1 Preliminary considerations

Phonological opacity remains one of the most controversial topics in theoretical phonology (see Baković Reference Baković2007 for a revised classification of opaque phenomena, and Baković Reference Baković, Goldsmith, Riggle and Yu2011 and Mascaró Reference Mascaró2011a for recent overviews). Opacity is the result of counter-feeding and counter-bleeding interactions between phonological processes. Among all types of opaque interactions, synchronic chain shifts represent a subset of counter-feeding interactions (see Kirchner Reference Kirchner1996; Parkinson Reference Parkinson1996; Łubowicz Reference Łubowicz2011; Reference Łubowicz2012, among others). In a regular chain shift, underlying /A/ maps onto surface [B], and underlying /B/ maps onto surface [C] (1).Footnote ^[1] In other words, underlying /B/ and derived [B] are not equally sensitive to the linguistic generalization banning B.

Crucially, underlying /A/ never maps onto surface [C] (2).

In parallel Optimality Theory (OT, Prince & Smolensky Reference Prince and Smolensky1993/2004), regular chain shifts cannot be accounted for. Both types of input–output mappings (/A/ $\rightarrow$ [B] and /B/ $\rightarrow$ [C]) are the result of a markedness over faithfulness constraint ranking (M $\gg$ F). To be more precise, some markedness constraint prohibiting [A], *A, must outrank some faithfulness constraint penalizing the mapping /A/ $\rightarrow$ [B], *A $\rightarrow$ B. The same holds for the mapping /B/ $\rightarrow$ [C]. Some markedness constraint against [B], *B, must dominate some faithfulness constraint disfavoring the mapping /B/ $\rightarrow$ [C], *B $\rightarrow$ C (3).Footnote ^[2]

However, in OT nothing prevents underlying /A/ from mapping onto surface [C], contrary to the facts. It must be assumed that the mapping /A/ $\rightarrow$ [C] incurs one violation of each of the faithfulness constraints. The transparent candidate [C] wins because it satisfies both high-ranked markedness constraints, *A and *B (4).

Within the framework of OT, synchronic chain shifts have been accounted for through an enrichment of the theory of faithfulness constraints (Kirchner Reference Kirchner1996, Gnanadesikan Reference Gnanadesikan1997). Kirchner (Reference Kirchner1996), for instance, applies local constraint conjunction (Smolensky Reference Smolensky1995) to chain shifts. His solution is to conjoin two faithfulness constraints in a specific domain. A locally conjoined faithfulness constraint is violated if the two faithfulness constraints that compose it are both violated for a specified domain (5).

Chain shifts are explained as a consequence of ranking the locally conjoined faithfulness constraint, in this case $\{\text{*}\text{A}\rightarrow \text{B}\& \text{*}\text{B}\rightarrow \text{C}\}_{\mathit{Segment}}$ , above the markedness constraint against the intermediate stage of the chain, *B. With this ranking, the desired opaque output [B] is obtained, instead of transparent [C] (6).

Nevertheless, local conjunction raises some theoretical problems, including the domain issue and what constraints can be conjoined (see Alderete Reference Alderete and Kusumoto1997; Spaelti Reference Spaelti1997; Łubowicz Reference Łubowicz2000, Reference Łubowicz, Alderete, Han and Kochetov2005; Moreton & Smolensky Reference Moreton and Smolensky2002; Itô & Mester Reference Itô and Mester2003; McCarthy Reference McCarthy2003; Miglio Reference Miglio2005; Walker Reference Walker2005).Footnote ^[3]

This paper examines a chain shift involving tonic metaphony in Servigliano (Italo-Romance, Marche region, Camilli Reference Camilli1929, Kaze Reference Kaze1989, Maiden Reference Maiden1991, Dyck Reference Dyck1995, Parkinson Reference Parkinson1996, Nibert Reference Nibert1998, Calabrese Reference Calabrese2011, Mascaró Reference Mascaró2011b, Walker Reference Walker2011). In Servigliano, underlying [–ATR] root mid vowels (/ɛ, ɔ/) raise to [+ATR] mid vowels ([e, o]), and underlying [+ATR] mid vowels (/e, o/) raise to [+high] vowels ([i, u]) when stressed and followed by high vowel inflectional suffixes (/--i, --u/). The paper also explores pre-tonic metaphony, whereby [–ATR] mid vowels raise all the way up to [+high] when followed by a stressed high vowel, and addresses the question of why tonic metaphony operates step-wise and pre-tonic metaphony operates in one fell swoop.

The main goal of the paper is twofold: first, to develop an analysis of the data using Optimality Theory with Candidate Chains (OT-CC, McCarthy Reference McCarthy2007), taking as a starting point the parallel OT analysis developed in Mascaró (Reference Mascaró2011b); second, to show that serialism, an intrinsic property of OT-CC, causes one analytical problem. On the one hand, in OT-CC the metaphony-triggering constraint Agree(+high,+ATR) proposed in Mascaró (Reference Mascaró2011b) needs to be split into two different constraints, one of which needs a more complicated formulation that requires a conditional clause. On the other hand, in order to explain the asymmetry between tonic metaphony, which operates step-wise, and pre-tonic metaphony, which operates as a fell-swoop change, positional faithfulness in OT-CC is needed, as in the parallel OT analysis by Mascaró (Reference Mascaró2011b); OT-CC has no inherent advantage in explaining this asymmetry, even if the fell-swoop raising in the pre-tonic domain is attributed to two different operations that violate different types of faithfulness constraints, as this paper proposes. In the light of the comparison between the two approaches, the paper concludes that the parallel OT analysis in Mascaró (Reference Mascaró2011b) is more elegant than an analysis in terms of a constraint-based derivational theory like OT-CC; the analysis in Mascaró (Reference Mascaró2011b) keeps the metaphony-triggering constraint as a lone constraint, and the OT-CC analysis cannot explain fell-swoop pre-tonic metaphony without exempting from using positional faithfulness.

The paper is organized as follows. Section 2 illustrates the data on tonic metaphony in Servigliano and summarizes the parallel OT analysis developed in Mascaró (Reference Mascaró2011b), which is based on local conjunction. Section 3 shows that Harmonic Serialism fails in accounting for the metaphonic chain shift in Servigliano. Section 4 explains the basics of OT-CC and develops an analysis that makes explicit the problems that this serial theory raises when accounting for a metaphonic chain shift. Section 5 presents the data on pre-tonic metaphony in Servigliano and the need for using positional faithfulness as in Mascaró (Reference Mascaró2011b). Section 6 concludes.

2 Tonic metaphony and local constraint conjunction (Mascaró Reference Mascaró2011b)

Servigliano, as is common in Romance languages, has a seven-vowel system in stressed position ([i, e, ɛ, a, ɔ, o, u]), with an [ATR] distinction in the mid vowel region (7).Footnote ^[4]

In this paper, distinctive binary features are assumed, and vowels are assigned their feature values as in (8) for four features: [high], [low], [ATR] and [back].

The distribution of [–ATR] mid vowels in stressed position depends on the following inflectional suffix. In the presence of a high vowel inflectional suffix ([--i, --u]), [–ATR] mid vowels are prohibited (*[ˈɛ,ˈɔ -- i, u]); when underlying, [–ATR] mid vowels alternate with [+ATR] mid vowels (9).

The very same high vowel inflectional suffixes also cause raising of [+ATR] mid vowels, which alternate with [+high] vowels (10).

These metaphonic alternations are a case of a productive, synchronic chain shift, in which [–ATR] mid vowels acquire [+ATR], and [+ATR] mid vowels acquire [+high] from high vowel inflectional suffixes, but in which [–ATR] mid vowels do not get both [+ATR] and [+high]. In Mascaró (Reference Mascaró2011b), a parallel OT analysis is developed for this metaphonic chain shift. According to him, tonic metaphony is triggered by the satisfaction of an agreement constraint Agree(+high,+ATR) (11).

By ranking Agree(+high,+ATR) above Ident(VF) (12), [+ATR] root mid vowels acquire [+high] from a high vowel inflectional suffix, as illustrated in tableau (14). Leftwards directionality (i.e. the fact that suffixes are triggers but not targets of tonic metaphony) is due to Ident-Suffix(VF) (13), a positional version of Ident(VF) relativized to protect only suffixal morphs.

This constraint ranking, however, does not prevent [–ATR] mid vowels from raising all the way up as [+ATR,+high] vowels (15).

Mascaró (Reference Mascaró2011b) solves this problem by resorting to local conjunction. By locally conjoining two Ident faithfulness constraints as in (16), and ranking this constraint above Agree(+high,+ATR), the one-step raising from [–ATR] mid vowels to [+ATR] mid vowels is accounted for (17).Footnote ^[5]

3 Harmonic serialism

Harmonic Serialism (HS, McCarthy Reference McCarthy2010) is a variant of OT that combines constraint ranking with serial derivations. Gen in HS generates only those candidates that differ from the input by one single operation, often defined in terms of one violation of a basic faithfulness constraint. The winning candidate is then fed back to Gen as a new input for another round of evaluation. This loop is then repeated until the fully faithful parse of the latest input wins. As argued for in McCarthy (Reference McCarthy, Hirotani, Coetzee, Hall and Kim2000), HS is in fact inadequate to deal with counter-feeding opaque interactions. If each step of an HS derivation shows harmonic improvement, there is no way to stop an intermediate representation B derived from underlying /A/ to map onto surface [C]. HS gradualness, in this respect, does not help in solving the problem. Mascaró (Reference Mascaró2013) has already shown that the Servigliano chain shift is as challenging in HS as it is in parallel OT. As shown in (18), at the second step of an HS derivation, an opposite ranking between Agree(+high,+ATR) and Ident(VF) would be needed in order to converge at this derivational stage. A ranking paradox in HS is fatal, as constraint re-ranking at different derivational steps is incompatible with harmonic improvement.

As becomes evident, local conjunction is superfluous in HS because the set of candidates can never violate more than one faithfulness constraint, in compliance with the gradualness requirement on Gen.

4 Optimality theory with candidate chains

As opposed to HS, in which evaluation is serial (i.e. it can apply n times until convergence), in Optimality Theory with Candidate Chains (OT-CC, McCarthy Reference McCarthy2007) Eval only applies once. Instead, serialism in OT-CC is implemented within candidates. Candidates in OT-CC are chains that connect an input to an output through intermediate representations, each of which represents a one-step change from the previous one. Candidate chains therefore show the properties of gradualness (i.e. only one operation at a time is permitted) and harmonic improvement (i.e. each successive form in a chain must improve harmony according to the language-particular hierarchy of constraints). The definition of candidate chains provided in McCarthy (Reference McCarthy2007) is as follows (19).

Parallel OT has a natural bias towards transparency; only feeding and bleeding interactions between processes can be accounted for because markedness constraints can only make statements about surface representations. In OT-CC, on the contrary, the existence of intermediate forms and a specific type of constraints, Precedence (Prec) constraints, allows for referring to these intermediate representations absent in parallel OT, and therefore accounts for opaque interactions. Prec constraints are a particular type of constraints in OT-CC that demand a specific ordering relation between faithfulness violations (20).

A Prec(A,B) constraint assigns a violation mark under two different conditions: (a) a violation of a faithfulness constraint B is not preceded by a violation of a faithfulness constraint A, and (b) a violation of a faithfulness constraint A follows a violation of a faithfulness constraint B. McCarthy (Reference McCarthy2007) illustrates how a Prec constraint can account for counter-feeding opacity with an example from Bedouin Arabic. In Bedouin Arabic, complex codas are prohibited and fixed via vowel epenthesis (*Complex-Coda $\gg$ Dep), and underlying /a/ raises to [i] in open syllables (Raise $\gg$ Ident(low)). However, vowel epenthesis counter-feeds raising, as underlying /ɡabr/ maps onto surface [ɡabur] ‘a grave’, not *[ɡibur]. Parallel OT is unable to select the actual opaque form (21).

In OT-CC, due to gradualness, the output *[ɡibur] necessarily follows an intermediate representation in which vowel epenthesis and no raising has applied. Valid chains from /ɡabr/ are shown in (22).

The candidate chain that should be selected is candidate chain (b) in (22). In OT-CC terms, a Prec constraint must block the application of raising after the application of vowel epenthesis. In a counter-feeding interaction of this type, a constraint like Prec(Ident(low),Dep) ranked below *Complex-Coda and above Raise is enough to discard the transparent candidate chain (c) (23). Both the winning candidate chain (a) and the transparent candidate chain (b) violate Prec(Ident(low),Dep), but only candidate chain (b) violates this constraint twice. This is so because not only is Dep violated without being preceded by a violation of Ident(low), as in candidate chain (a), but Dep is also followed by a violation of Ident(low).

Therefore, for counter-feeding interactions in OT-CC, the constraint that triggers the counter-fed process, in this case Raise, must be dominated by the Prec constraint.Footnote ^[7]

5 OT-CC and the metaphonic chain shift in Servigliano

From a serial perspective, it must be assumed that metaphonic raising is the result of two different spreading processes: (i) for the mappings /ɛ/ $\rightarrow$ [e], /ɔ/ $\rightarrow$ [o], leftward spreading of the feature [+ATR] underlyingly linked to an inflectional [+high] vowel suffix to an adjacent [–ATR] stressed mid root vowel, and (ii) for the mappings /e/ $\rightarrow$ [i], /o/ $\rightarrow$ [u], leftward spreading of the feature [+high] to a [+ATR] mid root vowel in the same condition.Footnote ^[8] In terms of OT-CC, the candidate chains in (24) must be gradual and harmonically improving according to the Servigliano constraint hierarchy. As in standard autosegmental phonology, I also assume that the feature [𝛼 F] linked to the target vowel, which occupies the same tier as feature [β F] linked to the trigger vowel, automatically delinks after spreading, and that this is a one-step operation in a candidate chain.

I propose that the one-step operation of spreading plus delinking in OT-CC violates a Dep-Link(F) constraint à la Morén (Reference Morén1999).

The constraint Dep-Link(F) is violated when a new association line connects a feature with a root node if and only if the feature and the root node are already present in the input. If the feature is inserted and has no correspondent in the input, for instance, Dep-Link(F) is not violated. Crucially, spreading plus delinking does not induce violations of a different type of faithfulness constraints, namely Ident(F). This is so because once spreading plus delinking takes place, the identity of a feature is not altered with respect to a segment, as the segment acquires a new feature that is not underlyingly linked to it. The constraint Ident(F) is violated when the input linking between a feature and a segment is maintained in the output and the value of the feature is changed (26).

The metaphony-triggering constraint proposed in Mascaró (Reference Mascaró2011b), Agree(+high,+ATR), ranked above Dep-Link(+high), accounts for spreading of [+high] to [+ATR] mid vowels (27).

However, Agree(+high,+ATR), which collapses the two features, makes the wrong prediction with respect to [–ATR] mid vowels. This constraint, being undominated, does not prevent [–ATR] mid vowels from raising all the way up to high in a step-wise manner, through [+ATR] spreading and then [+high] spreading (29). A transparent candidate chain like this should be ruled out (28).Footnote ^[9] For reasons of space, candidate chains are simplified; features on a separate tier are not represented. The constraint Dep-Link(+Fs) is used as a cover constraint for Dep-Link(+high) and Dep-Link(+ATR).

At first sight, one could think that a Prec constraint should explain the metaphonic chain shift. In counter-feeding interactions, a Prec constraint must always force the counter-feeding process to be preceded by the counter-fed process, that is, Prec(Dep-Link(+high),Dep-Link(+ATR)) (30).

The candidate chain ${<}$ ˈɛ--i $\rightarrow$ ˈe--i $\rightarrow$ ˈi--i ${>}$ violates Prec(Dep-Link(+high),Dep-Link(+ATR)) one more time than the candidate chain ${<}$ ˈɛ--i $\rightarrow$ ˈe--i ${>}$ . This is so because the former violates the two premises of the Prec constraint; a violation of the faithfulness constraint Dep-Link(+ATR) is not preceded by a violation of the faithfulness constraint Dep-Link(+high) (first violation), and the violation of Dep-Link(+ATR) is followed by a violation of Dep-Link(+high) (second violation). With respect to ${<}$ ˈɛ--i $\rightarrow$ ˈe--i ${>}$ , only the first premise of the Prec constraint is violated. Although the candidate chain ${<}$ ˈɛ--i $\rightarrow$ ˈe--i $\rightarrow$ ˈi--i ${>}$ violates Prec(Dep-Link(+high),Dep-Link(+ATR)) one more time than the candidate chain ${<}$ ˈɛ--i $\rightarrow$ ˈe--i ${>}$ , the former still satisfies Agree(+high,+ATR) more than the latter. This is why the candidate chain with fell-swoop raising is again wrongly selected as the most harmonic candidate (31).

An opposite ranking between Agree(+high,+ATR) and Prec(Dep-Link(+high),Dep-Link(+ATR)) would still select the wrong candidate, in this case the faithful one, ${<}$ ˈɛ--i ${>}$ , which vacuously satisfies the Prec constraint as it violates no faithfulness constraints (32).

For counter-feeding interactions, the Prec constraint must always be outranked by the markedness constraint that triggers the counter-feeding process, and dominate the markedness constraint that triggers the counter-fed process. As exemplified for Bedouin Arabic, in which vowel epenthesis counter-feeds open syllable raising, *Complex-Coda dominates Prec(Ident(low),Dep), which dominates Raise. This ranking allows for the counter-feeding process to apply.

It is now clear that for OT-CC to account for counter-feeding interactions, the two processes involved in the opaque interaction must be different, and as such they must result in violations of different faithfulness constraints. One possible solution is to split Mascaró’s (Reference Mascaró2011b) constraint into Agree(+ATR) (33) and Agree(+high). With the ranking Agree(+ATR) $\gg$ Prec(Dep-Link(+high),Dep-Link(+ATR)) $\gg$ Agree(+high), the actual output forms for both underlying [+ATR] and [–ATR] mid vowels are obtained (34).

However, there is a problem with the constraint Agree(+ATR). This constraint erroneously predicts that [+ATR] mid vowel suffixes also trigger [+ATR] tonic metaphony if defined as in (33). However, this is not the case (35).

For an analysis in OT-CC, an appropriate formulation of Agree(+ATR) should be like in (36).

This constraint presupposes a condition in its formulation: if [+high], then agree for [+ATR]. Although this formulation works empirically, it raises one major problem regarding its explanatory power: why is it the case that [+high] is in the if-clause and [+ATR] in the consequent-clause of the constraint? In other words, what does prevent the occurrence of Agree-type constraints demanding, for instance, that a vowel containing [–high] must agree for, let us say, [+back]? If the possibility of including a conditional clause in the formulation of an Agree-type constraint exists, then the set of Agree-type constraints increases undesirably.Footnote ^[10] In the parallel OT analysis in Mascaró (Reference Mascaró2011b), however, the metaphony-triggering constraint refers to two features that must both be spread; no splitting and no if-clause are necessary.Footnote ^[11]

6 Pre-tonic metaphony in Servigliano

Servigliano also displays another process of vowel harmony, distinct from tonic metaphony, in which the trigger is not an unstressed high vowel inflectional suffix, but a stressed high vowel. This process can be referred to as pre-tonic metaphony to differentiate it from tonic metaphony. In pre-tonic metaphony, a stressed high vowel raises all pre-tonic [+ATR] mid vowels to high (37).

Interestingly, pre-tonic metaphony, as opposed to tonic metaphony, also raises [–ATR] mid vowels to high; no chain shift is observed in the pre-tonic domain (38).

Mascaró (Reference Mascaró2011b) interprets this situation as an asymmetry between tonic metaphony and pre-tonic metaphony; tonic metaphony shows step-wise raising, whereas pre-tonic metaphony shows fell-swoop raising. As a possible solution in parallel OT, he proposes to relativize the local conjoined constraint Ident(high&ATR) to affect only stressed positions (39). If this constraint is ranked above Agree(+high,+ATR), it blocks fell-swoop raising in tonic metaphony, and allows it in pre-tonic metaphony.

For the OT-CC analysis explored in this paper, the Prec constraint predicts that fell-swoop raising is blocked not only in stressed positions, but also in pre-tonic positions. However, we can claim that pre-tonic metaphony from [–ATR] mid vowels to [+high] vowels is not a case of fell-swoop raising, but a two-step operation of first vowel reduction and then vowel harmony. Actually, vowel reduction targets [–ATR] mid vowels in the absence of high vowels, which map onto [+ATR] mid vowels (40).

We can claim, in accordance with Mascaró (Reference Mascaró2011b), that vowel reduction feeds one-step raising from a [+ATR] mid vowel, the result of vowel reduction, to a [+high] vowel. However, from the OT-CC perspective adopted here, it is clear that vowel reduction has nothing to do with a violation of Dep-Link(+ATR), as the examples in (40) suggest, because no spreading is involved in vowel reduction. On the contrary, vowel reduction is the result of applying an operation of feature value change (/–ATR/ $\rightarrow$ [+ATR]), which violates Ident(ATR) (26b).

If vowel reduction incurs no violation of Dep-Link(+ATR), the candidate chain with vowel reduction and then harmony in (41) does not violate Prec(Dep-Link(+high),Dep-Link(+ATR).

The right candidate chain showing fell-swoop raising is thus selected in OT-CC (42).

LUMs, or localized unfaithful mappings, are faithfulness violations at a particular spot in the input. It is precisely a difference in LUMs that makes candidate (a) and candidate (c) different. Although both candidates share the same final form in the chain, their first LUM is different. Candidate (a) violates Ident(ATR) when mapping /ɛ/ to [e], in which the value for the feature [ATR] is altered. Candidate (c), however, violates Dep-Link(+ATR) when mapping /ɛ/ to [e], in which an operation of spreading plus delinking has taken place.

Consider now the cases of tonic metaphony. In metaphonic contexts, however, the possibility of first violating Ident(ATR) and then Dep-Link(+high) must be excluded. On the one hand, to discard a candidate with that sequence of LUMs, we need a constraint like Ident(ATR) to be ranked above Prec(Dep-Link(+high),Dep-Link(+ATR). However, this ranking would also block the candidate chain for pre-tonic metaphony in (41). To solve this ranking paradox, one possible solution is to relativize the Ident(ATR) constraint to refer to the stressed position (Ident-Stress(ATR)), along the lines of Mascaró (Reference Mascaró2011b).

To recapitulate, pre-tonic metaphony does not violate Prec(Dep-Link(+high),Dep-Link(+ATR)), but context-free Ident(ATR), which is dominated by the former, and shows raising to [+high] as the result of changing the value for the feature [ATR]. In metaphonic contexts, the value for the feature [ATR] cannot be changed because this operation violates context-dependent Ident-Stress(ATR), which is undominated and ranked above Agree(+high) (43).

The fact that OT-CC helps in discovering a distinction between vowel reduction and harmony as two different processes, each of which violates a different faithfulness constraint, does not mean that OT-CC solves the asymmetry between metaphonic and pre-tonic contexts. Still, the use of positional faithfulness, as in Mascaró (Reference Mascaró2011b), is needed to account for the data. Therefore, OT-CC does not seem to represent any gain in terms of economy.

The other relevant analysis of Servigliano couched within parallel OT is the one in Walker (Reference Walker2011). In Walker (Reference Walker2011), two different constraints are used to explain tonic metaphony and pre-tonic metaphony, respectively. For tonic metaphony, a prominence-based licensing constraint for the class of height features ([high] and [ATR]) belonging to a high post-tonic vowel is used: License([Height] $\unicode[STIX]{x1D70E}_{post-tonic}$ ,ˈ $\unicode[STIX]{x1D70E}$ ). To account for step-wise raising, local conjunction of faithfulness constraints is also used, as in Mascaró (Reference Mascaró2011b). As opposed to Mascaró (Reference Mascaró2011b), however, Walker (Reference Walker2011) assumes that the two harmony processes, tonic metaphony and pre-tonic metaphony, are two distinct processes triggered by different constraints. One argument in favor of this is typological: other Romance languages have tonic metaphony, but not all of them show the effects of pre-tonic metaphony. The other factor in favor of assuming two distinct processes is the fact that the two processes have different domains of application, as only tonic metaphony can span across a boundary between a stem and a clitic. For pre-tonic metaphony, which also targets [–ATR] mid vowels, a maximal licensing constraint is proposed in Walker (Reference Walker2011), License([+high], $\forall$ V $_{\mathit{Left}}$ ). This constraint disfavors vowels that do not harmonize for [+high] with a following high vowel. As Mascaró (Reference Mascaró2011b) points out, the two adduced arguments in favor of assuming two different processes are weak. First, different Romance languages can have different extensions for the same phenomenon. Second, it seems reasonable to believe that the boundaries between proclitics and stems and between stems and enclitics are different, both morphologically and prosodically. Implementation of the analysis of Walker (Reference Walker2011) in OT-CC is possible, as two different raising-triggering constraints are posited. However, an explanation of both tonic metaphony and pre-tonic metaphony using the same constraint is desirable, as in Mascaró (Reference Mascaró2011b).Footnote ^[12]