Teresa Cabré
email: teresa.cabre@uab.cat

Francesc Torres-Tamarit

Maria Del

Ll

Keywords: hypocoristic, layered foot, Sardinian, truncation

This paper focuses on hypocoristic truncation in Sardinian. Besides disyllabic truncation, hypocoristic truncation in Sardinian also yields trisyllabic truncated forms by means of a process of reduplicative prefixation (e.g., Totore ← Servatore) and, more interestingly, a process of copy of what is analyzed as an internally layered ternary foot (e.g., (Va(tore)) ← Servatore). In this paper we develop an OT analysis of hypocoristic truncation based on output-output correspondence relations between bases and truncated morphemes that gives further support to internally layered ternary feet in the domain of the phonology-morphology interface.

Introduction

Truncation is a prosody-driven morphological process that is assumed to reduce bases to the size of minimal words [START_REF] Benua | Identity effects in morphological truncation[END_REF]. It has generally been assumed that minimal words are equivalent to the size of metrical feet [START_REF] Mccarthy | Foot and word in prosodic morphology: the Arabic broken plural[END_REF]. This follows from the dominance relations of the Prosodic Hierarchy, according to which a prosodic word immediately dominates a foot [START_REF] Nespor | Prosodic phonology[END_REF][START_REF] Selkirk | On the nature of phonological representations[END_REF]. The standard theory of metrical feet assumes the existence of minimally monosyllabic, but bimoraic feet (e.g., ("H)), or maximally disyllabic feet, which can be quantity sensitive (e.g., ("LL) for head-initial, trochaic feet, and (L"L) or (L"H) for head-final, iambic feet) or quantity insensitive, which can only be trochaic (e.g., ("σσ)) (Hayes 1995: 71).

Bimoraic and disyllabic truncation processes are widely attested crosslinguistically (for Romance, see Alber 2010; [START_REF] Alber | Templatic and subtractive truncation[END_REF][START_REF] Cabré | Minimality in the Catalan truncation process[END_REF][START_REF] Cabré | Prosodic trapping in Catalan[END_REF][START_REF] Colina | Spanish truncation processes: the emergence of the unmarked[END_REF]Piñeros 2000aPiñeros , 2000b[START_REF] Piñeros | Truncamientos en español [Truncations in Spanish][END_REF][START_REF] Prieto | Truncation processes in Spanish[END_REF]. Hypocoristic truncation in Sardinian is of special interest because besides disyllabic truncation (e.g., Mena ← Filumena), it also yields trisyllabic truncated forms [START_REF] Molinu | Le strutture non marcate negli ipocoristici del sardo [The unmarked structure in Sardinian hypocoristics[END_REF][START_REF] Molinu | Gli ipocoristici dei nomi di persona in sardo [The hypocoristics of personal names in Sardinian[END_REF][START_REF] Molinu | Le polymorphisme des hypocoristiques en sarde [The polymorphism of hypocoristics in Sardinian[END_REF]. Trisyllabic truncated forms pose a challenge for foot-based analyses of truncation.

Two types of trisyllabic truncated hypocoristics can be identified in Sardinian: those that derive from reduplicative prefixation (e.g., Totore ← Servatore) and, more interestingly, those that consist of a (full) copy of the last three syllables of the base, which surface with amphibrach (weak-strong-weak) rhythm (e.g., Vatore ← Servatore), only if the syllable of the base preceding a pretonic open syllable is closed. The process of trisyllabic truncation is an additional process of hypocoristic formation, in the sense that there are no trisyllabic hypocoristics without a disyllabic counterpart. With respect to reduplicative prefixation, if a disyllabic truncated hypocoristic has a stressed closed syllable, it cannot be preceded by a reduplicative prefix (e.g., *Babaldu ← Baldu ← Teobaldu cf. Memena ← Mena ← Filumena).

The theoretical claim of this paper is that feet can be internally layered to include a third unstressed syllable (Martínez-Paricio and [START_REF] Martínez-Paricio | The binary-to-ternary rhythmic continuum in stress typology: Layered feet and non-intervention constraints[END_REF][START_REF] Martínez-Paricio | Trisyllabic hypocoristics in Spanish and layered feet[END_REF]. By analyzing trisyllabic truncated hypocoristics in terms of internally layered ternary (ILT) feet, the general assumption that truncated forms equal the size of a metrical foot can be maintained. An analysis based on ILT feet also explains the size of the reduplicative morpheme in cases such as Totore without the need for morpheme-specific size constraints, along the lines of Generalized Template Theory, according to which the shape of prosodic morphemes and templatic effects follow from independently motivated constraints (McCarthy andPrince 1993, 1994).

The remainder of the paper is as follows. Section 2 describes the methodology used to gather the Sardinian data on hypocoristics. Section 3 describes stress in Sardinian and argues in favor of quantity sensitivity. Section 4 outlines the theoretical framework upon which the analysis of hypocoristic truncation hinges, which depends on foot-based truncation and ILT feet. Section 5 presents an OT analysis of hypocoristic truncation. Finally, Section 6 concludes the paper.

Methodology

The data analyzed in this paper were obtained by different means. Most of the data are taken from previous literature [START_REF] Lepori | Vocabolario moderno sardo-italiano: 8400 vocaboli[END_REF][START_REF] Molinu | Le strutture non marcate negli ipocoristici del sardo [The unmarked structure in Sardinian hypocoristics[END_REF][START_REF] Molinu | Gli ipocoristici dei nomi di persona in sardo [The hypocoristics of personal names in Sardinian[END_REF][START_REF] Molinu | Le polymorphisme des hypocoristiques en sarde [The polymorphism of hypocoristics in Sardinian[END_REF][START_REF] Rubattu | Nùmenes de persona [Personal names[END_REF][START_REF] Wagner | Fonetica storica del sardo[END_REF]. Additionally, a questionnaire containing a set of proper names with different lengths (Frantziscu, Caterina, Escolàstica, etc.), different stress patterns (Eleonora, Domìnigu) and different syllable structure complexity (Domìnigu, Serva-tore, Frantziscu, etc.) was designed to collect data from various Campidanian locales in April 2013 (one male speaker from Sìnnia, one male speaker and one female speaker from Seddori, one male speaker from Sestu, and one female speaker from Biddecrèsia). In some cases the subjects proposed several hypocoristic forms for the same proper name (this was the case for Frantziscu → Chicu, Ciciu, Chiscu, Chichinu), whereas in other cases they did not propose any truncated forms at all for the given proper name. Once the questionnaire was completed, we also asked them to add other hypocoristics commonly used and not elicited by the questionnaire. A total of 143 tokens including first hand and second hand data were obtained. The dataset is freely available in [START_REF] Cabré | Dataset on hypocoristic truncation in Sardinian[END_REF]. The total number of tokens for each of the three hypocoristic types (disyllabic, trisyllabic and reduplicated) is given in (1).

(1) Distribution of tokens across types The interviews were conducted by native speakers and the last two authors of the paper were also present during the recording sessions. The language register used by the interviewers was always that of a casual conversation between interlocutors in a relaxed atmosphere. All the speakers were recorded in their homes or public spaces in their villages using a Marantz Professional PMD660 digital recorder and a Rode NTG-2 microphone.

Whenever possible, in order to facilitate the reading and comprehension of the paper, we have offered both the orthographic and phonetic transcription of the Sardinian examples. To this end, the official guidelines for Limba Sarda Comuna (Regione Autònoma de Sardigna 2006) and [START_REF] Cardia | Arrègulas po ortografia, fonetica, morfologia e fueddàriu de sa norma campidanesa de sa lìngua sarda[END_REF] have been followed.

Stress in Sardinian

Before developing an analysis of hypocoristic truncation in Sardinian, the stress facts of the language need to be understood. So far there is no full-fledged formal analysis of stress assignment in Sardinian, but the most relevant aspects of stress assignment in non-verbal elements were already described in [START_REF] Bolognesi | The phonology of Campidanian Sardinian: A unitary account of a self-organizing structure[END_REF] (see also [START_REF] Pittau | Grammatica del sardo-nuorese[END_REF][START_REF] Roca | Stress in Romance languages[END_REF].

Disyllabic, vowel-final forms

According to [START_REF] Bolognesi | The phonology of Campidanian Sardinian: A unitary account of a self-organizing structure[END_REF], who describes the Sestu Campidanese variety of Sardinian, all disyllabic native words, which constitute 52% of the lexicon, have initial stress (e.g., domu ["dOmu] 'house'). Therefore, it seems reasonable to assume that the unmarked metrical foot in Sardinian is trochaic, as is common in Romance. 1 Bolognesi (1998) further supports this hypothesis by reporting secondary stress in derived nominal elements (e.g., menduledda [mendu"KEã:a] 'almond+dim' cf. mèndula ["menduKa] 'almond'; marteddeddu [marte"ã:eã:u] 'hammer+dim' cf. marteddu [mar"teã:u] 'hammer'; cugurredda [kuGur"rEã:a] 'caterpillar+dim' cf. cugurra [ku"Gurra] 'caterpillar'; piticheddeddeddu [pit:ik:eã:e"ã:eã:u] 'small+dim+dim+dim'). 2 For oddnumbered, morphologically complex words longer than three syllables, a secondary stress is reported to fall on the initial syllable of the word, not on the peninitial syllable (e.g., crojuetedda [kroZuE"t:Eã:a] 'lizard+dim', marigoseddu [maRiGO"zeã:u] 'bitter+dim', impresarieddu [impreza"Rjeã:u] 'kind of fish+dim'). This stress pattern creates an amphibrach (weak-strong-weak) rhythm at the right edge of the word. Amphibrach rhythmic patterns will be relevant in our analysis of trisyllabic hypocoristic truncation. As we will see, the possibility to create a right-aligned ILT foot when the first syllable of the base is heavy and can therefore be parsed into its own foot allows for preserving the last three syllables of the base name (e.g., (Va(tore)) ← (Ser)(va(tore))).

Trisyllabic, vowel-final forms

After disyllabic words, the second largest group of words in the native lexicon of Sardinian corresponds to trisyllabic forms (42% of the lexicon according to Bolognesi 1998), of which 13%, a clear minority, exhibit antepenultimate stress. According to [START_REF] Bolognesi | The phonology of Campidanian Sardinian: A unitary account of a self-organizing structure[END_REF], antepenultimate stress in trisyllabic words is essentially unpredictable and must therefore be assigned idiosyncratically in the lexicon (e.g., ànima 1 Independent evidence for trochaic feet comes from copy vowel epenthesis after vowel-final forms which would otherwise display final stress (e.g., the loanwords caffè [ka"f:Ei] 'coffee', mercè [mRa"ts:Ei] 'you.2sg.formal', gattò [gat"tOu] 'cake'). In addition, we performed a search of vowel-final words with final stress from [START_REF] Rubattu | Dizionario Universale della Lingua di Sardegna[END_REF], which includes both a Campidanese (55,000 entries approx.) and a Logudorese dictionary (73,000 entries approx.). For the Campidanese dictionary, we found a total of 139 words (e.g., suchefà 'bean', gilè 'vest', merì 'noon'), and for Logudorese, a total of 245 words (e.g., pompè 'shoe', tabì 'silk'). We can therefore confirm that, irrespective of whether epenthesis applies categorically or not in all these forms, final stress in vowel-final words is actually marginal in Sardinian. 2 Secondary stress in Sardinian has not been explored in detail yet. [START_REF] Vanrell | Sardinian intonational phonology: Logudorese and Campidanese varieties[END_REF] observed initial F0 prominences (a rising movement associated with the first syllable of the prosodic word), but, as opposed to [START_REF] Bolognesi | The phonology of Campidanian Sardinian: A unitary account of a self-organizing structure[END_REF], no evidence for binary rhythm was reported.

["anima] 'soul', ìligi ["iKiZi] 'quercus ilex', gèneru ["dZEneru] 'son-in-law'). The presence of an initial closed syllable in three-syllable words does not necessarily attract primary stress (e.g., marteddu [mar"teã:u] 'hammer ', cardaxu [kar"daZu] 'cauldron', cannuga [kan"nuGa] 'instrument made of cane', but mèndula ["menduKa] 'almond', ùrtimu ["urtimu] 'last'). No percentages are available to elucidate whether an initial closed syllable in three-syllable words favors antepenultimate stress. Although [START_REF] Bolognesi | The phonology of Campidanian Sardinian: A unitary account of a self-organizing structure[END_REF] argues that forms like marteddu [mar"teã:u] are a proof against quantity sensitivity in stress assignment, trisyllabic forms with an initial closed syllable followed by two open syllables and penultimate stress can be simply analyzed as containing an initial bimoraic foot consisting of one heavy syllable followed by a bimoraic foot consisting of two light syllables, following [START_REF] Bolognesi | The phonology of Campidanian Sardinian: A unitary account of a self-organizing structure[END_REF] assumption that syllables are exhaustively parsed into feet in Sardinian: (H)("LL). The reason why stress falls on the penultimate syllable is that the head foot in Sardinian is always the rightmost, and then stress class resolution would be responsible for leaving the first heavy syllable unstressed. Therefore, trisyllabic forms with an initial closed syllable and penultimate stress cannot be taken as evidence in favor of quantity insensitivity: these forms simply surface with the unmarked stress pattern of Sardinian, which is penultimate stress. Most important, however, is that [START_REF] Bolognesi | The phonology of Campidanian Sardinian: A unitary account of a self-organizing structure[END_REF]

Consonant-final forms

The source of word-final consonants in Sardinian according to [START_REF] Bolognesi | The phonology of Campidanian Sardinian: A unitary account of a self-organizing structure[END_REF] consists mainly of inflectional endings: -s, which is the plural suffix (e.g., domus ["dOmuz(u)] 'houses'), and also the first plural, second singular and second plural ending of present indicative verbs (e.g., manducas ["mandukaz(a)] 'eat.2sg.pres.ind'); and -t, the third singular ending of present indicative verbs (e.g., piaghet [pi"aGED(E)] likes.3sg.pres.ind'). 3 Besides inflectional -s and -t, Bolognesi (1998) lists 11 native content words containing a word-final consonant: caput 'head' (although Rubattu's dictionary gives capu instead of caput, without a final -t), tempus 'time/weather', corpus 'body', pegus 'sheep', lunis 'Monday', martis 'Tuesday', mèrcuris 'Wednesday', mellus 'better', peus 'worse', forsis 'perhaps', and antzis 'instead'. In phrase-final position, these words should surface with antepenultimate stress, and even preantepenultimate stress in the case of mèrcuris, due to the insertion of an epenthetic copy vowel (e.g., lunis ["lunizi] 'Monday', tempus ["tempuzu] 'time/weather'; see [START_REF] Torres-Tamarit | Opacity in Campidanian Sardinian: Metaphony and copy-vowel epenthesis[END_REF]. This set of words with an underlying final consonant might suggest that stress in Sardinian is quantity insensitive, as stress never falls on the final closed syllable. However, drawing such a generalisation from this small set of words is risky. We further performed a search of consonant-final words ending in -s from [START_REF] Rubattu | Dizionario Universale della Lingua di Sardegna[END_REF] and most of them had no final stress. For Campidanese, words ending in -as are the most common (512 words), followed by words ending in -us (503 words) and words ending in -is (319 words). Words ending in -es and -os are much less common (11 and 5 words, respectively). For Logudorese, words ending in -as are also the most common (445 words), followed by words ending in -os (374 words) and -es (105 words). Then we also find words ending in -is (105 words) and words ending in -us (78 words). All these terminal elements seem to be inflectional nominal suffixes, and could therefore be analyzed as extrametrical, without compromising quantity sensitivity.

In order to check the extent to which a final closed syllable might attract stress in Sardinian, we also performed a search of consonant-final words from [START_REF] Rubattu | Dizionario Universale della Lingua di Sardegna[END_REF] for both Campidanese and Logudorese in which both monosyllabic words and words ending in -s were set apart. As we expected, polylsyllabic consonant-final words are extremely rare. For Campidanese, only 23 polysyllabic consonant-final words were found. Of these, 10 were transcribed as having final stress. 4 In Logudorese, 13 words out of 35 consonant-final words were transcribed as having final stress (some of these words being compounds). 5 Another group of consonant-final words end in -at in both varieties (there are no words ending in other vowels followed by -t except for zenit 'zenith', with penultimate stress). All words ending in -at never have final stress and are mostly conjunctions (e.g., Camp. and Log. ossiat 'namely', Log. sincabèsserat 'if anything'), pronouns (e.g., Log. calesisiat 'anyone', Camp. itasisiat 'whatever') and adverbs (e.g., Log. calesicherzat 'anyway', Camp. aundisiollat 'everywhere'). From these findings we conclude that, for some consonant-final words, stress assignment is sensitive to the weight of the final syllable. For other words, the final consonant is extrametrical. In phrase-final position however, we expect these words to surface with an epenthetic copy vowel in Campidanese, which renders final stress non-surface-true, that is, opaque.

To conclude this section, let us briefly summarize the main features of stress in Sardinian. Feet in this language are trochaic (e.g., head-initial), and final consonants contribute to the weight of the syllable and attract stress (although word-final epenthesis wipes out this effect phrase-finally). Marked, exceptional stress is also possible, and some consonant-final words have penultimate stress; antepenultimate stress is also possible. Inflectional endings always remain unstressed, which could be explained by assuming that the domain for stress is the morphological stem. Finally, we enumerate the arguments in favor of analyzing stress assignment in Sardinian as quantity sensitive. First, despite the rarity of consonant-final words in the language, a considerable number of these words show final stress; interestingly, the majority of consonant-final words with non-final stress can be analyzed as containing an inflectional, terminal element that ends in a consonant, which would not compromise quantity sensitivity. Second, despite the extremely low frequency of closed syllables in the lexicon [START_REF] Bolognesi | The phonology of Campidanian Sardinian: A unitary account of a self-organizing structure[END_REF] states that about 90% of all syllables in Campidanese Sardinian are open), words longer than two syllables with a penultimate closed syllable never display antepenultimate stress. This suggests that the penultimate closed syllable is heavy and therefore attracts stress; closed syllables in the third-to-last position of a word do not attract primary stress because an unmarked trochee can be built on the last two syllables of the word. A further argument in favor of quantity sensitivity in Sardinian actually comes from the analysis of trisyllabic hypocoristic truncation. All trisyllabic hypocoristics in Sardinian like Vatore and Parrina derive from bases with an initial closed syllable (e.g., Servatore, Gasparina). Assuming quantity sensitivity allows for parsing this first syllable into its own bimoraic foot (e.g., (Ser)vatore, (Gas)parina). This parsing leaves space for building a layered foot on top of the last three syllables (e.g., (Ser)(va(tore)), (Gas)(pa(rina))). It is this layered foot the one that is preserved in the truncated form (e.g., (Va(tore)), (Pa(rina)). When the initial syllable of a four-syllable base is open (e.g., Filumena), no trisyllabic hypocoristic is attested in Sardinian (e.g., *Lumena). This is so because the third-to-last syllable is already parsed into an initial bimoraic foot together with the first open syllable of the base (e.g., (Filu)(mena)). Trisyllabic patterns of hypocoristic truncation will be explained in detail in §5.

Theoretical framework

The foot-based analysis of truncation

In her analysis of hypocoristic truncation in Japanese, [START_REF] Benua | Identity effects in morphological truncation[END_REF] showed that the size of truncated forms can be easily derived from the constraints responsible for the size of minimal words [START_REF] Mccarthy | The emergence of the unmarked. Optimality in prosodic morphology[END_REF], those that consist of only one foot (e.g., bimoraic truncated stems with diminutive suffixation in Japanese: Mido-čan ← Midori; Yoko-čan, Yoo-čan ← Yooko; Hana-čan, Haa-čan, Hač-čan ← Hanako). Miminal words emerge when the three constraints in (2) are all obeyed, which are referred to as prosodic word restrictors. Only when these three constraints are satisfied does the minimal prosodic word emerge. PARSE-σ ensures that no syllable is left unparsed. For its part, FOOT-BINARITY sees to it that feet are strictly binary. Finally, the alignment constraints ALL-FEET-LEFT/RIGHT guarantee the existence of only one foot, as the presence of more than one foot would correlate with violations of these constraints. When applied to hypocoristic truncation, the size of truncated forms follow from these three independently motivated constraints. A fourth constraint is needed to select the optimal foot form. For Sardinian hypocoristic truncation, this constraint is TROCHEE, formulated in (3).

(3) TROCHEE Assign one violation mark for every foot whose head is not initial. [START_REF] Mccarthy | Doing Optimality Theory: Applying theory to data[END_REF] Foot-based truncated forms satisfy all the previously mentioned constraints but violate a lower-ranked faithfulness constraint MAX-BT, formulated in (4).

(4) MAX-BT Assign one violation mark for every syllable in the base that does not have a correspondent in the truncated form. (This constraint counts syllables and not segments for ease of exposition.) [START_REF] Mccarthy | Doing Optimality Theory: Applying theory to data[END_REF] The constraint MAX-BT is an output-output correspondence faithfulness constraint that maximizes the number of segments in correspondence between a fully prosodified base and the output of the truncated morpheme. In tableau (5) we illustrate how the constraints introduced so far interact to derive foot-sized truncation. The input consists of a string of four syllables parsed into two trochaic feet the second of which is the head of the prosodic word. The winning candidate is (5a), a head-initial disyllabic foot, which only violates MAX-BT but satisfies the three prosodic word restrictor constraints PARSE-σ, FOOT-BINARITY and ALL-FEET-RIGHT, plus the foot form constraint TROCHEE. Only ALL-FEET-RIGHT is included in the tableau. From this tableau, two ranking arguments are demonstrated: both PARSE-σ and ALL-FEET-RIGHT dominate MAX-BT. The constraints FOOT-BINARITY and TROCHEE are undominated and do not dominate any other constraint.

(5) Foot-sized truncation One last relevant aspect to take into account in deriving truncation is determining which portion of the base is preserved in the truncated form. This is generally achieved by ANCHOR constraints, which demand that segments standing in input-output correspondence preserve alignment with respect to designated edges of prosodic constituents.

To give an example, in his analysis of Spanish hypocoristic truncation, Piñeros (2000a) makes use of the constraint ANCHOR(BT)Left to derive left-anchored truncation (e.g., Fernan ← Fernando), formulated in (6). ( 6) ANCHOR(BT)Left Any element at the left periphery of SF (source form) has a correspondent at the left periphery of TF (truncated form). (Piñeros 2000a) For a different pattern of hypocoristic truncation in Spanish in which the preserved portion of the base is the foot (e.g., Mando ← Armando), Piñeros (2000a) makes use not of an ANCHOR constraint, but rather an anti-deletion faithfulness constraint MAX relativized to refer to the head of the prosodic word, that is, the main-stressed foot. This constraint is formulated in (7). 6 (7) HEAD(PWd)MAX Every element contained in the head of the PWd (e.g., the main-stressed foot) of SF must have a correspondent in TF. (Piñeros 2000a) We will see that the relevant constraint responsible for selecting which portion of the base is preserved in the truncated form in Sardinian is HEAD(PWd)MAX. In §4.2 we briefly introduce the theory of ILT feet on which the analysis of hypocoristic truncation in Sardinian crucially depends.

Internally layered ternary feet

Contrary to standard assumptions in metrical theory that posit that feet are maximally disyllabic, we present additional evidence for ILT feet (Martínez-Paricio 2013, Martínez-Paricio and Kager 2015), a metrical configuration in which a foot is immediately dominated by another foot. This structure does not constitute an independent primitive category in the prosodic hierarchy, but is rather a grammatical byproduct that arises from language-particular constraint rankings.

Recent studies in metrical theory have shown that reference to ILT feet facilitates a more restrictive account of a wide range of phonological phenomena. For languages with ternary rhythmic stress, it can be proposed that ternary rhythm arises whenever the word contains an ILT foot (Martínez-Paricio and Kager 2015). Also, ILT feet have been shown to facilitate a simpler and more unified account of a wide range of footconditioned segmental and tonal distributions (e.g., specific cases of vowel reduction, vowel lengthening, strengthening and weakening of consonants, particular tonal distributions, and tone spreading domains; see [START_REF] Bennett | Foot-conditioned phonotactics and prosodic constituency[END_REF][START_REF] Bennett | The uniqueness of metrical structure: Rhythmic phonotactics in Huariapano[END_REF][START_REF] Breteler | Deriving bounded tone with layered feet in Harmonic Serialism: The case of Saghala[END_REF][START_REF] Breteler | Layered feet laid bare in Copperbelt Bemba tone[END_REF][START_REF] Caballero | Choguita Rarámuri (Tarahumara) phonology and morphology[END_REF][START_REF] Caballero | Morphologically conditioned stress assignment in Choguita Rarámuri[END_REF][START_REF] Davis | The distribution of aspirated stops and /h/ in American English and Korean: An alignment approach with typological implications[END_REF][START_REF] Harris | Wide-domain r-effects in English[END_REF][START_REF] Iosad | Prosodic structure and suprasegmental features[END_REF][START_REF] Jensen | Against ambisyllabicity[END_REF][START_REF] Kager | Stress in windows: Language typology and factorial typology[END_REF]Martínez-Paricio 2012, inter alia). The most important prediction of these analyses is that beyond the traditional strength dichotomy between a foot head (the strong branch of a foot) and a foot dependent (the weak branch of a foot), a model with ILT feet predicts further subtle strength contrasts between two distinct foot dependents.

Based on the theory of prosodic recursion by [START_REF] Itô | Prosodic minimality in Japanese[END_REF]Mester (2007, 2013), we assume that each projection of a foot can be defined as minimal (a foot that does not HEAD(PWd)MAX in Piñeros (2000a), is better formulated as a faithfulness constraint rather than as an alignment constraint because ANCHOR-STRESS shows no alignment effects, as opposed to, for instance, ANCHOR-LEFT. We also adopt this view and consider that HEAD(PWd)MAX is a faithfulness constraint in which the head of the PWd must have a correspondent in the truncated form as the head of the PWd. See also [START_REF] Mccarthy | Faithfulness and prosodic circumscription[END_REF] for a discussion of ANCHOR constraints. dominate another foot) or non-minimal (a foot that dominates another foot), maximal (a foot that is not dominated by another foot) or non-maximal (a foot that is dominated by another foot). These authors' and our proposal is that grammars can make direct reference to these labels, which follow from dominance relations. We represent in figure

(1) the shape of an ILT foot, and in figure (2), a disyllabic, non-ILT foot.

5 Hypocoristic truncation

Data

Disyllabic truncation is the most common pattern of hypocoristic truncation in Sardinian (90 tokens in our dataset, as shown in 1). Most disyllabic truncated hypocoristics correspond to a copy of the main foot found in penultimately stressed bases. These bases with penultimate stress are analyzed as containing a disyllabic trochaic foot aligned with the right edge of the word (e.g., 8a. Filumena, (LL)("LL)), an ILT foot in bases ending in a sequence of a heavy syllable followed by a light syllable (e.g., 8d.

Frantziscu, (H)(("H)L)), or an ILT foot in bases ending in a sequence of three light syllables not preceded by a heavy syllable (e.g., 8e. Simone, (L("LL))). In most disyllabic truncated hypocoristics there is a total identity between the main foot in the base and the whole truncated form, except for bases that consist exclusively of an ILT foot (e.g., 8e. Simone, (L("LL))), in which case only the minimal foot is preserved in the truncated form (e.g., Mone, ("LL)); if the maximal foot was preserved, the output of truncation would be identical to the base, that is, an instance of vacuous truncation. Some examples of disyllabic truncated hypocoristics appear in (8). In all of them, foot boundaries are indicated by parentheses and the stressed vowel is marked with an acute accent. Note that metrification is exhaustive and that one base is diminutivized (Isperantzina). Besides disyllabic hypocoristic truncation, Sardinian displays another process of hypocoristic formation that yields truncated forms that exceed the size of a disyllabic foot. These truncated forms consist of exactly three light syllables, which we interpret as an ILT foot consisting of a minimal, trochaic foot to which an immediately preceding unstressed syllable is adjoined to a maximal foot (e.g., (L("LL))). Trisyllabic truncated hypocoristics in Sardinian are of two types depending on the mechanism used to retrieve the immediately preceding unstressed syllable. One type of trisyllabic hypocoristic truncation is simply a copy of the head foot already present in the base, which is an ILT foot, as shown in (9). For a complete list of cases (23 tokens in our dataset), we refer the reader to [START_REF] Cabré | Dataset on hypocoristic truncation in Sardinian[END_REF]. Note however that some of the trisyllabic truncated forms are variants that derive from the same base.

(9) Trisyllabic truncated hypocoristics I, (L("LL))

(Ser)(va(tóre)) → (Va(tóre)) (Ber)(tu(méu)) → (Tu(méu)) (Gas)(pa(rína)) → (Pa(rrína)) (Mar)(ghe(ríta)) → (Ghi(ríta))

Interestingly, in bases containing an initial sequence of two light syllables, which we analyze as being parsed into a foot due to exhaustive parsing, trisyllabic truncation is unattested (10).7 A few other cases of trisyllabic truncated hypocoristics have been attested that incorporate into the ILT foot a third-to-last closed syllable (e.g., Gantine ← Costantinu and Bus.tia.nu ← Se.bas.tia.nu, and other versions of the same form like Bostanu and Sostianu). In other cases, the pretonic closed syllable in the base corresponds to an open syllable in the truncated hypocoristic (e.g., Tzicana ← Frantziscana, Ba.cia.nu ← Se.bas.tia.nu, and other versions of the same form like Betanu, Bitau, Bucianu, Cotzianu and Pitanu). These latter cases show the preference in Sardinian for ILT feet consisting of strictly three moras. A few of these examples appear in (11).

(11) Trisyllabic truncated hypocoristics II, (L("LL))

(Cos)(tan)(tínu) → (Gan(tíne)) (Fran)(tzis)(cána) → (Tzi(cána)) Se(bas)(tiánu)

→ (Be(tánu))

The other type of trisyllabic truncated hypocoristic undergoes a process of augmentation by means of reduplicative prefixation (30 tokens in our dataset). The reduplicative prefix in the truncated hypocoristic is identical to the immediately following stressed syllable, as illustrated in ( 12), and allows an ILT foot to be built.

(12) Trisyllabic truncated hypocoristics with a reduplicative prefix, (L("LL))

(Filu)(ména) → (Me(ména)) (Lui)(gínu) → (Gi(gínu)) (Ser)(va(tóre)) → (To(tóre)) (Pas)(cáli) → (Ca(cáli))

The process of reduplicative prefixation always applies to a pre-existing disyllabic truncated form and, like diminutivisation, is an additional process of hypocoristic formation. Only disyllabic truncated hypocoristics can undergo reduplicative prefixation since hypothetical reduplicated hypocoristics such as *Sasara (derived from a base Sara) are unattested. We also need to bear in mind that disyllabic bases cannot be truncated unless a diminutive suffix has been added. In such cases, the process of reduplicative prefixation can also take place (e.g., Luigi → Luiginu → Ginu → Giginu). Finally, forms in which the reduplicative prefix copies a CVC stressed syllable, simplifying it to CV or not (e.g., *Ba(l)baldu ← Baldu ← Teobaldu) are also unattested. As we will see, this restriction follows from parsing HL-final sequences like the one in Teobaldu into an ILT foot, (("H)L).

All patterns of hypocoristic truncation in Sardinian are summarized in (13).

(13) Summary of hypocoristic types

Disyllabic Trisyllabic binary foot ("LL) (Mena) ILT foot (("H)L) (L("LL)) ((Bal)du) (Va(tore)), (To(tore))

The metrification of bases

In order to explain both disyllabic and trisyllabic truncation as preservation of the head of the prosodic word, a maximal foot, the metrification of the bases in ( 8), ( 9) and (11) needs to be derived. Before this however, we will show how ILT feet with amphibrach (weak-strong-weak) rhythm and disyllabic ILT feet with trochaic (strong-weak) rhythm derive from constraint ranking. Two types of constraints that regulate the location of head and dependents within a foot are needed (Martínez-Paricio and Kager 2015: 473). The first type is classical foot form constraints like TROCHEE, defined in (3), and IAMB, which assigns one violation mark for every foot whose head is not final, the opposite of TROCHEE. In addition to these two constraints, however, a pair of constraints that regulate the position of the adjunct within the ILT foot are needed. The left and right versions of this pair of constraints are defined in ( 14). These constraints are categorical (e.g., one violation mark is maximally assigned per locus of violation) and also conform with vertical locality, a condition posited by Martínez-Paricio and [START_REF] Martínez-Paricio | The binary-to-ternary rhythmic continuum in stress typology: Layered feet and non-intervention constraints[END_REF] to restrict the types of prosodic categories that can occupy each of the three categories in what they call non-intervention alignment constraints. These constraints obey vertical locality because the locus of alignment (a minimal foot) and the separator category (a parsed syllable) are immediately dominated by the domain constituent (a maximal foot), and the separator category (a syllable) and the domain category (a foot) are adjacent in the prosodic hierarchy. a. ALIGN-R(Ft min , σ, Ftmax) For every minimal foot Ft min , assign one violation mark if some footed syllable intervenes between Ft min and the right edge of its containing Ftmax. (This constraint favors (σ(σσ)) over ((σσ)σ), and (σ(σ)) over ((σ)σ).)

b. ALIGN-L(Ft min , σ, Ftmax) For every minimal foot Ft min , assign one violation mark if some footed syllable intervenes between Ft min and the left edge of its containing Ftmax. (This constraint favors ((σσ)σ) over (σ(σσ)), and ((σ)σ) over (σ(σ)).)

We claim that a final sequence of three L syllables in Sardinian, when the sequence is not preceded by another L syllable, is parsed into an ILT foot with a left adjunct and a minimal trochaic foot (e.g., (σ("σσ))). A left adjunct emerges when ALIGN-R(Ft min , σ, Ftmax) dominates ALIGN-L(Ft min , σ, Ftmax); initial stress within the minimal foot is derived by the ranking TROCHEE ≫ IAMB. Tableau (15) illustrates these rankings. In the following tableaux, only candidates satisfying TROCHEE and FOOT-BINARITY (the constraint against degenerate feet) will be considered. We further assume that all ILT feet violate the constraint NO-RECURSION, formulated in ( 16). ( 16) NO-RECURSION Assign one violation mark for each additional parse of an element into the same category. [START_REF] Itô | The extended prosodic word[END_REF] As shown in (8d, i), we claim that a final sequence of a heavy and a light syllable are parsed into an ILT foot (e.g., (Fran)((tzis)cu), (Teo)((bal)du)). We will see that the whole ILT foot, which is the head foot, is preserved in truncated hypocoristics (e.g., ((Chis)cu), ((Bal)du)). An alternative parsing with an uneven trochaic foot ("HL), however, would violate the Iambic/Trochaic Law (I/TL) of [START_REF] Hayes | Metrical stress theory: Principles and case studies[END_REF], formulated in (17). In the definition of this constraint we only refer to trochaic feet. The tableau in (19) illustrates the ranking necessary to obtain a final HL sequence parsed into an ILT foot (e.g., (("H)L)). First, exhaustive parsing derives from ranking PARSE-σ above ALL-FEETmax-RIGHT, as can be observed from comparing candidate (c) with candidate (a), the winning candidate. Leaving the last L syllable unparsed (candidate c) is therefore not a viable option. In our analysis, the constraints ALL-FEETmax-RIGHT and ALL-FEETmax-LEFT refer to maximal feet, that is, to both binary feet and the maximal foot in ILT feet. Non-maximal, embedded feet, however, are not targeted by these constraints. The new definition for these constraints is formulated in (18). The final L syllable in a sequence of HL syllables can be either adjoined via recursion to its preceding H syllable to create an ILT foot (candidate a), be parsed together with the H syllable in a disyllabic, uneven trochee, or be left unparsed. Candidate (c) containing ("H)L is less harmonic than candidate (a) containing (("H)L), the optimal candidate, due to its violations of the high-ranked constraint PARSE-σ. Candidate (b) is ruled out because it violates I/TL. Therefore, we claim that in Sardinian trochaic feet with unequal weight are avoided in favor of ILT feet. Building an ILT foot however incurs a violation of ALIGN-R(Ft min ,σ,Ftmax), because the dependent of the maximal foot within the ILT foot is at the right. The constraint PARSE-σ dominates ALL-FEETmax-RIGHT, ALIGN-R(Ft min , σ, Ftmax) and NON-RECURSIVITY, and I/TL dominates ALIGN-R(Ft min , σ, Ftmax) and NON-RECURSIVITY. The ranking of the two alignment constraints ALL-FEETmax-RIGHT and ALL-FEETmax-LEFT is unknown. In fact, the two possible rankings ALL-FEETmax-RIGHT ≫ ALL-FEETmax-LEFT and ALL-FEETmax-LEFT ≫ ALL-FEETmax-RIGHT lead to contradictory ranking arguments. A LHL base is metrified as L(("H)L) (e.g., Ma((tir)de)), not as *(L("H))L (e.g., *(Ma(tir))de). This is so because Ma((tir)de) truncates to ((Tir)de), not to *(Ma(tir)). In order to get the actual output, ALL-FEETmax-RIGHT must dominate ALL-FEETmax-LEFT, as illustrated in the tableau in (20a). However, a HLLL base must be metrified as (H)(L("LL)) (e.g., (Ser)(va(tore))), not as *((H)L)("LL) (e.g., *((Ser)va)(tore)), which requires the opposite ranking, as illustrated in (20b). A third constraint is needed to resolve this contradictory ranking: ALL-FEET non-min -RIGHT, formulated in ( 21). This constraint makes reference to non-minimal feet, that is, ILT feet. As shown in ( 22), ALL-FEET non-min -RIGHT must be ranked above both ALL-FEETmax-RIGHT and ALL-FEETmax-LEFT. Which one of the two dominated constraints is dominated by ALL-FEET non-min -RIGHT cannot be discovered: ALL-FEET non-min -RIGHT dominates either one or the other. Although according to the tableau in (22b) there is an L dominated by a W, meaning that ALL-FEET non-min -RIGHT dominates ALL-FEETmax-RIGHT, if the order between the two lower-ranked constraints were switched, then ALL-FEETmax-LEFT would be the constraint dominated by ALL-FEET non-min -RIGHT in (22a). What is important here is that ALL-FEET non-min -RIGHT is unviolated in Sardinian, and its unviolability derives the metrifications in ( 22) necessary to derive the truncated forms ((Tir)de) and (Va(tore)), which preserve the head foot of the base (see the next subsection). Take into account that the winning candidate in (22a) also violates ALIGN-Right(Ft min , σ, Ftmax), and as a consequence ALL-FEET non-min -RIGHT dominates ALIGN-Right(Ft min , σ, Ftmax) (not included in the tableau but illustrated in 26). Also, the losing candidate in (22a) violates ALL-FEET non-min -RIGHT, a constraint satisfied by the winner. Therefore, ALL-FEET non-min -RIGHT dominates ALL-FEET non-min -LEFT, violated by the winner (not included in the tableau but illustrated in 26).

(21) ALL-FEET non-min -RIGHT Assign one violation mark for every syllable intervening between the right edge of a non-minimal foot and the right word edge. (Based on [START_REF] Kager | Feet and metrical stress[END_REF][START_REF] Mccarthy | Doing Optimality Theory: Applying theory to data[END_REF] Finally, ILT feet are also avoided in HLL inputs, which are metrified as (H)("LL) (e.g., (Pas)(cali), (Al)(fredu)), and not (H("LL)), in which the H syllable is the dependent of a maximal foot, or ((H)L)("L), which would violate FOOT-BINARITY due to the final degenerate foot (a candidate not included in the following tableau). The constraint responsible for discarding (H("LL)) is WSP (from the Weight to Stress Principle of Prince 1990), defined in (24). The constraint WSP prevents heavy syllables from occupying a foot dependent position. The tableau in (25) shows that WSP dominates both ALL-FEETmax-RIGHT and ALL-FEETmax-LEFT. Thus, ILT feet with heavy dependents are avoided despite misalignment of feet.

(25) HLL → (H)("LL) (e.g., (Pas)(cali))

HLL WSP ALL-FEETmax-R ALL-FEETmax-L NO-REC a. (H)("LL) ** * b. (H("LL)) *W L L *W
The constraint rankings established so far are listed in (26). FOOT-BINARITY, against monomoraic feet, and ALIGN-HEAD-RIGHT, against left-aligned head feet (the head foot in Sardinian is always the rightmost), were not included in any tableaux and are therefore not included in this list.

(26) List of ranking arguments I

AL-R(Ft min ,σ,Ftmax) ≫ AL-L(Ft min ,σ,Ftmax) (15) TROCHEE ≫ IAMB (15) PARSE-σ ≫ ALL-FEETmax-R (19) ≫ AL-R(Ft min ,σ,Ftmax) (19) ≫ NON-REC (19) ≫ ALL-FEETmax-L (23)

Analysis of truncation

The metrifications that derive from the grammar in ( 26) are the input to the process of hypocoristic truncation. As we explained in §4.1, hypocoristic truncation in Sardinian preserves the rightmost foot, that is, the head of the prosodic word. The constraint responsible for this is the output-output faithfulness constraint HEAD(PWd)MAX, defined in (7) and repeated in ( 27). This constraint demands maximization of the prosodic word head of the base (or source form, SF) in the truncated form.

(27) HEAD(PWd)MAX Every element contained in the head of the PWd (e.g., the main-stressed foot) of SF must have a correspondent in TF. (Piñeros 2000a) The tableaux in (28) illustrate the contrast shown in ( 9) and (10) between how (LL)("LL) bases (e.g., (Filu)(mena)) and (H)(L("LL)) bases (e.g., (Ser)(va(tore))) truncate. Recall from (10) that only the latter can yield a trisyllabic truncated form (e.g., (Va(tore))), but not the former (e.g., *(Lu(mena))). This is so because the last three syllables in the base (Ser)(va(tore)) are parsed into the head foot, as opposed to (Filu)(mena), in which the head foot only contains the last two syllables of the base and excludes the pretonic syllable. Building an ILT foot at the right word edge is only possible if the syllable preceding the final sequence of LLL syllables is heavy, parsable into its own foot. The undominated position of HEAD(PWd)MAX favors preservation of the main-stressed foot of the base in the truncated form. The main-stressed foot in the input is always maximal: disyllabic in (LL)("LL) bases but internally layered in (H)(L("LL)) bases. In tableau (28a) we see that the constraint HEAD(PWd)MAX forces the preservation of the main-stressed ILT foot of the base in the truncated form. Candidate (b), with a binary foot, fatally violates this constraint because it does not preserve the prosodic word's head totally. One violation is assigned for the maximal foot's dependent syllable in the base that has no correspondent in the truncated form. Therefore, HEAD(PWd)MAX dominates NO-RECURSION. In other words, ILT feet are allowed in truncated forms as a response to maximally preserve the head foot of the base, which is also an ILT foot. The winning candidate also violates MAX-BT once, because it does not preserve the first syllable of the base. The only candidate that satisfies MAX-BT is candidate (c), with no truncation. This candidate, however, fatally violates ALL-FEETmax-RIGHT and ALL-FEETmax-LEFT because it contains more than one foot. Recall that these alignment constraints are size restrictor constraints, together with PARSE-σ and FOOT-BINARITY ( §4), and are thus responsible for the monopodal candidate to be the optimal one. In tableau (28b) we see that candidate (a), with a binary foot, wins the competition because it satisfies all constraints except for the dominated constraint MAX-BT. Candidate (b), referring to the unattested form *(Lu(mena)), performs better on MAX-BT than candidate (a) because it preserves one more syllable from the base. It also satisfies HEAD(PWd)MAX because it preserves all syllables located in the head foot. However, it fatally violates NO-RECURSION, which dominates MAX-BT. Although NO-RECURSION is dominated by HEAD(PWd)MAX (see tableau 28a), NO-RECURSION decides between candidates (a) and (b) in (28b) because both candidates satisfy HEAD(PWd)MAX. Candidate (b) in (28b), with an ILT foot, preserves the last two syllables of the base, which are parsed into the main-stressed foot, and this perfectly satisfies HEAD(PWd)MAX. However, candidate (b) gratuitously violates NO-RECURSION with no improvement of any other higher-ranked constraint. Therefore, ILT feet are avoided as long as all segments of the main-stressed foot of the base are preserved. This is a crucial point in our analysis. In fact, this is a case of the emergence of the unmarked, in which a disyllabic foot is preferred over an ILT foot if a higher-ranked constraint, HEAD(PWd)MAX in this case, is not active. HEAD(PWd)MAX demands not to copy the main-stressed foot of the base onto the truncated form, but rather to preserve all of its segments; it is an output-output MAX constraint prohibiting deletion between the base and the truncated form. It is important to note that a form like (Ser)(va(tore)) can also be truncated as (Tore), with preservation of the minimal disyllabic foot, instead of the whole ILT foot. In order for (Tore) to win the competition (candidate b in 28a), NO-RECURSION should dominate HEAD(PWd)MAX, all the rest being equal. The fact that it is the minimal foot that is still preserved in a form like (Tore), instead of, for instance, the initial non-head foot (e.g., *(Ser)), still depends on HEAD(PWd)MAX, despite being dominated (as shown in candidate c in 29). In order to explain this case of optionality between the two forms, (Va(tore)) and (Tore), we claim that HEAD(PWd)MAX and NO-RECURSION are partially ordered in the grammar, and that every time EVAL applies, a total ranking between the two constraints is imposed: HEAD(PWd)MAX ≫ NO-RECURSION or NO-RECURSION ≫ HEAD(PWd)MAX. The ranking NO-RECURSION ≫ HEAD(PWd)MAX is shown in (29). 8 This very same ranking is the one responsible for truncation in cases such as (Mone) ← (Si(mone)), which are derived from trisyllabic bases parsed into just one ILT foot. 9 (29) (H)(L("LL)) → ("LL) (e.g., (Tore)) ← (Ser)(va(tore))) Finally, we briefly discuss how bases with antepenultimate stress are truncated in Sardinian. Antepenultimate stress in Sardinian is marked, and it can also be derived by assuming an ILT foot with dactylic rhythm (strong-weak-weak) (e.g., Do((mìni)gu), (Esco)((làsti)ca)). Interestingly, the dactylic ILT foot is very rarely preserved as such in hypocoristic truncation in Sardinian (e.g., only one form, ((Mìni)gu), derived from Do((mìni)gu), has been found in all sources [START_REF] Rubattu | Nùmenes de persona [Personal names[END_REF]). Instead, disyllabic trochaic forms are attested (e.g., (Migu) and (Mimu) ← Do((mìni)gu), (Lata) ← (Esco)((làsti)ca)). Disyllabic outputs result from ranking ALIGN-Right(Ft min ,σ,Ftmax), against right adjuncts in ILT feet, above HEAD(PWd)MAX. These truncated forms further demonstrate that right-anchoring also plays a role in hypocoristic truncation in Sardinian (e.g., the unattested forms *(Mini) and *(Lati) perform worse than the actual 8 An anonymous reviewer suggests a plausible interpretation of the facts according to which disyllabic forms like (Tore) are an instance of a further process of truncation of the trisyllabic forms. This process would take the minimal, non-maximal foot of the trisyllabic form as a separate faithfulness site. 9 The Vatore-type trisyllabic pattern in Sardinian resembles another pattern found in Catalan hypocoristic truncation [START_REF] Cabré | Prosodic trapping in Catalan[END_REF] that produces LH disyllabic truncated forms with final stress only if the syllable of the base preceding the pretonic open syllable is closed: Serrat (also Rat) ← Montserrat, Tomeu (also Meu) ← Bartomeu, but *Aquim ← Joaquim, *Sabel ← Isabel. An analysis similar to Sardinian could be posited for Catalan: Tomeu is possible because the base is metrified as (Bar)(to(meu)), with the initial heavy syllable parsed into its own foot, but *Sabel is unattested because the pretonic syllable in the truncated form is parsed into a separate foot in the base that does not contain the stressed syllable: (Isa)(bel).

forms (Migu) and (Lata) with respect to the constraint ANCHOR(BT)Right, see 6). 10The tableau in (30) illustrates this ranking. To conclude this subsection, we need to refer to the few trisyllabic hypocoristic forms that contains an initial closed syllable (e.g., (Gan(tine)), see 11). We have shown that inputs ending in a sequence of HLL syllables are parsed as (H)("LL). (Gan(tine)) is clearly an exceptional form. The form (Tzi(cana)), which derives from Frantziscana, has actually no initial closed syllable in the truncated form because it does not copy the coda consonant from the base. Forms like (Gan(tine)) could be accounted for with some type of exceptionality mark or mechanism, whether it is a lexically indexed constraint or input specification in order to turn the coda consonant into a non-moraic segment in the truncated form.

We list in (31) the ranking arguments introduced in this section.

Analysis of reduplicative prefixation

Once ILT feet are assumed, the second type of trisyllabic truncated hypocoristics in Sardinian, those that derive from reduplicative prefixation (e.g., (To(tore))), easily follow. We claim that reduplicative prefixation is only possible when a truncated base corresponds to a ("LL) disyllabic foot. This is so because only in this case can the disyllabic foot be expanded to include a pretonic syllable and build an ILT foot. The ILT foot serves as an upper-bound prosodic category in reduplicative prefixation, and this is why reduplicative prefixation is not attested in (("H)L) truncated bases, which already contain an ILT foot (e.g., *Na(l)((nal)du)).

Prefixing reduplication, as opposed to suffixing reduplication, is predicted from ranking BR-ANCHORLEFT above BR-ANCHORRIGHT [START_REF] Alderete | Reduplication in Hawaiian: Variations on a theme of minimal word[END_REF]. These two constraints are defined in (32).

(32) BR-ANCHOR [START_REF] Alderete | Reduplication in Hawaiian: Variations on a theme of minimal word[END_REF] a. BR-ANCHORLEFT

The left peripheral element in the reduplicant has a correspondent in the left peripheral element in the base.

b. BR-ANCHORRIGHT The right peripheral element in the reduplicant has a correspondent in the right peripheral element in the base.

Furthermore, the reduplicant in Sardinian hypocoristics corresponds to a contiguous substring of the base, and therefore a constraint like BR-CONTIGUITY is needed, formulated in (33). The evaluation of an input /(Tore), RED/ is illustrated in [START_REF] Ll | RED →[END_REF]. Candidate (c), with a perfect copy of the base, incurs two fatal violations of ALL-FEETmax-RIGHT and two violations of ALL-FEETmax-LEFT. These constraints must therefore dominate BR-MAX. In candidate (b), the reduplicant is not parsed into any foot. This again produces the misalignment of the main foot with the left edge of the word. Candidate (b) shows that ALL-FEETmax-LEFT dominates NO-RECURSION. The winning candidate is the one that satisfies ALL-FEETmax-LEFT at the expense of violating NO-RECURSION and BR-MAX. The constraints BR-ANCHORLEFT, favoring prefixing reduplication, and BR-CONTIGUITY, favoring contiguous copying, are undominated.

The same constraint hierarchy excludes reduplicative prefixation from bases like ((Mun)du), derived from Re((mun)du), which already contain a disyllabic ILT foot. This is a welcome prediction of our analysis because such bases never show reduplicative prefixation. As we have stated before, in our analysis ILT feet act as an upper-bound prosodic category for augmentation. If a reduplicative prefix attaches to a base containing an ILT foot, the reduplicate should either be parsed into its own foot (*(Mun)((mun)du) or *(Mun)((mun)du)) or be left unparsed (*Mu((mun)du) or *Mun((mun)du)). All possible parsings of these forms are discarded because of their fatal violations of size restrictor constraints, as shown in (36).

An alternative analysis with binary feet and unparsed syllables

In this final section we discuss an alternative analysis of trisyllabic truncation in terms of binary feet and unparsed syllables. [START_REF] Felíu | Output constraints on two Spanish word-creation processes[END_REF] developed such an analysis for a specific process of trisyllabic truncation in Spanish nominals (e.g., proleta ← proletario 'proletarian'; see also Torres-Tamarit 2021). As we will see, an analysis that allows for unparsed syllables cannot explain why a form like *Mun((mun)du) is unattested in Sardinian.

In her analysis, [START_REF] Felíu | Output constraints on two Spanish word-creation processes[END_REF] breaks up the constraint PARSE-SYLLABLE into two constraints: a weak version of PARSE-SYLLABLE, which is only violated by a pair of adjacent unfooted syllables, and *FOOTLESS, violated by any unparsed syllable (that is, standard PARSE-SYLLABLE). The ranking PARSE-SYLLABLE(weak version) ≫ MAX-BT ≫ *FOOTLESS derives trisyllabic truncated forms, as illustrated in (37).

(37) pro(leta) ← prole(tario) 'proletarian' This analysis relies on the special parsing constraint PARSE-SYLLABLE(weak version), which has the same effects of the rhythm constraint *LAPSE, against pairs of adjacent unstressed syllables. In our opinion, a drawback of any rhythm-based analysis of truncation is that other types of rhythm constraints that have been proposed in the literature predict unattested patterns. For example, there is extensive literature that argues for rhythm constraints like *EXTENDEDLAPSE [START_REF]A factorial typology of quantity-insensitive stress[END_REF] or *LONGLAPSE [START_REF] Kager | Feet and metrical stress[END_REF], which penalize every unstressed syllable that is not adjacent to a stressed syllable or the word edge, that is, a sequence of three unstressed syllables. If a constraint like *LONGLAPSE were ranked above MAX-BT and alignment, a five-syllable input /σσσσσ/ would be mapped onto a truncated form with just four syllables [σσ("σσ)], as illustrated in (38). Four-syllable truncated forms are predicted under a rhythm-based analysis using a constraint like *LONGLAPSE above MAX-BT but they seem not to exist in any lan-guage. 11 Furthermore, an analysis with binary feet and unparsed syllables could not explain why reduplicative forms like *Mu(n)mundu are banned in Sardinian. [START_REF] Molinu | Le strutture non marcate negli ipocoristici del sardo [The unmarked structure in Sardinian hypocoristics[END_REF][START_REF] Molinu | Gli ipocoristici dei nomi di persona in sardo [The hypocoristics of personal names in Sardinian[END_REF][START_REF] Molinu | Le polymorphisme des hypocoristiques en sarde [The polymorphism of hypocoristics in Sardinian[END_REF], in her analysis of hypocoristic truncation in Sardinian, also assumes that the reduplicated syllable is unparsed and directly attached to the prosodic word node. Again, this does not explain why forms like *Mu(n)mundu are unattested in Sardinian. The only way to avoid such a reduplicated form would be to impose a maximal size of three moras to the whole truncate form, something like PWd=3µ, but such a size constraint seems completely ad hoc. The same would hold for an alternative analysis using ternary feet, which would make no prediction regarding those unattested forms, except if feet were restricted to have maximally three moras, against the general consensus on the universal character of the constraint FOOT-BINARITY. ILT feet in Sardinian are also maximally trimoraic, but this follows from the satisfaction of independently needed constraints: FOOT-BINARITY is obeyed in the non-maximal foot, and WSP prohibits a H syllable to be parsed as the dependent of the non-minimal foot.

Conclusion

In this paper we have developed an OT analysis of hypocoristic truncation in Sardinian based on output-output correspondence relations between bases and truncated morphemes in the spirit of [START_REF] Benua | Identity effects in morphological truncation[END_REF] and the latest work on hypocoristic truncation by [START_REF] Alber | An exploration of truncation in Italian[END_REF] and Alber and Arndt-Lappe (2012) (see also Piñeros 2000a, 2000b, 2002for Spanish, and Cabré 1993, 1998;Cabré and Kenstowicz 1995 for Catalan). We have assumed, like in previous work, that truncation is driven by constraints that regulate which portion of the base is preserved in the truncated form, size restrictor constraints, and faithfulness constraints targeting correspondence relations.

Most importantly, we have presented data on trisyllabic hypocoristics, which are the result of two different processes of truncation. There is one pattern of reduplication in which the first syllable of a disyllabic truncated form is reduplicated, yielding a trisyllabic hypocoristic with amphibrach rhythm, and a second pattern of trisyllabic truncation that incorporates an initial unstressed syllable, a syllable which is in corre-11 Four-syllable truncated forms are in fact attested in Spanish, for instance, but have been analyzed as truncate-based morphological compounds (Marijose ← María José, Maritere ← María Teresa, Martínez-Paricio and Torres-Tamarit 2019, Torres-Tamarit 2021). Japanese also has both trimoraic and four-mora truncated forms (arumi ← aruminyuumu 'aluminium', kosume ← kosumechikku 'cosmetics', terebi ← terebijoN 'television'; irasuto ← irasutoreeshoN 'illustration', asupara ← asuparagasu 'asparagus', furasuto ← furasutoreeshoN 'frustration', [START_REF] Itô | Prosodic minimality in Japanese[END_REF]). The four-mora cases have been analyzed by [START_REF] Itô | Prosodic minimality in Japanese[END_REF] as prosodic compounds whose members are strictly bimoraic, and the trimoraic cases have been analyzed as bimoraic stems that take an optional suffix to create words. spondence with the syllable preceding stress in the base. We have developed an analysis of trisyllabic truncated hypocoristics based on layered feet (Martínez-Paricio and Kager 2015; Martínez-Paricio and Torres-Tamarit 2019). Our claim is that only by assuming layered feet can we maintain the general assumption that truncated forms equal the size of a metrical foot. The theoretical contribution of this paper has been to give additional support for minimal recursion of feet from the domain of the phonology-morphology interface.

( 2 )

 2 Prosodic word restrictors a. PARSE-σ Assign one violation mark for every unfooted syllable. (McCarthy 2008) b. FOOT-BINARITY Assign one violation mark for every foot that does not contain at least two moras or two syllables. (McCarthy 2008)c. ALL-FEET-LEFT/RIGHT Assign one violation mark for every syllable intervening between the left/right edge of a foot and the left/right word edge.[START_REF] Kager | Feet and metrical stress[END_REF][START_REF] Mccarthy | Doing Optimality Theory: Applying theory to data[END_REF]

  Fig. 1: ILT foot

( 10 )

 10 Impossible trisyllabic truncated hypocoristics (Filu)(ména) → *(Lu(ména)) (Disi)(dóro) → *(Si(dóro)) (Miche)(línu) → *(Che(línu)) (Sera)(fínu) → *(Ra(fínu))

( 14 )

 14 Alignment constraints on the position of the adjunct within ILT feet (Martínez-Paricio and Kager 2015)

( 15 )

 15 ILT amphibrach foot (e.g., (Si(mone)))LLL AL-R(Ft min , σ, Ftmax TROCHEE AL-L(Ft min , σ,

(

  17) I/TL Assign one violation mark for every disyllabic trochaic foot with unequal weight.[START_REF] Mccarthy | Doing Optimality Theory: Applying theory to data[END_REF]

(

  18) ALL-FEETmax-LEFT/RIGHT Assign one violation mark for every syllable intervening between the left/right edge of a maximal foot and the left/right word edge. (Based on[START_REF] Kager | Feet and metrical stress[END_REF], Mc- Carthy 2008)

(

  19) LLHL → (LL)(("H)L) (e.g., (Teo)((bal)du))

(

  20) Contradictory rankings a. LHL → L(("H)L) (e.g., Ma((tir)de))

(

  24) WSP Assign one violation mark for every heavy syllable in a dependent foot position.(Based on McCarthy 2008.)

(

  28) Truncation tableaux a. (H)(L("LL)) → (L("LL)) (e.g., (Va(tore)) ← (Ser)(va(tore))) LL)("LL) → ("LL) (e.g., (Mena) ← (Filu)(mena))

(

  30) L(("LL)L) → ("LL) (e.g., (Migu) ← Do((mìni)gu)) Do((mìni)gu) AL-R(Ft min ,σ,Ftmax) ANCHOR(BT)R HD(

  min ,σ,Ftmax) ≫ HD(PWd)MAX (30)

(

  33) BR-CONTIGUITYThe reduplicant corresponds to a contiguous substring of the base.[START_REF] Mccarthy | Faithfulness and identity in prosodic morphology[END_REF] Finally, a faithfulness constraint BR-MAX is required, which is violated when segments in the base have no correspondents in the reduplicant, defined in (34).(34) BR-MAX Base segments must have correspondents in the reduplicant.[START_REF] Alderete | Reduplication in Hawaiian: Variations on a theme of minimal word[END_REF]

(

  36) ((Mun)du), RED → ((Mun)du) ((Mun)du), RED PARSE-σ FOOT-BIN ALL-FEETmax-R a. ((Mun)du) b. (Mun)((Mun)du)

( 38 )

 38 σσσσσ → σσ("σσ)

  explicitly says that in the presence of a penultimate closed syllable, antepenultimate stress is categorically banned, as is common in Romance (e.g., coranta [kO"Ranta] 'forty' cf. *["kORanta]; molenti [mO"KEnti] 'donkey' cf. *["mOKEnti]; burrumballa [burrum"balla] 'mess/confusion' cf. *[bur"rumballa]).

The source of antepenultimate stress in Sardinian is sometimes the result of copy vowel epenthesis to avoid word-final consonants in phrase-final position (see[START_REF] Flack | Constraints on onsets and codas of words and phrases[END_REF] for phrase-dependent wellformedness effects on syllable structure). As far as we know, both Campidanese and Logudorese exhibit this process.

e.g., calmùc 'Kalmyk', nicenòn 'geranium', ruàn 'canvas', armuàr 'wardrobe', contuàr 'shop counter', fumistèr 'flue', Barrabàs 'Barabbas, Satan', Bancràs 'Pancratium', puès 'therefore, since', abadùs 'both'.

e.g., tosèl 'canopy', Lusbèl 'Lucifer', Bellèm 'Bethlehem', misser 'honorary title', assàs 'very', atràs 'behind', buscapés 'firecracker', linghepès 'flunkey, bootlicker', puès 'therefore, since', trepodrès 'quail', barrupès 'gossipy', giùs 'right', poddighimpiùs 'finger'.

[START_REF] Alber | Templatic and subtractive truncation[END_REF] discuss whether ANCHOR constraints are better formulated as alignment constraints or faithfulness constraints. They argue that ANCHOR-STRESS, analogous to

The status of ungrammaticality that we attribute to these forms is based on their absence from our dataset. We have further asked one native speaker of Sardinian about these forms and he does not accept them as possible hypocoristics. Our dataset includes however three trisyllabic truncated forms that derive from LLLL bases: Bonedda ← Bonariedda, Carina ← Catarina and Malena ← Madalena. We do not consider these forms to be counterexamples to our claim that (LL)(LL) bases cannot be truncated into trisyllabic forms. This is because the truncation mechanism used to derive these three forms is different. They display two anchoring targets: the initial syllable and the head foot of the base. In all the other forms in our dataset there is only one anchoring target: the head foot of the base. We do not analyze these cases in section 5.3 because of their marginal status.

A form like *(Nigu) is also ruled out because the head syllable of the head foot of the base is not preserved as such in the truncated form; a constraint like ANCHOR-STRESS, as defined by Alber and Arndt-Lappe (2012), would discard such a candidate.

Acknowledgments: Some parts of this research were presented at the Italian Dialect Meeting (May 2012, Leiden, the Netherlands), at the Coloquio de Gramática Generativa (May 2013, Madrid, Spain), at the Phonetics and Phonology in Europe conference (June 2015, Cambridge, United Kingdom), at the workshop "Methods in Empirical Prosody Research" at the 34th Romanistentag (July 2015, Mannheim, Germany), and at the workshop Il Sardo in Movimento (September 2017, Vienna, Austria). We are grateful to the audiences at these talks for their helpful comments and discussion. All the speakers who participated unselfishly in the recordings as well as colleagues from Sardinia or elsewhere who put us in contact with potential participants (Claudia Aru, Francesc Ballone, Amos Cardia, Silvio Cruschina, Claudio Sanna, and Carlo Schirru) deserve a special mention for their time and dedication. We also thank Francesc Ballone for carefully proofreading the excerpts in Sardinian. This research has been funded by the Spanish Government via the projects FFI2016-76245-C31P and FFI2017-87699-P, and by the Catalan Government via the project 2017 SGR 634 AGAUR-Generalitat de Catalunya. We also want to thank the editors and two anonymous reviewers for their helpful and encouraging comments on the manuscript.

Tore), RED BR-ANCHL BR-CONT ALL-FEETmax-R ALL-FEETmax-L NO-REC BR-MAX a. (To(tore)