Overtly Headed XPs and Irish Syntax–Prosody Mapping

Phonological phrasing reflects syntactic phrasing, but imperfectly. Match Theory (Selkirk, 2011) explains this imperfect mapping within the framework of Optimality Theory (Prince & Smolensky, 1993/2004): mapping constraints demanding isomorphism interact with prosodic well-formedness constraints that motivate mismatches. A number of recent analyses of Irish phonological phrasing (Elfner, 2012, 2015; Bennett et al., 2016, 2019) have been influential in shaping Match Theory. In particular, Elfner (2012) refined the definition of matching to refer not to edges only, but to terminal strings. Elfner (2012) also notices a ranking paradox in the Irish phrasing of V-S-OO compared to V-SS-O, and offers an analysis using Harmonic Grammar (Legendre et al., 1990). We also discover a second ranking paradox involving the effects of STRONGSTART in sentence-initial versus sentence-medial contexts. In the present paper, we provide a solution to this ranking paradox using OT with strict domination by introducing an additional MATCH constraint that targets XPs with phonologically overt heads: MATCH(OhP,φ). All ranking arguments presented in this paper are derived from fully defined OT systems with complete candidate sets, since within OT, a candidate is optimal if it is better on a constraint ranking than all competitors admitted by GEN. For syntax–prosody mapping, candidates are 〈syntactic tree, prosodic tree〉 pairs, and as a result, the candidate space grows exponentially as the number of terminals in the trees grows. We surmount this problem using the Syntax Prosody in OT app (SPOT; Bellik et al., 2020) to automate candidate generation and evaluation, and OTWorkplace (Prince et al., 2020) to compute and analyze typologies. The paper is organized as follows. Section 2 presents background information about Irish syntax and our assumptions about the visibility of the syntax to phonology, as well as the prosodic data. In §3.1, we explain the first ranking paradox, and show that it can be resolved by introducing a MATCH constraint that targets overtly headed syntactic phrases. However, the resulting system with MATCH(XP,φ) and MATCH(OhP,φ) does not solve the second paradox, which we address in §3.2 by refining the definition of STRONGSTART. The complete OT system that combines these solutions is presented in §4. Section 5 discusses and concludes.


Introduction
Phonological phrasing reflects syntactic phrasing, but imperfectly. Match Theory (Selkirk, 2011) explains this imperfect mapping within the framework of Optimality Theory (Prince & Smolensky, 1993/2004: mapping constraints demanding isomorphism interact with prosodic well-formedness constraints that motivate mismatches. A number of recent analyses of Irish phonological phrasing (Elfner, 2012(Elfner, , 2015Bennett et al., 2016Bennett et al., , 2019 have been influential in shaping Match Theory. In particular, Elfner (2012) refined the definition of matching to refer not to edges only, but to terminal strings. Elfner (2012) also notices a ranking paradox in the Irish phrasing of V-S-OO compared to V-SS-O, and offers an analysis using Harmonic Grammar (Legendre et al., 1990). We also discover a second ranking paradox involving the effects of STRONGSTART in sentence-initial versus sentence-medial contexts.
In the present paper, we provide a solution to this ranking paradox using OT with strict domination by introducing an additional MATCH constraint that targets XPs with phonologically overt heads: MATCH(OhP,ϕ). All ranking arguments presented in this paper are derived from fully defined OT systems with complete candidate sets, since within OT, a candidate is optimal if it is better on a constraint ranking than all competitors admitted by GEN. For syntax-prosody mapping, candidates are syntactic tree, prosodic tree pairs, and as a result, the candidate space grows exponentially as the number of terminals in the trees grows. We surmount this problem using the Syntax Prosody in OT app (SPOT; Bellik et al., 2020) to automate candidate generation and evaluation, and OTWorkplace (Prince et al., 2020) to compute and analyze typologies.
The paper is organized as follows. Section 2 presents background information about Irish syntax and our assumptions about the visibility of the syntax to phonology, as well as the prosodic data. In §3.1, we explain the first ranking paradox, and show that it can be resolved by introducing a MATCH constraint that targets overtly headed syntactic phrases. However, the resulting system with MATCH(XP,ϕ) and MATCH(OhP,ϕ) does not solve the second paradox, which we address in §3.2 by refining the definition of STRONGSTART. The complete OT system that combines these solutions is presented in §4. Section 5 discusses and concludes.
2 Background 2.1 Irish syntax We follow Elfner (2012Elfner ( , 2015 in adopting the syntactic analysis of Irish clause structure developed by Chung & McCloskey (1987) and McCloskey (1991McCloskey ( , 1996McCloskey ( , 2001McCloskey ( , 2011. According to this analysis, in a finite main clause, the verb undergoes successive head-movement through v and T to a polarity head Σ. The subject moves to Spec,TP, and if there is an object, it remains in situ. 1 Within the DP, we follow Elfner (2012Elfner ( , 2015 and McCloskey (p.c.) in positing a functional head F between D and N, to which N obligatorily moves, deriving the correct noun-adjective word order. 2 (2) Irish DP with one adjective  (Elfner, 2012) (4b). We also abbreviate complex heads by representing only their leftmost (most deeply embedded) adjunct, and omit traces.
Finally, XP labels such as TP, NP, and VP play no role in the phonology, and are replaced by the labels OhP (= overtly headed phrase) and ShP (silently headed phrase) (see Nespor & Vogel 1986 on the categoryinsensitivity of prosodic phonology) (4c). Of the branching XPs in the input trees in this study, every ΣP and FP is overtly headed: ΣP is headed by the moved verb, and FP is headed by the moved noun. All other branching XPs (TPs, DPs, NPs, vPs, VPs) are covertly headed. They either have inherently silent heads, or lexical heads that have moved. 3 (4) a. Removing unary XPs: We assume, following Elfner (2012Elfner ( , 2015, that the inventory of prosodic categories is limited to the set posited by Ito & Mester (2007, 2009a,b, 2010, 2013, with prosodic recursion being permitted and sometimes giving rise to different phonological phenomena at different levels of embedding (see also Ladd, 1986;Gussenhoven, 1991Gussenhoven, , 2005. (5) Prosodic hierarchy ι (the intonational phrase) > ϕ (the phonological phrase) > ω (the prosodic word) In addition to its category label ι, ϕ, or ω, a prosodic constituent bears two features determined by its hierarchical relation to other constituents of the same category: [±minimal] and [±maximal]. A node of category κ is [+minimal] if and only if it does not contain any descendant of category κ, and [+maximal] if and only if it is not contained in any node of category κ. Phonological constraints can refer to combinations of these features. Elfner (2012Elfner ( , 2015 presents a theory of phonological phrasing in Irish within Match Theory, in which phrasing can be inferred from the tonal diagnostics in (6).

Prosodic data from Irish
These diagnostics allow us to interpret the tones in (7) to mean that díofaidh LH and rúnaí LH are at the left edges of non-minimal ϕs, while dathúil HL and blathanna HL are at right edges of ϕs. This suggests that the prosody of this sentence has the structure (díofaidh LH ((rúnaí LH dathúil HL ) blathanna HL )), which comes close to matching its syntactic structure. Likewise, in (8), the rise on cheannaigh LH indicates that it is at the beginning of a non-minimal ϕ, while the falls on múinteoirí HL and bána HL mean that these words are at the right edges of ϕs. Applying these diagnostics to transitive and intransitive sentences with default word order and one, two, or three words in each DP yields the phrasings in (9), reported by Elfner (2012). These phrasings reveal that Irish ϕs are usually isomorphic to XPs. However, they sometimes deviate from perfect syntax-prosody matching (9a, b, d) to satisfy prosodic markedness constraints, primarily STRONGSTART and BINARITY.
(9) Phrasings proposed by Elfner (2012Elfner ( , 2015 a These are the mappings that we aim to capture in our analysis below. 3 Analytical Puzzles 3.1 Puzzle 1: Overt Headedness The puzzle noticed by Elfner (2012) concerns the rankings needed to account for the complete pattern of matching and mismatching in Irish. Rebracketing occurs in V-SS (9a) and V-S-OO (9d), which are phrased as ((V S) S) and ((V S)(O O)). These mismatches occur in order to avoid having an initial phonological word be sister to a ϕ, which would violate STRONGSTART, defined in (10).
(10) Elfner's STRONGSTART(ω) (paraphrased): Assign one violation for every node whose leftmost daughter is an ω, and is lower in the prosodic hierarchy than its sister constituent immediately to its right.
(11) BINMAX(ϕ, branches): Assign a violation for every ϕ that has more than two immediate daughters.
However, rebracketing is also blocked in V-SS-O (9c), which receives a faithful parse that violates STRONGSTART. Why do we not see *((V S)(S O))? The unattested rebracketed phrasing satisfies binarity and STRONGSTART, but violates MATCH. To avoid the unattested rebracketing of V-SS-O, we need the ranking MATCH(XP,ϕ) ≫ STRONGSTART. But this is a ranking paradox; the Elementary Ranking Conditions (ERCs; Prince, 2002) for these two winners are contradictory, as shown in (12).
To resolve this paradox, we need a constraint that penalizes mismatching the subject in V-SS-O more than it penalizes mismatching the TP containing both subject and object. One difference between these XPs is that the matched subject FP is overtly headed, while the mismatched TP is not. We therefore define the additional MATCH constraint in (13).
(13) MATCH(XP OvertlyHeaded ,ϕ) (abbreviated as MATCH(OhP,ϕ)) Assign a violation for every OhP (overtly headed XP) that does not have a matching ϕ in the output.
This constraint is also proposed by Van Handel. We will show in detail in §4 that the introduction of MATCH(OhP,ϕ), 4 does indeed resolve the paradox.

3.2
Puzzle 2: Toleration of medial "weak starts" With the inclusion of the full candidate set, we discovered a second puzzle, depicted in (14). Tableaux for V-S-O, V-SS-O, V-S-OO, and V-SS-OO show that MATCH(OhP,ϕ) must outrank STRONGSTART, which in turn outranks MATCH(XP,ϕ), as established above. But for the perfectly isomorphic phrasings of V-SSS-OO and V-SS-OOO, MATCH(XP,ϕ) must dominate STRONGSTART. 4 The distinction between OhPs and ShPs is reminiscent of a part of Truckenbrodt's (1995Truckenbrodt's ( , 1999 Lexical Category Condition. However, we do not adopt the LCC, since our definition of XP-visibility differs in three crucial ways. (i) We follow Elfner (2012Elfner ( , 2015 in treating functional XPs like TP and ΣP as visible for mapping. (ii) ShPs are not invisible to all of the constraints we propose in §4, but are ignored by only one particular constraint. (iii) The distinction OhP/ShP is different from the distinction LexP/FuncP; a LexP might be silently headed, and a FuncP might be overtly headed. Considering the ω-ϕ sister sequences that are and are not tolerated, we can observe that the tolerable pair occurs ι-medially. In the first loser, ω 1 -ϕ 2 is not tolerated. In the second winner, ω 2 -ϕ 5 is tolerated. MATCH(OhP,ϕ) does not distinguish the winners and losers here. Both winners match all OhPs. This suggests a solution to the second puzzle through a refinement to STRONGSTART as in (15) to only penalize a rise in prosodic category when it occurs at the left edge of an intonational phrase.
(15) STRONGSTART Init Assign a violation for every ι-initial ω that is sister to a ϕ.
This indexation of STRONGSTART to the ι differs from Elfner's indexation of STRONGSTART to a particular category in three respects. First, it is indexed to the category of the parent (ι), whereas Elfner's STRONGSTART is indexed to the category of the child that is prosodically weaker than its sister. Second, it penalizes a rise in prosodic category between the first child and any sister, rather than being restricted to a rise in category between the first and second sister as in Elfner (2012Elfner ( , 2015 and Selkirk (2011). This innovation was also independently suggested by Chen (2020), under the name STRONGSTRONGSTART. Finally, STRONGSTART Init treats an ω as ι-initial even if it is not an immediate daughter to the ι, exactly like STRONGSTART(κ,π) in Hsu (2016). These three modifications enable STRONGSTART Init to penalize the ι-initial rise in category ω 1 -ϕ 2 in the first loser in (14), without penalizing ω 2 -ϕ 5 in the second winner. If STRONGSTART Init replaces STRONGSTART in the above (14), it resolves the ranking paradox between STRONGSTART and MATCH. This is demonstrated in the following section, which lays out our full analysis.

Analysis
By combining MATCH(OhP,ϕ) and STRONGSTART Init , we can capture the phrasing of all the transitive sentences in (9). We define an explicit OT system in the sense of Alber et al. (2016). GEN for our system consists of pairs of syntactic and prosodic trees. The syntactic inputs, defined in (16), are transitive and intransitive sentences, where each DP can have up to two adjectives. This GEN defines a number of trees for which we lack data, which were included in our calculation of the typologies and ranking arguments, but which will not be discussed in this paper for reasons of space. The input trees for which we do have data from Elfner (2012) are listed in (17) The prosodic trees in our system, defined in (18), are trees rooted in ι in which all intermediate nodes are branching ϕs, and terminal nodes are prosodic words. These were calculated with SPOT (Bellik et al. (2020)). Note that for an input tree with 6 terminals (V-SS-OOO), this GEN function yields 229 prosodic output trees, and an input with 7 terminals (V-SSS-OOO) yields 1,068 outputs, so automation is crucial.

(18) GEN Outputs
For an input sTree, an output pTree is a prosodic tree such that a. Every maximal syntactic word X 0 in the input is mapped to an output phonological word ω. b. The linear order of words is preserved. c. The root node is of category ι. 5 d. All non-terminal non-root nodes are of category ϕ. e. Every node of category ϕ immediately dominates at least two other nodes.
Having defined GEN for the system, we turn to the constraint set CON (19), which consists of two MATCH constraints enforcing syntax-prosody mapping, and two markedness constraints enforcing prosodic wellformedness. As discussed above, MATCH(OhP,ϕ) and STRONGSTART Init are our innovations in the analysis of Irish prosody (for an application of MATCH(OhP,ϕ) in Italian, see Van Handel, 2019).
(19) CON a. Syntax-prosody mapping constraints i. MATCH(XP,ϕ) (Selkirk, 2011;Elfner, 2012Elfner, , 2015) Assign a violation for every input XP that does not have a matching ϕ in the output, where matching is defined as in (20). ii. MATCH(XP OvertlyHeaded ,ϕ) (Van Handel, 2019) Assign a violation for every input OhP (overtly headed XP) that does not have a matching ϕ in the output, where matching is defined as in (20). b. Markedness constraints i. BINMAX(ϕ,branches) (Elfner, 2012(Elfner, , 2015) Assign a violation for every ϕ that immediately dominates more than two nodes. ii. STRONGSTART Init (new proposal) Assign a violation for every ι-initial ω that is sister to a ϕ.
(20) Definition of matching (Elfner, 2012:, our wording) Two constituents α and β are matching iff the terminal string of α is identical to the terminal string of β.
We created violation tableaux for this system using SPOT (Bellik et al., 2020), and calculated rankings and a typology using OTWorkplace (Prince et al., 2020). The typology, shown in (25) below, contains three languages, one of which (L2) is compatible with all the transitive inputs for Irish. However, none of the three captures the prosody of the single intransitive sentence for which we have data.

4.1
The prosodic grammar of Irish We will examine the ERCs in L2 ("Irish" in this system) for the three sentences (V-S-OO, V-SS-O, and V-SS-OO), in order to understand how the system derives the correct parses for each of these. In the tableau for V-S-OO in (21), there are two possible optima. 6 The winner is a rebracketed, mismatching candidate (a). It violates MATCH(XP,ϕ), because ShP (the silently-headed TP) has no matching ϕ, but satisfies STRONGSTART Init . The isomorphic loser (b) satisfies MATCH(XP,ϕ), since OhP is mapped to ϕ 1 and ShP is mapped to ϕ 2 . However, it fatally violates STRONGSTART Init because ω 1 is sister to ϕ 2 . The success of mismatching candidate (a) here shows that STRONGSTART outranks MATCH (XP,ϕ) To establish the ranking of MATCH(OhP,ϕ), we can examine the ERC in (22)  The V-SS-OO case in (23) is similar to the V-SS-O case in (22), providing the same ERC. What these have in common is that it is impossible to phrase the verb with the word to its left, avoiding a STRONGSTART Init violation, without violating MATCH(OhP,ϕ). This is because a multi-word subject is an OhP. This is also the case for V-SSS-OO and V-SS-OOO, which also have fully matching phonological phrasings (tableaux not shown). 4.2 Factorial Typology By looking at the rest of the factorial typology, we can better understand how the Irish pattern fits into the range of possible mapping patterns predicted by this system. The grammars for the three languages here can be seen in the Hasse diagrams in (24), and the optima for each language appear in the typology table in (25). Bold text in cells indicates a phrasing reported by Elfner. 7 The interaction of the three constraints follows a general pattern seen wherever two constraints are in a special-general relationship, and are both opposed by a third, call it the antagonist. MATCH(OhP,ϕ) is a special case of MATCH(XP,ϕ), since whenever MATCH(XP,ϕ) is satisfied, MATCH(OhP,ϕ) necessarily is, too. STRONGSTART Init is antagonized to both MATCH constraints: Since all syntactic inputs begin with a word (the verb) that is sister to an XP, all isomorphic prosodic structures would violate STRONGSTART Init . Satisfying MATCH(XP,ϕ) entails violating STRONGSTART Init , and vice versa. We can expect, therefore, that of the three languages, one will perfectly satisfy the antagonist (STRONGSTART Init ), one will perfectly satisfy the general constraint (MATCH(XP,ϕ)), and one will satisfy the special constraint (MATCH(OhP,ϕ)) but violate the general constraint. These predictions are borne out. In L1, the antagonist STRONGSTART Init is top-ranked (24a). Ranking STRONGSTART Init over both MATCH constraints results in rampant rebracketing; no prosodic output is isomorphic to the syntactic input.
The opposite pattern occurs in L3 (24c), where the general MATCH(XP,ϕ) is ranked over the antagonist STRONGSTART Init . There is no crucial ranking between STRONGSTART Init and the more specific MATCH(OhP,ϕ). In L3, all prosody is isomorphic to syntax. This language always respects MATCH(XP,ϕ), even at the expense of STRONGSTART Init ; no rebracketing occurs. Between these two extremes, we find L2, in which the antagonist STRONGSTART Init is ranked between the special MATCH(OhP,ϕ) and the general MATCH(XP,ϕ) (24b). L2 always respects MATCH(OhP,ϕ), but will violate the general constraint MATCH(XP,ϕ) to satisfy STRONGSTART Init . This ranking produces the intermediate matching/mismatching pattern seen in Irish, because it allows rebracketing of silently headed XPs, while blocking rebracketing of overtly headed XPs.