisseberth (1970).
e) DEP-μC -Do not insert a consonantal mora. 6 Assign a constraint violation for any consonantal mora in the output that is not present in the input.
f) *σμμμ -No trimoraic syllables. 7 Assign a violation for any syllable that has three moras.
g) DEP-V -Do not insert a vowel. Assign a constraint violation for any vowel in the output that does not have a correspondent in the input.

The individual grammars
The ranking of the constraints determines the grammar of each dialect. The grammar of each dialect is presented below as a Hasse diagram, where each line represents the relative ranking of the constraints it connects. Each constraint that is connected by a line to a constraint below it is understood to outrank (or dominate) that constraint. Because of the property of strict dominance, it also outranks the constraints that are dominated by the constraints that it outranks. For example, if constraint A outranks constraint B, and constraint B outranks constraint C, then constraint A outranks constraint C by transitivity. In order to highlight the differences between dialects, I begin the discussion of each dialect with the corresponding Hasse diagram. For each individual ranking presented in the Hasse diagrams, a corresponding ranking argument, in the form of an argument tableau, can be constructed. Because of the large number of constraint dominations in this study, only the most crucial comparative tableaux are presented. The Hasse diagram for Hijazi Arabic is presented in (9). If DEP-V were to dominate either WBP or MAX-μV then either the candidate with a deleted vocalic mora or the fully faithful candidate would wrongly surface, as in Egyptian or Emirati and the conservative dialects, respectively. In addition, if DEP-V were to dominate *σμμμ then [ˈnaːr.na] with a trimoraic initial syllable would wrongly surface.
In Hijazi Arabic, as in Egyptian and Emirati Arabic, it is preferable to epenthesize than to allow a tri-moraic syllable to surface. This is due to the fact that *σμμμ and WBP dominate DEP-V, which results in If DEP-V were to dominate *σμμμ or WBP, then the candidate with a trimoraic syllable or the fully faithful candidate with a rhyme slot that is not associated with a mora would wrongly surface, respectively. While the form [ˈbint.na] surfaces in the conservative varieties, the /t/ is not associated with an epenthetic mora in these varieties either. This will be discussed in more detail later. Also, *CCC prevents faithful forms in Hijazi Arabic, but as the tableau shows, these forms would be eliminated even if *CCC were not ranked highly.
In Hijazi Arabic, as in all the other dialects examined in this study, potential heavy syllables, such as in the second syllable of /ʤamal-na/ are also affected by these constraints. Since potential heavy syllables only have two timing slots in the rhyme (at least one of which will always be a vowel slot), unlike potential super-heavy syllables, they will never violate constraints like *σμμμ or *CCC. In turn, a consonantal mora can be epenthesized at the expense of satisfying WBP without violating other high-ranked constraints. 8 In Arabic, generally speaking, the presence of two moras in a penultimate syllable attracts stress; otherwise, stress would fall on the antepenult. 9 Because the antepenult is not stressed in forms like this in any of the dialects examined, it is clear that a mora is being epenthesized in all of the dialects. Another possible repair strategy to satisfy WBP would be vowel epenthesis, but this is not encountered in any of the dialects examined. Because consonantal mora epenthesis is the winning strategy, DEP-μC must be low-ranked in all dialects. Now that we have considered Hijazi Arabic we turn next to the second dialect, Egyptian Arabic. The Hasse diagram for Egyptian Arabic is presented in (10). 9 In some southern Arabian dialects, stress falls on a syllable that contains a geminate coda even when the following syllable contains two moras as in ['dar.ra.sat.ni] 'she taught me' (Alahmari 2018). 10 A potential candidate such as [ˈdʒa μ .ma μ l μ .na μ ] would be eliminated by the markedness constraint WSP (Kager 1999, 155), which is assumed to be highly ranked in these dialects.
(10) Egyptian The ranking of the constraints for Egyptian Arabic is pretty similar to Hijazi Arabic, except for the relation between DEP-V and MAX-μV. The main difference between the two dialects is that in Hijazi Arabic, MAX-μV dominates DEP-V, but in Egyptian Arabic, DEP-V dominates MAX-μV. If WBP were to dominate either DEP-V or MAX-μV, then either the candidate with epenthesis or vocalic mora deletion would wrongly surface, as in Hijazi or Egyptian Arabic, respectively.
In Emirati, like in Hijazi and Egyptian Arabic, /ʤamal-na/ surfaces with an epenthesized consonantal mora, as [ʤa.ˈmal.na], even though DEP-V and WBP are ranked differently with respect to one another. The important factor is that they both dominate DEP-μC.
The main difference between Emirati and all other dialects is the role of *CCC. 11  If WBP were to dominate *σμμμ, MAX-μV, or DEP-V, then /naːr-na/ would wrongly surface with an epenthetic consonantal mora, a deleted vocalic mora, or an epenthesized vowel, respectively. Tableau 8 also shows that *σμμμ and DEP-V outrank WBP as related to /bint-na/ as well as showing that *CCC and WBP outrank DEP-μC, resulting in the winning candidate in which two consonants serve in the coda with only one epenthesized mora.
In the following tableau, if *CCC were to dominate DEP-V, then /bint-na/ would wrongly surface with an epenthetic vowel. If DEP-μC outranked WBP then the faithful candidate, which does not assign moras to coda consonants would wrongly surface. If WBP outranked *σμμμ then the candidate that assigns two moras to the coda consonants would wrongly surface. Since DEP-μC is the lowest ranked and *σμμμ is a highly ranked constraint, the winning candidate surfaces with one epenthesized mora, the faithful candidate loses by two violations of WBP The rankings above show the OT accounts of the differences and similarities between these dialects. The following section considers the historical steps by which these dialects could have diverged.

Historical analysis
The process of changing one ranking to another is used to analyze the change from one grammar to another. According to Cho (1998), the only operations that may change a grammar are the unranking of two constraints that were previously ranked relative to one another, or the ranking of two constraints that were not previously ranked relative to one another in an immediate domination relationship. One assumption that is made is that the dialects with no epenthesis or shortening (Algerian, Kuwaiti, and Palestinian) are more conservative than the dialects with these processes. It is also assumed that the fewer the number of operations to get from one grammar to another, the more closely related the grammars are. The number of operations from each grammar to each of the others is presented in the table in (13).
(13) The number of steps between the grammars of each dialect 12

Hijazi Egyptian Emirati Others
Hijazi Others ---- The number of operations from one grammar to another that is presented in the table in (13) simply represents a hypothetical shortest path from each grammar to another, and not (yet) the proposed set of historical changes. Wichmann et al. (2010) provide a quantifiable method for determining the geographic homeland of a group of related languages. They take into account a simple linguistic difference metric and the geographical distance between the languages. Based on the assumption that the area with the most linguistic difference in the smallest area is the homeland, they then compute which of the languages corresponds most closely to the location of the homeland. The linguistic difference metric of Wichmann et al. (2010) could be replaced with the OT reranking metric presented here, and originating in Cho (1998). Using this to calculate the homeland of Arabic dialects would likely result in an area around Hijaz as the homeland of Arabic dialects, since Hijazi, Egyptian, and Emirati dialects form a cluster of geographically close, but linguistically diverse dialects. This result is compatible with historical facts regarding the spread of Arabic. This is also compatible with Holes' (2004) description of modern Arabic dialects as forming a dialect continuum, with Hijazi being similar to its direct neighbors, Egyptian and Emirati. This would be an interesting study to pursue in future research.
The dialect with the least number of changes from the conservative group of dialects is Emirati. The grammar represented by Emirati can thus be considered to represent an intermediate stage between the conservative varieties and the other varieties. Emirati, Hijazi, and Egyptian all went through a stage similar to the modern grammar of Emirati, and Hijazi and Egyptian diverged from it, while Emirati maintained its constraint ranking. Egyptian and Hijazi later diverged when Egyptian underwent a new innovation. Egyptian, then, represents the most innovative dialect, and is the least conservative of all of these varieties. Egyptian can be assumed to have gone through all the previous stages, represented by the grammars of Emirati and Hijazi. This may be compatible with the life cycle of phonological processes as suggested in Bermúdez-Otero (2020).
This progression is represented in the diagram in (14), which includes the number of steps required to advance to the next grammar.
(14) The dialects based on degree of innovation The steps between each of the grammars are listed below. The symbols >> and << indicate that a domination relationship was established between the two constraints (the constraint on the open side came to dominate the constraint on the pointed side), and the symbol X indicates that the ranking relationship was destroyed.
(15) Steps from conservative grammar (12) to Emirati grammar (11) First step MAX-Cslot >> DEP-V Second step *σμμμ >> DEP-V Third step *CCC X DEP-V Fourth step *CCC >> DEP-V In the first step in (15), MAX-Cslot dominates DEP-V. In the second step, the constraint against trimoraic syllables (*σμμμ) dominates DEP-V. In the third step, the domination relationship between *CCC and DEP-V is destroyed (i.e. there is no domination relationship between these two constraints in this step). In the fourth step, *CCC dominates DEP-V.

A historical OT typology of internal super-heavy syllables in Arabic Dialects
the most innovative dialect, and is the least conservative of all of these varieties. Egyptian can be assumed to have gone through all the previous stages, represented by the grammars of Emirati and Hijazi. This may be compatible with the life cycle of phonological processes as suggested in Bermúdez-Otero (2020). This progression is represented in the following diagram, which includes the number of steps required to advance to the next grammar. Emirati 4 Hijazi 2 Egyptian The steps between each of the grammars are listed below. The symbols >> and << indicate that a domination relationship was established between the two constraints (the constraint on the open side came to dominate the constraint on the pointed side), and the symbol X indicates that the ranking relationship was destroyed.
(15) Steps from conservative grammar (12) to Emirati grammar (12) First step MAX-Cslot >> DEP-V Second step *σμμμ >> DEP-V Third step *CCC X DEP-V Fourth step *CCC >> DEP-V In the first step in (15), MAX-Cslot dominates DEP-V. In the second step, the constraint against trimoraic syllables (*σμμμ) dominates DEP-V. In the third step, the domination relationship between *CCC and DEP-V is destroyed (i.e. there is no domination relationship between these two constraints in this step). In the fourth step, *CCC dominates DEP-V.
(16) Steps from Emirati grammar (11) to Hijazi grammar (9) First step MAX-μV >> DEP-V Second step WBP X DEP-V Third step DEP-V >> DEP-μc Fourth step WBP >> DEP-V In the first step in (16), MAX-μV dominates DEP-V. In the second step, the relationship between WBP and DEP-V is destroyed. In the third step, DEP-V dominates DEP-μc, and in the final step, WBP dominates DEP-V.
(17) Steps from Hijazi grammar (9) to Egyptian grammar (10) First step MAX-μV X DEP-V Second step MAX-μV << DEP-V In the first step in (17), the domination relationship between the faithfulness constraints MAX-μV and DEP-V is destroyed. In the second step, MAX-μV is dominated by DEP-V.
It is assumed that when the ranking relationship between two constraints is destroyed, all ranking relationships that exist due to transitivity through that original relationship are also destroyed. For example, if A >> B >> C, then A is assumed to outrank C by transitivity; then, when the relationship between B and C is destroyed, as indicated by the 'X' symbol in (18), B no longer dominates C. Moreover, the constraint A, which originally dominated B, no longer dominates C through transitivity. Another assumption relates to a starting configuration of A and B both outranking C, as in (19) If a single operation then makes A outrank B, as in (20), then the new transitivity relationship between A and C, through B, is assumed to replace the original direct relationship between A and C. The new Hasse diagram would be just like the starting configuration of (18), repeated in (21). Because of this, if C is then unranked with regard to B, as in (21), then it is also no longer ranked relative to A. In other words, if the domination relationship between the last two points in the diagram is destroyed, it implies that the relationship between the first and the last points in the diagram is also destroyed.
An interesting point is that consideration of just these forms does not shed light on the progression of changes that most likely took place. For example, there is only one difference in the forms that separate Hijazi, Emirati, and Egyptian dialects from one another: /naːr-na/ surfaces In the first step in (16), MAX-μV dominates DEP-V. In the second step, the relationship between WBP and DEP-V is destroyed. In the third step, DEP-V dominates DEP-μc, and in the final step, WBP dominates DEP-V.
(17) Steps from Hijazi grammar (9) to Egyptian grammar (10) First step MAX-μV X DEP-V Second step MAX-μV << DEP-V In the first step in (17), the domination relationship between the faithfulness constraints MAX-μV and DEP-V is destroyed. In the second step, MAX-μV is dominated by DEP-V.
The line labelled (1) represents dialects that underwent the changes (OT operations) listed in (15) that resulted in epenthesis in forms like /bint-na/; the line labelled (2) represents dialects that underwent the changes listed in (16) that resulted in epenthesis in forms like /naːr-na/; and the line labelled (3) represents dialects that underwent the changes listed in (17) which resulted in vocalic mora deletion (i.e., vowel shortening) instead of epenthesis in forms like /naːr-na/.
It is assumed that when the ranking relationship between two constraints is destroyed, all ranking relationships that exist due to transitivity through that original relationship are also destroyed. For example, if A >> B >> C, then A is assumed to outrank C by transitivity; then, when the relationship between B and C is destroyed, as indicated by the 'X' symbol in (18), B no longer dominates C. Moreover, the constraint A, which originally dominated B, no longer dominates C through transitivity.
Another assumption relates to a starting configuration of A and B both outranking C, as in (19) If a single operation then makes A outrank B, as in (20), then the new transitivity relationship between A and C, through B, is assumed to replace the original direct relationship between A and C. The new Hasse diagram would be just like the starting faithfully as [ˈnɒːr.na] in Emirati, with epenthesis as [ˈnaː.ra.na] in Hijazi, and with vowel shortening as [ˈnar.na] in Egyptian. Based on these data, Emirati appears to be the most conservative variety, and Hijazi and Egyptian both appear to be more innovative than Emirati, though it is unclear which would be more innovative than the other. In this sense, the OT analysis, using Cho's (1998) distance metric, provides both more and different insight into diachronic evolution than simply comparing the number of forms which are different.
The two main ways to represent shared innovation in related languages or dialects are tree diagrams and wave diagrams (Millar 2007, §7.4).
The tree diagram in (22) groups together Emirati, Hijazi, and Egyptian as a distinct group from the conservative dialects, and further groups Hijazi and Egyptian as more similar.
(22) A branching tree diagram based on the analysis of constraint reranking that shows which branch is most innovative Egyptian Hijazi Emirati Kuwaiti Palestinian Algerian In (22), new innovation is represented by branching, while a continuing straight line shows that there was no new innovation in regards to potential super-heavy syllables. For example, Emirati, Hijazi, and Egyptian Arabic are all grouped together, but because the line they all diverge from continues straight to Emirati, it is understood that Emirati only has innovation that occurred before the three dialects first diverged. Likewise, Hijazi only has innovation that occurred before Hijazi and Egyptian diverged.
The main problem with this tree diagram is that it implies that there was some point when Egyptian, Hijazi, and Emirati Arabic were all the same dialect, to the exclusion of Kuwaiti. As Bassiouney (2009) points out, Emirati, Hijazi, and Kuwaiti Arabic are all Arabian dialects, while Egyptian constitutes its own separate group of Arabic dialects. Because of this, Egyptian should not be grouped with Emirati and Hijazi, and Emirati and Hijazi should be grouped with Kuwaiti Arabic. However, remember that Holes (2004, 3-4) points out that modern Arabic dialects form a complicated sort of dialect continuum. According to Millar (2007, §7.4), tree diagrams are notoriously inadequate at representing the relation-ships between dialects, because they imply a homogenous ancestral language that underwent a sudden split. What is more likely to have happened is that each of these phonological innovations spread to a set of nearby dialects, but did not affect all closely related dialects. As Millar (2007, 231) points out, innovations can spread between related varieties after they have "begun to diverge quite strongly". This can be represented clearly in a wave diagram, such as the one below in (23), with the numbered circles indicating sets of innovation. The first set of innovations affected Emirati, Hijazi, and Egyptian Arabic (circle 1); the second set affected only Hijazi and Egyptian Arabic (circle 2); and the last set of innovations affected only Egyptian Arabic (circle 3).
(23) A wave diagram based on the analysis of constraint reranking that groups dialects based on shared innovation

Hijazi
The line labelled 1 in (23) represents dialects that underwent the changes (OT operations) listed in (15) that resulted in epenthesis in forms like /bint-na/; the line labelled 2 represents dialects that underwent the changes listed in (16) that resulted in epenthesis in forms like /naːr-na/; and the line labelled 3 represents dialects that underwent the changes listed in (17) which resulted in vocalic mora deletion (i.e., vowel shortening) instead of epenthesis in forms like /naːr-na/.
Another advantage of this wave diagram is that it also shows that the conservative varieties do not share innovations with each other, and that they are not related in any way phonologically (in terms of potential super-heavy syllables), except that they happen to have mostly fully faithful forms and have not undergone any further innovations in this aspect of their phonologies.

Discussion and Conclusion
This study provides an OT analysis of potential super-heavy syllables in six Arabic dialects: Hijazi, Egyptian, Emirati, Kuwaiti, Algerian, and Palestinian. These represent 4 of the 5 main dialect areas of Arabic (Hijazi, Emirati, and Kuwaiti all represent Arabian dialects).
Kuwaiti, Algerian, and Palestinian Arabic are all considered conservative with regard to how they deal with potential super-heavy syllables. In these dialects, all forms with potential super-heavy syllables surface faithfully (i.e., the output form is the same as the input form, with no changes). Epenthesis and mora deletion are blocked because DEP-V and MAX-μV, respectively, are undominated, and a mora is not epenthesized to a third rhyme slot because *σμμμ dominates WBP.
Emirati is the closest of the other dialects to these conservative dialects. In Emirati Arabic, a vowel is epenthesized before a third consonant when there are three consonants in a row (e.g., in forms like /bint-na/). This epenthesis allows the second consonant to syllabify as the onset of the syllable containing the epenthetic vowel. This epenthesis and resyllabification process can be understood to be due to the fact that the *CCC constraint dominates DEP-V in Emirati, preventing three consonants from ever occurring in a row, and allowing epenthesis, which is used to resolve this problem.
Hijazi Arabic, like Emirati, does not allow three consonants to surface in a row, and repairs such structures with epenthesis. However, unlike in Emirati, /naːr-na/ is not allowed to surface faithfully either. This is because WBP and *σμμμ dominate DEP-V. Importantly, *CCC could be demoted, or even removed from the ranking altogether, and the same candidates would win. This demonstrates that in Emirati, *CCC -i.e., a constraint against three consonants in a row -is the main concern of the grammar, while in Hijazi, WBP and *σμμμ being undominated together makes it impossible for structures containing three rhyme timing slots to surface at all.
Egyptian Arabic's grammar is very similar to Hijazi Arabic. What makes the grammar of Egyptian different from the grammar of Hijazi is only the relative ranking of MAX-μV and DEP-V. Since DEP-V dominates MAX-μV in Egyptian Arabic, deletion of a vocalic mora (i.e. vowel shortening) is preferred to vocalic epenthesis as a repair strategy in forms where two of the rhyme timing slots in a potential super-heavy syllable are vocalic. Because of this, forms like /naːr-na/ surface as [nar.na] in Egyptian Arabic.
This study shows that an approach like Cho's (1998) quantification of steps between the grammars can shed light on how grammars change. This topic could be expanded in future studies by examining more Arabic dialects and the sonority effect of the coda cluster in these dialects. In many Arabic dialects, sonority plays a role in vowel epenthesis between coda consonants -many dialects do not allow rising sonority, such as Hijazi, therefore vowel epenthesis would be the solution to break up a dispreferred coda cluster of rising sonority.
There are still some outstanding issues that are yet to be answered. These include how the loss of case could have sparked the changes that ended up giving rise to epenthesis in some of the dialects, the quality of the epenthetic vowel, stress of the epenthetic vowel and its interaction with vowel and mora epenthesis and deletion, and how the number of constraint reranking operations could be used for other purposes, like the determination of homelands, per Wichmann et al. (2010). Each of these topics could be a potential focus of future research. The wave diagram in (23) may not be sufficient to describe all observed changes among Arabic dialects.

Comments invited
PiHPh relies on post-publication review of the papers that it publishes. If you have any comments on this piece, please add them to its comments site. You are encouraged to consult this site after reading the paper, as there may be comments from other readers there, and replies from the author. This paper's site is here: https://doi.org/10.2218/pihph.6.2021.6668