1.1 The phonology: floating segments, the CVCV framework, and extrametricality

Floating segments have been argued for in countless analyses, the most well-known of which being accounts of the templatic patterns in languages such as Arabic (e.g. McCarthy 1981), as well as those accounting for liaison consonants in French (e.g. Encrevé 1988), and the behaviour of some affixes in English with regard to vowel shortening (Rubach 1996). In (5a) the final consonant of petit is unpronounced, as it is not associated with a position on the CV tier. In (5b), however, an onset position is available at the beginning of the following V-initial word. Within a theory where all syllables have the form CV this position comes for free, as every vocalic position on the skeletal tier is preceded by a consonantal position. The present analysis is couched within such a theory, an offshoot of the Government Phonology (GP) framework (Kaye et al. 1985), namely CVCV (Lowenstamm 1996; Scheer 2004). In this framework, no morpheme begins with a V or ends with a C on the timing tier. C or V positions may be unassociated to melody (and therefore phonologically null, as in (5b) before linking occurs). Conversely, a floating segment may have no link to a position on the timing (CV) tier (5a).⁵

Within this type of framework, a floating vowel, just like a floating consonant, will associate with an available empty V position whenever possible, as in (6). In the case of cohering affixes, this means that these vowels will associate to the empty final nucleus of the base to which they attach. As noted above, this position will be available in every overtly consonant-final base.⁶

In the case of French liaison, linking entails association across a word boundary. In the case of English cohering affixes, linking/liaison applies within the word, whether within or across a cyclic domain (see §1.2 on cyclic domains). In both cases liaison applies whenever an open CV slot is available.

An anonymous reviewer asks how an account that proposes floating segmental structure can be distinguished from a morphological diacritic account, given that in both cases cohering and non-cohering affixes are distinguished by characteristics that are stored as part of their lexical entries. The crucial distinction here, as detailed in Scheer (2008; 2012), is that phonological analyses, such as the liaison analysis herein, appeal to a phonological structure that has predictable effects on the output of the derivation. The attachment of floating segments entails a relationship between the floating segment and the CV-tier into which it is incorporated. In a French liaison context, a floating consonant becomes the onset of the initial syllable of the following word, and must therefore meet the proper phonotactic restrictions on onsets in the language. Floating vowels in English similarly link to the nuclei of preceding syllables, and therefore are required to be parsed as part of the syllables containing the consonant to their left. The implications of this phonological integration of floating segments will be crucial to the arguments below. A morphological diacritic, on the other hand, makes no predictions regarding the phonological behaviour of the item it is associated with. There is nothing inherent in the label ‘Level 1’ that triggers stress-shift, just as there is nothing inherent in the SPE diacritic ‘+’ that indicates ‘Level 1’ phonological behaviour. In short, the crucial difference between a morphological diacritic and a phonological representation is that the latter makes module-internal phonological predictions; it answers the question of why affixes behave phonologically the way that they do, while the former is a purely descriptive device (Scheer 2008). The floating status of vowels, just like any other (auto)segmental feature of a representation, makes phonological predictions, and is therefore not diacritic. The specific prediction of the floating-vowel analysis that is the focus of this paper is the pattern in (3iii); an affix that behaves as cohering when affixed outside of another category-defining affix will always be cohering. In English, this is due to the nature of floating segmental structure. In future work this research program will expand to cover other languages, wherein I make the same prediction regardless of the exact trigger for cohering phonological behaviour in each. The predictions of a phonological analysis that accounts for the pattern in (3) cans be stated as in (7)

1. A.Affixes that merge to roots: These affixes may or may not have an initial floating segment, but will be treated by the phonology as cohering, as all forms interior to a phonological cycle are (see §1.2 for the definition of a phonological cycle). Extrametrical elements must be final in the root+affix domain.

   • Both a root+cohering affix and a root+non-cohering affix will output a single phonological domain: [root+affix]. All affixes that merge to roots will pattern as cohering.

2. B.Affixes that merge to categorized bases: These affixes may or may not have an initial floating segment. If they do, they will phonologically merge into the structure to their left (see Newell & Piggott 2014 on Phonological Merger). If they do not have an initial floating segment they will form a separately-computed phonological structure (and will be footed separately if they contain enough phonological material that is metrifiable (not extrametrical)).

   • A base+cohering affix will output a form where the affix is part of the same phonological structure as its base [base+cohering affix], while a base + non-cohering affix will output a form where the affix is not part of the same structure as its base [base] [non-cohering affix].

3. C.Affixes that may have variable bases of attachment (roots and categorized bases): These affixes may or may not have an initial floating segment. In the case they attach to a root they will behave as specified in (7A). In case they attach to a categorized base they will behave as in (7B).
4. D.Impossible affixes: Type 1: An affix that has variable behaviour and behaves as in (7B) when attached to a root, and as (7A) when attached to a categorized base. Type 2: An affix that behaves as cohering when attached to some categorized bases and non-cohering when attached to other categorized bases.

Note that these impossible affixes are predicted to be possible in any account where affixes may be arbitrarily assigned to different Levels or to different Co-phonologies.⁷ We will see below that they cannot arise when the distinction between cohering and non-cohering affix behaviour is due to liaison.

Final phonological items in the toolbox necessary for the following analysis are the Main Stress rule of English (Chomsky & Halle 1968; Halle 1973; Hayes 1982; Halle & Vergnaud 1987; Halle 1998 and references therein) and the notion of Extrametricality (Liberman & Prince 1977; Hayes 1982; among others). The English stress system is one wherein, at its base, trochaic feet are built right-to-left in a phonological domain (and Secondary stress feet may be built from left-to-right), and main stress is assigned to the head of the rightmost foot in the word. This pattern is affected by a system of extrametricality. It has been proposed that the final syllables of nouns and derived adjectives (8ai, 8bi) and the final consonants of verbs (8aii) and non-derived adjectives (8bii) are extrametrical, and therefore ignored for the computation of stress (e.g. Hayes 1982).

See Scheer & Szigetvári (2005) for a discussion of how stress and extrametricality are more accurately captured within the CVCV framework than in standard metrical theories (and see Faust & Ulfsbjorninn 2018 for a proposal of how to derive extrametricality in Arabic in the CVCV framework). We will not attempt to justify any particular theory of extrametricality here, but will accept that it exists. What is important for the current analysis is that extrametrical elements are restricted to the edge of phonological domains. Extrametrical elements, and their distribution in relation to cohering and non-cohering affixes, will become important in §2.

The above phonological suppositions are all that is necessary to explain the generalizations seen in (3) above, and the distribution of stress in English derived words. As stated above, I restrict the discussion to stress, syllabification and footing as these processes display regularities that indicate synchronic phonological activity.

Note that each structural assumption above is amply independently motivated in the literature. Neither floating segments, a metrical system of stress, nor extrametricality have been primarily proposed to account for the difference between cohering and non-cohering affixes. It is the confluence of these structural assumptions that accounts for the different behaviours of English affixes. In addition to the phonological conventions above, however, a derivational, modular account of English morpho-phonology must appeal to the notion of morpho-syntactic cyclicity. This will be discussed in the following section.

1.2 The morpho-syntax: cyclicity (phases), and its relation to modularity

As stated in the introduction, in non-Lexicalist theories, such as Distributed Morphology (Halle & Marantz 1993; 1994; Marvin 2002; 2013; Embick 2010), some of the cohering/non-cohering pattern falls out from the derivation. Within DM, the distinction between affix classes has been claimed to be reducible to selectional restrictions, as promoted by scholars such as Fabb (1988) in an affix-based account, and much expanded upon in Giegerich (1999) and Plag (1999) in stem-based accounts. Specifically, a DM-style analysis proposes that cohering affixes (©) such as -al in parental may be affixed directly to an acategorial root (here parent), while in derivations like government there is a null verbalizing head between the root govern and the non-cohering affix -ment (n-©). In general terms, cohering affixes are local to the root, and non-cohering affixes are not.

Before such structures can be said to lead to the cohering/non-cohering distinction, DM needs an additional tool; a syntactic theory of cyclicity, such as one that includes phases (Chomsky 1999; 2008). A phase-based account of cyclicity holds that certain syntactic heads trigger the transfer of morpho-syntactic structure to the interpretive interfaces. The default assumption in such a framework is that these interpretation-triggers (phase heads) send the domain to be interpreted to both interfaces, Logical Form (LF) and Phonological Form (PF), simultaneously, as in the following derivations of (9a,b) in (10a,b).⁸ I follow the basic DM proposals that (i) roots are acategorial, and (ii) category-determining derivational morphemes (the heads of vP, aP, nP) are phase heads (= the edge of a phase).

In (10a) the categorizing -al is interpreted with the root parent, as it is the first (and only) cyclic head in the derivation. In (10b) the first categorizing head is also spelled out with the root. Here, as the v head is phonologically null, only the string govern is interpreted at PF in this first phase. In the second cycle of interpretation, -ment is interpreted.

Phase heads and their behaviour have been subject to much debate, and the current state of affairs regarding the status of phase heads in the derivational domain is as follows (the inflectional domain (v(oice)P, CP, DP) will not be treated in this article). The root and the first phase head that combines with it are interpreted together (along with possibly other non-phasal material not considered here (see Embick 2010). Various research programs have converged on the proposal that first-phase heads are spelled out with their complements, contra the proposal of Nissenbaum (2000), and Chomsky (2001b) that all phase heads send their complements to PF and LF. Marantz (2013 and previous work), Marvin (2002; 2013), and Arad (2003) demonstrate that roots cannot be semantically interpreted if they are not categorized.⁹ Embick (2010) argues that evidence from allomorphy forces the conclusion that phase heads trigger interpretation of their complement iff it contains another phase head. Newell (2009) also argues that derivational phase heads will spell out with their complements. I argue there that this is due to a lack of feature checking (and subsequent lack of movement to the periphery of derivational domains) of the type that is seen in the functional domains (e.g. Wh-movement to the specifiers of v(oice)P and CP). The features of category-defining heads are valued, therefore there is no reason to delay their interpretation upon completion of the phase. Svenonius (2004) argues that phases are unified domains (along the lines of the Prolific Domains proposed by Grohmann 2003), and that only the merger of a morpheme that is not a member of a particular domain can indicate to the computational system that transfer to the interfaces is called for. So, upon the construction of, say, a verbal domain v, the merger of a non-verbal head a would trigger the spell out of v in its entirety. All of this research converges upon the conclusion that first phase heads are local to the root (they are inside the phonological and semantic domain of the root) and that each subsequent phase head will be interpreted outside of this first phase. Therefore, in a derivation of the syntactic structure [[[[√] v ] n] a] (e.g. govern-Ø-ment-al), the interpretive domains at PF and LF will be [[[√v ] n] a].

These cyclic domains entail that, as stated above for the derivation of (10a), a suffix that determines the category of the root, being the first phase head, will fall within the phonological cycle of the root. This automatically gives us its cohering behaviour, as there is no derivational (or representational) boundary between the root and its categorizer. All members of a phonological string that enter the phonology at the same time will be treated as a unit (a single linearized string of segments or autosegmental parts thereof). In (10b), the overt suffix, being the second phase head, will be interpreted separately from the root leading to its non-cohering behaviour; it is parsed in a different cycle from its base of attachment and therefore the default interpretation is that it forms a separate phonological domain. In this case, the segments within the second phase will be linearized in relation to each other, before the entire second phase is linearized to the right of its base of attachment. This type of derivation also allows for an analysis of ‘dual-affiliated’ affixes. Aronoff (1974; 1976), Siegel (1977), Selkirk (1982), Giegerich (1999) (among others) have demonstrated that many non-cohering affixes have both cohering and non-cohering behaviour, as do some affixes traditionally classed as cohering. This Level-ambiguity can be exemplified by the stress-affecting (11a) vs. stress-neutral (11b) behaviours of -able (see also Bermúdez-Otero 2015).

The two morpho-phonological behaviours of -able fall out of a system where this affix may merge to either an acategorial root (11a) or to a verb (11b). Within CVCV we can see that in (11a) the vowel of the affix is present in the first cycle and able to govern the preceding vowel, indicated with the upper arrow in (12a). The lower arrow represents intra-constituent government between consonants that form a licit onset-onset sequence (a complex onset in traditional accounts of syllabification). In the case of the intra-constituent government in (12a), this renders V₄ invisible to V₃, allowing the latter to govern, and suppress, V₅. Assuming the final syllable of -able to be extrametrical, the stress algorithm of English will only permit initial stress in (11a), as (kɔ́mpɹə/kɔ́mpɹ̩) is the only possible foot that can be created over this melodic string. Note that in English empty vocalic positions are not always considered when computing the number of syllables to be footed (for the parametrized behaviour of empty nuclei see, for example, Kaye 1995; Scheer 2004; Scheer & Szigetvári 2005; Faust & Ulfsbjorninn 2018).

In (11b) the final pronounced vowel in compare is stressed (its stress/length is not represented in (12b)). Notably, the pronounced vowel in V₅ in (12b) will govern and supress V₆. After the computation of government/stress in the verbal domain, -able will be suffixed. As this affix contains no floating segments, it will not interact with or modify the syllabification of compare. As the initial syllable of the affix is too small to be footed on its own, it will not attract stress. Each cycle is computed separately in the phonology. We can think of this as the simplest option: the first cycle does not need to be reassessed by the phonology, so it will not be. Nothing more need be stated to give the cohering vs. non-cohering behaviour of this type of affix. No actual representational phonological boundaries are inserted. These derivations also mirror a semantic pattern that has been noted in the literature (for example, Kiparsky 1982; Arad 2003; Marantz 2001, 2007; 2013); the cohering -able combines with the root to give a non-concatenative reading, while the non-root-attaching, non-cohering -able's meaning is purely concatenative. In §4 we will return to the semantic predictions of a DM+Phase analysis, offering further support for the phonological analysis to come in §2.

A note here on the Phase Impenetrability Condition (PIC) (Chomsky 2001), presaged in the phonological literature as the preservation of metrical structure (Kiparsky 1979) or Strict Cyclicity (Kaye 1995), is necessary. It has been widely demonstrated in both the syntactic and phonological literature that inner cycles become, in certain ways, invisible to further computation. In the syntactic literature on Phases, it is proposed that domains that are sent to PF are no longer accessible to syntactic operations; that they are frozen (Chomsky 2001; Uriagereka 1999, and subsequent work in the field). In the phonological literature, this freezing-effect has been appealed to in different ways, some derivational (e.g. The Strict Cyclicity of Kaye (1995), the Russian Doll theorem of Bermúdez-Otero (2015)), some representational (e.g. The Prosodic Hierarchy, wherein rules apply, for example, only within a Phonological Word but not at the level of the Phonological Phrase). However, it is also abundantly clear that phonological representations and derivations are not subject to the same restrictions as are their morpho-syntactic counterparts. Operations like infixation, for example, have been demonstrated to cross cyclic boundaries, therefore modifying the output of a previous cycle of interpretation, contra the PIC. In fact, the status of the PIC has been argued to be epiphenomenal not only in the phonology, but also in the morphology and in the syntax (Bošković 2007, 2014; Embick 2014; Newell 2017). It is therefore taken as given here that phonological representations that are the output of a cycle/phase of interpretation are not modified unless the requirements internal to the phonological module necessitate it, but that previous phonological cycles may undergo any phonologically justified modifications. The specifics of when they may be modified are taken up in §2.

We return now to the question of morphemes that fall within or outside of the first phase. If all cohering affixes were affixed within the first cycle, and all non-cohering affixes affixed within the second cycle, and if syllable and foot construction were limited to applying to cycle-internal segmental material, then the floating vowel proposal in §1.1 would be superfluous. However, the distinction between the cohering and non-cohering patterns cannot be strictly due to whether an affix is or is not interpreted within the first phonological cycle, as amply argued in the literature critical of Lexical Phonology (Fabb 1988; Halle & Vergnaud 1987; and especially Plag 1999, among others). In these works, is it shown in great detail how individual affixes have selectional restrictions that are distinctly separate from their phonological behaviour. Specifically, as pointed out in Lowenstamm (2014), DM and phases, like LP, makes the wrong predictions for the phonological computation of Level 1 affixes that are not merged directly to a root (within the first phase). These criticisms are the subject of the following section.

2.1 Floating vowels and V-final bases

One potential problem for a floating vowel analysis of cohering morphology would be if an affix with an initial floating vowel were to follow a vowel-final base. In such a derivation, we might expect the floating vowel to remain unpronounced, just as the unattached floating consonants in French are when they precede a C-initial word as in ((5a) peti(t) garçon). What is clear, however, is that the initial vowels of cohering affixes in English are always pronounced, even after ostensibly vowel-final bases, as in, for example, heroic. Here we see that the hiatus between the base and the affix is not resolved through deletion, but rather by epenthesis of a glide.

There are two options for resolving this issue here. The first is to say that hiatus is resolved at the melodic level in English, and that it forces the epenthesis of an overt consonant between the final vowel of hero and the initial vowel of -ic. As this consonant is pronounced, it must be linked to a C on the CV tier. As all linked Cs on the CV tier must be followed by a V within CVCV theory, this epenthesis creates a position to which the floating vowel of the suffix may be linked.

The second option to account for the hiatus resolution pattern seen in the case of cohering affixes is to propose that there are no (or very few) V-final bases in English. This is what is proposed in Szigetvári (2016) for British English. Note that English notoriously does not permit a lax, short, vowel in the final open syllable of a lexical (as opposed to functional) word (biː ‘bee’ vs. *bɪ). If the final long vowels in English are all actually diphthongs; Vs followed by a glide, as proposed by Szigetvári, then these are consonant-final items that serve as bases of attachment for cohering affixes in English as discussed in the previous sections of this article. The ‘problem’ of hiatus resolution in the case of initial floating vowels is therefore non-existent. The derivation of heroic is consequently one where the base comes with the final glide and its following empty vocalic position. (37b) is the entire derivation of such a word.

In line with the above, the hiatus ‘problem’ also goes away for cohering affixes attached outside of other suffixes. All vowel-final affixes in English end in a long vowel or a diphthong. They are, therefore, glide final (-ity |ɪɾij|, -ory |ɔɹij|, -ary |ɛrij|, -ology |ɔlədʒij|, -ography |ɔgrəfij|, -ee |iːj|, -ify |ɪfɑj|), and therefore all contain a final empty nucleus that may house the floating vowel of a cohering affix. Such a derivation occurs phase-by-phase as follows.

The stress-attracting nature of the cohering affix (documéntary/documentárian) is explained exactly as in §2. Incorporation of the floating vowel merges the output domains of the two phases, forcing the footing of previously extrametrical segments ((dɔ̀kju)(mɛ́ntə)<ɹij>/ (dɔ̀kju)(mən)(tɛ́ɹij)<ən>, where the third syllable in the latter is unstressed for some speakers due to clash resolution).

The rare cases where we might propose that a short vowel does precede a cohering affix may offer evidence for the epenthesis account of hiatus resolution. Words like algebraic and moraic (Bermudéz-Otero, p.c.) cannot be accounted for by proposing an underlying glide in the representation of the root. In these cases, the floating vowel will probe (represented as ⇔ in (39)) into the inner domain, searching for an empty V position. This probing is no different from what is normally assumed to occur in, say, French liaison; the system verifies the phonological properties of the adjacent string. In doing so, the final vowel of the first phasal domain will become visible. This derivation ensures that the high vowel's features are structurally adjacent to the final a, giving us a structure where a undergoes pre-‘vocalic’ tensing and vowel shift (Jensen 1993). English does not permit lax vowels prevocalically (Liberman & Prince 1977). Hiatus resolution will trigger the insertion of a CV unit and the appropriate glide. Note that whether CV insertion precedes or follows tensing is not at issue here, and I offer no analysis of how tensing is derived.

Vowel-final bases are not an issue for the current account, as any account must propose a hiatus resolution operation to repair these VV sequences in English. Within RBP a rule of hiatus resolution will apply before the linking of floating segments (as the conditions for CV-insertion are present underlyingly, and the conditions for linking are only present after CV-insertion). In an OT-type account, FAITH-V will outrank DEP-CV, allowing for the pronunciation of all floating vowels. A third option is that these forms are no longer phonologically derived (they are either stored or the roots are subject to allomorphy). Note that all vowel-initial affixes select for the diphthong-final base (algebr[ɛi]-ize, algebr[ɛi]-ism, algebr[ɛi]-ic) (Raffelsiefen p.c.). If so, neither RBP nor OT will have anything to say about this alternation within a modular theory, as exceptions must be relegated to the domain of (pre-phonological) allomorphy.

2.2 C-initial cohering affixes

Another potential issue for the analysis proposed herein would be if there were any consonant-initial cohering affixes. This would be problematic, as C-initial affixes would obviously not be accounted for within an analysis that attributes their cohering nature to the presence of an initial floating vowel. I will argue here however, as in §2.2.1, that this possible problem is non-existent.

There are some C-initial affixes that have been proposed to be ‘Level 1’ in the literature, namely -t, -th, -st, -rd, and -tion.

I propose here that the first four affixes in (40) are not, in fact, cohering affixes. Rather, we have no evidence for such a classification of these affixes, save the fact that they merge with bound roots. Remember that all affixes, both those traditionally classed as Level 1 or as Level 2 are cohering when interpreted within the first phase; when affixed directly to a root. As the nominalizing -t and the ordinal -st, -rd, and -th affixes are only ever affixed to roots we have no way of determining if they would be cohering outside of another affix.³⁰ The liaison account promoted herein predicts that they would not be.

The final affix in (40), -tion, is interesting in that it has multiple allomorphs; tion = {-tion, -ation, -ition, and -ion}.

Remarkably, the consonant-initial allomorph in (41a) is restricted to derivations where tion is attached to a root; where it would be cohering regardless of the status of its initial segment(s). No examples of words containing overt affixes between the root and -tion exist, and -tion causes phonological effects such as vowel shortening (cf. intervene) that are typical of cohering affixes (Rubach 1996). Outside of other affixes, tion always has a vowel-initial exponent; -ation in the environment of -ize and -ify(k), -ition in the environment of a subset of coronal-final bases (ending in [n] definition, [z] transposition, [r] apparition and [d] addition), and -ion after -ate. It is evident that the form of the latter is an allomorph rather than due to the deletion of [t] after the [t] of -ate, as there is another allomorph, -ation that would permit a more faithful output form (*amalgamatation). It is also clear that, within the current framework, the [i]-initial form is present in (41d), as otherwise we could not explain the cohering and stress shifting nature of the affix (amálgamate/amalgamátion). No allomorph of this suffix contravenes the liaison analysis of affixation in English.

One interesting possible true exception to the proposal that all cohering affixes begin with a floating vowel is the verbal affix -en as in widen or lengthen. In addition to the restriction that this affix attach to monosyllabic bases, a characteristic that does not receive a better account here than in any other framework, it is also restricted to following obstruent consonants (42a) and is banned from following sonorants, including glides (42b) (Raffelsiefen 1999; 2015).³¹

This restriction is explained if the underlying form of -en is not [ən], as traditionally assumed, but is rather a floating C, [n]. As a sonorant consonant, it will link to a final empty nucleus, just as a floating vowel would (note that sonorant Cs are licit nuclei in English). As onsets must be less sonorous than their nucleus according to the phonotactic restrictions of English (and most languages), [n] may not link to an empty position following a sonorant consonant, ruling out forms like those in (42b).

What the above derivation also predicts is that no affixes with initial floating vowels will be permitted to affix to a form containing verbal -en, as there is no final empty nucleus following the suffixal consonant, and no hiatus would trigger the epenthesis of a vocalic slot when merging a floating V to the n-final domain. This is the case (see also Plag 1999, 70 for a discussion of other restrictions on affixation to -en). The only suffixes that can be attached outside of -en are non-cohering, as demonstrated by the maintenance of the syllabic n, as in widening, toughenable, awakenment, and flattenee.

In the end, as with the non-issue of vowel-final bases of attachment in §2.2.1, consonant-initial affixes pose no problem for the initial floating vowel analysis of cohering affixes. Additionally, the account of -en as a floating consonant offers motivation for the phonotactic restrictions on -en-affixation that have up to now been stipulated.

2.3 Summary of the computation

Before moving on to a discussion of previous analyses, let us review the phonological computational systems implied by the above. As this analysis places great weight on the specific underlying representations of morphemes (CVCV) and can be simply explained using the tools of an RBP system such as Government Phonology, I will only give a detailed account of the derivation in these terms. This, of course, does not imply that an OT account of the liaison analysis of English stress could not be built (I have pointed to some of its necessary rankings throughout the discussion), but it appears to me that the RBP account better captures the proposal that each operation is triggered directly by phonological structural relations.

In an RBP system like GP, rules are triggered when the environment for their application is met, and not otherwise. Rules that are always triggered upon spell-out (in each cycle) will therefore be syllabification and footing. Proponents of GP generally promote the proposal that CV and metrical structure is stored, but allow that for newly acquired lexical items rules of syllabification and metrification must be active in the language (this concurrent Stem-level phonological computation and Stem-storage is similar to what is proposed in Stratal OT). In any case, upon spell-out is where these operations will apply, when they do. Extrametricality is not derived here by a rule, but is rather part of the underlying representation. Syllabification and Footing will apply only to new segmental strings introduced upon phonological interpretation of each cycle. These rules will not re-apply to the output of previous cycles because this re-application cannot be structurally motivated; previously computed strings already have syllabic and metrical structure. In a second cycle, if any floating melodic material is present, a rule of linking will apply. This linking rule will be preceded by a rule of CV-epenthesis iff hiatus resolution is triggered on the melodic tier. The linking of a floating vowel to a position that used to be empty necessitates a re-calculation of syllabic relations (governing relations in CVCV). If the position linked to was extrametrical, it will not be any longer, as it is now not the rightmost structure in its string. This recalculation has a domino effect throughout the affected domain, but goes no further than it must. Specifically, any CV string or syllable that is modified will be recomputed. This recomputation of phonological structural relations will not breach an independent domain because, for example, the final segment in a string like govern has no structural relationship to the first segment of the following domain -ment, in government. Therefore, resyllabification and footing of -ment after the affixation of -al in governmental will not impact the structure of govern. Primary vs. Secondary stress will be determined over the entire word, and will therefore be assigned post-cyclically.

In sum, within each cycle operations will apply in the following order:

1. A.Search: floating material will search for empty structure on the CV tier.
2. B.Hiatus Resolution (may be unnecessary): If, upon Search, a hiatus is discovered, insert CV structure on the CV tier.
3. C.Link: Link any floating melody to any linearly available empty positions on the CV tier. (Unlinked melody will not be pronounced, linked-to structure will lose its status as extrametrical).
4. D.Syllabify (compute government relations over newly introduced melody and over any strings that are modified by this computation)
5. E.Foot (compute metrical relations for newly built syllables/government relations)

3.1  Halle & Vergnaud (1987)

For Halle & Vergnaud (H&V), Level 1 affixes are cyclic, in that they trigger the application of cyclic phonological rules. A H&V derivation of a word where a Level 1 (cyclic) affix (-al) is attached outside a Level 2 (non-cyclic) affix (-ment) is therefore as follows.

The above derivation, unlike in phase theory as it is currently understood, does not call upon a principle, such as the Phase Impenetrability Condition (Chomsky 1999; 2001a), that restricts the modification of previously interpreted cycles. For H&V, upon merger of the cyclic affix -al the entire string governmental is reassessed phonologically (cyclic rules are reapplied) allowing for a demotion of the primary stress on the first syllable of the root. This analysis encounters at least three problematic issues. The first is common to all accounts that distinguish Level 1 and Level 2 affixes with lexical diacritics; a theory that allows affixes that may behave as though they are Level 1 or Level 2 indiscriminately makes determining when to apply a phonological cycle complicated in ways not dealt with in H&V. In such an account, each dually affiliated affix must be stored as two independent affixes, a complication that reduces the analysis to a description of when phonology has applied.

The second problem encountered by H&V's account is that the reapplication of cyclic phonological rules (specifically here, syllabification and stress assignment) across the entire word upon affixation of an outer Level 1 affix is arbitrarily applied. Consider the discussion of comp[ə]nsátion vs. cond[ɛ]nsátion in §2.

Thirdly, it is apparent that the phonology is not reapplied to the entire string upon the application of phonological rules triggered by outer Level 1 affixes, despite the ability of main stress to shift. As noted in §2, we can see that syllabification on an inner domain is not reassessed in a root-affix_n-©-affix_© construction. Consider a word like probabilistic, with an output form as in (45) (-ic is not extrametrical cf. héro ∼ heróic).

The output in (45) indicates a foot structure that leaves the final syllable of the root domain untouched. Were syllabification and metrical phonological rules to reapply to the entire string upon affixation of -ic, we should expect the syllabic [l̩] (and the preceding [b]) in probab[l̩] to be resyllabified as the onset of the following syllable, giving the ungrammatical four-syllable form *(próba)(blístic). The analysis in §2, however, gets the expected parse in (45).

3.2  Kaye (1995)

Turning to Kaye (1995), it is interesting that the translation of his morpho-phonological system found in Scheer (2011) comes the closest of any of the previous analyses to the one proposed here. There are, however, issues that are not discussed in Scheer's translation that are important distinguishing factors between Kaye (1995) and the current analysis, in addition to the general issues with analyses that depend on a lexicalized distinction between Level 1 and Level 2 affixes.

For Kaye, Level 2 affixes are labelled ‘analytic’ and Level 1 ‘non-analytic’. His account is the contrary of H&V's: Level 2 affixes are cyclic, while Level 1 affixes are not. A further distinction between Kaye and H&V’s accounts is that in the former a cycle is only triggered over the complement; Level 2 affixes are outside the phonological domain to which they attach. Kaye notes, correctly, that a non-analytic morpheme affixed to a root is phonologically indistinguishable from a monomorphemic form. In root+Level 1 domains the phonotactics and the restrictions on syllabification inherent to English phonology all hold. For example, the Level 1 prefix in- cannot precede an l-initial morpheme, as the sequence nl is illicit in English at Level 1 (46).³³ Also, vowels must be short in closed syllables within a root+Level 1 domain, just as within a morpheme (47). These restrictions do not hold when a Level 2 affix is attached.

In a form like parentally the first affix will be interpreted in the domain of the root, and the second will be an outer affix; adjoined phonologically. This is exactly what we expect in the DM+Phase analysis and for that matter, in H&V as well. The additional distinction between H&V and Kaye (besides which affixes are considered cyclic) comes in the form of a no-look-back device in the latter's framework. Kaye institutes a precursor to Chomsky's Phase Impenetrability Condition (PIC) based on Chomsky's (1973) Strict Cyclicity, formulated as follows. “The principle of strict cyclicity states that the association created in the inner domain cannot be undone in an external domain.” (307). The fact that, in Kaye's system, a word-level cycle of phonology must apply causes this phonological PIC to be necessary in order to ensure the persistence of domains created at previous cycles. Note that this is my own extension of Kaye's predictions, as he does not treat any multiply-affixed forms.

Kaye's system therefore can also capture the phonological behaviour of Level 1 affixes attached outside other morphemes. In a word like probabilistic the analytic affix -ist will be outside of the phonological domain of its complement, and the phonological cycle at the word level ensures that -ist and the outer Level 1 affix are in the same domain; a domain that remains separate from the one determined in the first phonological cycle due to Kaye's version of Strict Cyclicity.

Kaye's no-look-back analysis does not have the problem with refooting/resyllabification that underlies H&V's account. It does, however, share with H&V the problem that Level 2 affixes may also be ‘cross-listed’ as Level 1 affixes, making the triggering of a phonological cycle in any of these accounts purely descriptive.

One issue that is unique to Kaye's system that is not discussed in Scheer (2011) is that Kaye proposes that the affixation of a Level 1 morpheme does not trigger a cycle of phonology, but rather triggers the search for a listed form. In essence, for Kaye all Level 1 morphology is allomorphic.

Kaye claims that Level 1 (non-analytic) forms must be listed due to the fact that pseudo-processes such as velar softening (electricity) and tri-syllabic laxing (opacity) that occur at Level 1 are impossible to formulate in Government Phonology.³⁴ Here is where Kaye's system diverges from the predictions in Scheer's phase-compatible translation. If Kaye's proposal is to be taken seriously, we have two options. The first is that any form where a Level 1 affix is attached outside a Level 2 affix must be listed and non-listed at the same time. If we consider again [(pɹɔ̀.bə)bl̩(ɪ́.stɪk)], the phonological domain boundary between probable and –ist exists, indicating productive phonology has been applied, but at the same time the non-analytic, allomorphic, cycle triggered by the affixation of -ic (an affix that does trigger velar softening, e.g. thoracic ([θoɹǽsɪk], cf. [θóɹæks], /θoɹæks-ɪk/)) should eradicate this boundary; there are no phonological boundaries within an allomorph. In fact, as mentioned above, Kaye's proposal is that all listed forms must be phonologically indistinguishable from monomorphemic words. This is clearly not the case.

3.3  Bermúdez-Otero (2018)

Kaye's proposal is similar to the most recent proposal in Stratal OT for accounting for Level-2 > Level-1 sequences of affixation (Bermúdez-Otero 2018b). Within Stratal OT, level of affixation is determined by the base and not by the affix (following Giegerich 1999; Kiparsky 2005). Bermúdez-Otero argues that, in a word like develop-ment-al, the base of attachment of -al must be a Stem and that the Stem-Level nature of development is discernable via its inability to host inflectional morphology (*develop-ment-s-al).³⁵ He concludes that the develop-ment to which -al is affixed must have been derived at the Stem Level. As the Word-Level phonology has not applied before affixation of -al, or before the affixation of any outer Stem-Level affix, there should be no Word-Level (non-cohering) phonological effects internal to Stem-Level (cohering) affixes. Besides this being untrue (see the discussion of probabilistic among other examples above), it is unclear how the system itself would determine that -ment is to be treated as Stem-Level before the affixation of -al, given that it must be a Word-Level affix before the affixation of other Word-Level affixes (e.g. develop-ment-less). It appears here that the level of the base is being determined by an outer-affix, a look-ahead device that is neither desirable, nor necessary within the liaison account of affixation. In the end, this analysis is subject to the same criticisms as is Kaye (1995).

3.4  Lowenstamm (2014)

Lowenstamm (2014) proposes what at first appears to be a fairly radical divergence from the traditional Level-affiliation accounts. He notes that the classification of a morpheme as category-defining, and therefore as cyclic in DM, cannot predict the attested phonological patterns in English, as discussed in §1.2. He says, “At the risk of belaboring the obvious: in pre-Phasal Spellout theories, domains of phonological interpretation (cycles) are projected from properties of affixes. In DM, in sharp contrast, domains of phonological interpretation (phases) are defined in strictly categorial fashion, and irrespective of what particular Vocabulary Item may eventually ornate a given category.” Yet in (51a) all of the words given have the same morpho-syntactic structure, (51b), making their divergent phonological behaviours anomalous.

To circumvent the above problem, Lowenstamm proposes that all derivational morphemes are roots, and that roots are not phase/cyclic heads/Level-affiliated. Phase heads in his system are null category-defining heads (a, v, n). The structure of a word like atomicity, with two ‘Level 1’ affixes is therefore as follows in (52). The three roots, atom, ic, and ity are merged with the null head n, which sends its complement to PF and LF. A single cycle of phonology is predicted.

A ‘Level 2’ affix in this system is also a root, but unlike a ‘Level 1’ affix (which selects for a root as its complement) it selects for an already categorized structure; an nP, vP, or aP. ‘Level 2’ affixes will therefore always merge outside of a phase head, and outside of a phonological domain (reminiscent of Kaye 1995 in §3.2). An additional restriction on these xP-attaching affixes is that they must immediately be categorized; their ‘root-hood’ is never accessible to further selection. A word like objectionable will therefore have the following structure.

A third class of affix, a ‘universal selector’ may merge with either a root or an xP. This is proposed to account for cross-listed affixes. -able in (53) merges with an nP, but in (54) merges with a root, demonstrating the behaviour of a universal selector.

As with all other analyses of the Level 1/Level 2 distinction, this sort of appeal to lexicalized selectional restrictions boils down to a description of the attested outputs, and it sneaks Level-affiliation back in through the guise of these selectional restrictions. But Lowenstamm's account has further issues. I will focus here on one of these issues that clearly demonstrates the wrong predictions made by this type of framework, leaving other complications aside for reasons of space.

Lowenstamm notes, following Ross (1974; 1979); Aronoff (1976), and Fabb (1988), that -al disprefers attaching outside of -ment if the latter is affixed to a verb (segmental vs. *attachmental). If this is the case, Lowenstamm contends, it appears that -al can ‘see through’ to the complement of -ment, a pattern of selection that is unexpected given locality constraints generally assumed in the morpho-syntactic literature.³⁶ According to Lowenstamm, -al selects for roots. It will therefore not be able to attach outside of a -ment that has selected for an xP, as xP selectors will lead to the immediate categorization of the Level 2 affix, bleeding the selectional restrictions of -al.

But, as -ment is a universal selector, when it affixes to a root rather than to a verb the root-selecting -al will be permitted to merge.

What is interesting is that, in addition to the three well-known exceptions to this rule (governmental, developmental, judgemental) Lowenstamm notes that the affixation of -ly outside of -al causes many more (perhaps all) verb-ment-al forms to become grammatical.³⁷

For Lowenstamm, this pattern means that -ment here attaches to the root attach rather than the verb, giving the following structure.

In (58), just like in the Stem-Storage solutions of Kaye and Bermúdez-Otero, Lowenstamm predicts that the domain from the root to -al will behave as if it were phonologically monomorphemic. But, the stress pattern of -ment nouns always depends on the stress pattern of the verbal base to which -ment is attached when this base exists independently, as is the case for attachmental. We know that stress clash is not required to be resolved when stress precedes -ment (59a), therefore the lack of stress on the heavy syllable preceding -ment in (59b) runs counter Lowenstamm's predictions.

Given the grammaticality of these ‘X-mentally’ forms, -al, and any Level 1 affix, is permitted to merge to a Level 2 (xP-attaching, non-cohering) affix. The distributional claims in Lowenstamm's account do not follow through.³⁸

For reasons like the above, Lowenstamm's (2014) proposed solution to the phonological challenge to the DM+Phases framework cannot be correct. This takes nothing away, however, from the point he raises that is at the core of the floating vowel proposal herein; outer Level 1 affixes cohere to their bases even though a cyclic account predicts that they should not.

3.5 Raffelsiefen (1999; 2015)

Raffelsiefen's work goes into incredible detail regarding the restrictions on the bases of affixation of vowel-initial affixes in English. She proposes that all vowel-initial affixes are cohering, and that their syllabification with their bases (due to a highly-ranked Onset constraint) explains their ability to condition stem-allomorphy.³⁹ Citing Raffelsiefen (1999), an anonymous reviewer asks why I ignore this type of non-metrical data as an indicator of domain-size. They note that “… practically every affix that triggers morpho-phonological changes has its own patterns of alternation with regard to very different phonological properties (of which the overwhelmingly discussed stress shifts or resyllabification are only two among many.” and they argue that the varying behaviour of individual affixes must lead to the conclusion that the cohering/non-cohering distinction is too simplistic, and that affix-specific co-phonologies must be appealed to. However, these additional restrictions must all be classed as allomorphy, rather than phonology, within a modular theory. An example of such a pattern discussed by Raffelsiefen (2015) is the restriction on sibilants flanking an unstressed vowel to explain why -ation will not affix to -ize-final bases (e.g. fantas[aj]ze but *fantas[ɪ]zation). That this pattern needs to be a restriction on bases of affixation of -ation and not a general rule of English phonology is clear (cf. class[ɪ]sm, hors[ɪ]z and all of the forms created by the various -s inflectional affixes in the language). The motivation for including this restriction in the phonological grammar (of -ation), however, is not so clear. The inclusion of any allomorphic restrictions in the co-phonology of an affix mixes two distinct types of operations and makes global predictions regarding domains of allomorphy that are not borne out (see Embick 2010 for a manuscript-length discussion of this issue). This clash of analyses raises a question that is central to the formulation of phonological theories; should we include affix-specific patterns within a theory of phonology, or are lexically listed properties the domain of morphology?⁴⁰ The CP approach argued for by Raffelsiefen posits that many (or all) affix-specific alternations (which are often admitted to be allomorphic) are governed by the phonological computation alongside the regular phonological operations of the language. Accordingly, each alternation is evidence for another phonological rule or constraint that must be included within the phonological computational system of the language under discussion. Level 1(Stem)/ Level 2(Word) analyses (SPE, Lexical Phonology, Stratal Optimality Theory, and to an extent Distributed Morphology), on the other hand, generally advance a hybrid position; certain phonological alternations and restrictions are determined either in the morphology or via particular pre-specified properties of the lexical entry of a morpheme (for the latter see Scheer 2016), while regular phonological rules/constraints fall within the domain of phonological computation. It is proposed here that this latter type of analysis effectively bleeds the necessity for affix-specific phonological rules, constraints, or co-phonologies without any loss of explanatory power. What is gained by such an account is a modular framework, wherein there are precise restrictions on which elements of the grammar may interact: morphological and phonological constraints or rules apply in separate grammatical modules. A more detailed motivation for the rejection of affix-specific phonologies can be found in Bermúdez-Otero (2012). Importantly, a CP account predicts that domains for allomorphy should be distinct from domains of phonology, leaving the fact that consonant-initial outer affixes neither condition nor undergo allomorphy to an unexplained factor that is different from their non-cohering behaviour.