On optional wh-/focus fronting in Igbo: A SYN-SEM-PHON interaction

Abstract This paper discusses surface optionality in focus fronting in the Benue-Congo language Igbo. A focused XP can occur in-situ or ex-situ. We argue that the optionality does not have its origins in the syntax: in fact, exactly one focused XP has to move to the designated focus position in the left periphery in the syntax. The alternation between in-situ and ex-situ rather arises at PF: either the lowest or the topmost copy of the focus chain is pronounced. The choice is determined by semantic-pragmatic factors, i. e., we see an interaction between PF and LF. This constitutes a challenge for a strict version of the Y-model of grammar.


Introduction
This paper deals with (apparent) optionality in focus fronting in the Benue-Congo language Igbo. The basic word order in an all-new context is subject -verb -direct object -adjuncts (SU-V-DO-ADJ), see (1): 1 (1) Òbí Obi

hù -rù see-rV
Àdá Ada n'-áhí á P-market 'Obi saw Ada at the market.' declarative The relevant case of optionality arises when a XP is in focus (term focus), e. g., when it is questioned or when it constitutes the answer to a question (new information focus). In this case, the focused XP can either remain in the position that it surfaces in in an all-new declarative sentence as in (1) -a pattern we will refer to as the in-situ strategy; or the focused XP occurs at the left edge of the clause, an alternative that we will call the ex-situ strategy in what follows. The two options are illustrated for the direct object of a transitive verb for question formation (see (2)) and for new information focus, see (3) n'-áhíá P-market 'Obi saw Ada at the market.' foc-DO ex-situ Both the in-situ and the ex-situ strategy are well formed from a purely syntactic point of view. In this sense, we are dealing with optionality. Based on novel data, we will argue that the ex-situ/in-situ optionality does not arise in the syntax. In fact, there is no syntactic optionality in focus fronting in Igbo: exactly one focus XP has to move to the focus position (SpecFoc) in the left periphery in the syntax, also in (apparent) in-situ cases. We provide evidence that the optionality arises at PF: either the copy at the bottom or at the top of the focus movement 2 The syntax of in-situ and ex-situ focus in Igbo 2.1 The Igbo language Igbo (Benue-Congo, Blench 1989) is spoken in Southern Nigeria by about 30 million people (grammars: Green and Igwe 1963;Carrel 1970;Manfredi 1991;Mbah 2006;Emenanjo 2015). Igbo is a tone language and distinguishes between low tone (à), high tone (á), and downstep (ā). Tone in Igbo has both lexical and grammatical functions (see Nwachukwu 1995). The language has remnants of a case system in nouns: the 2sg and 3sg personal pronouns have a nominative-accusative distinction; nouns in general distinguish between a base form and a genitive form, used to encode possession. There is relatively rich verbal inflection concerning tense and aspect marking as well as the expression of derivational categories, e. g., applicative.
In Amaechi and Georgi (2019) we argue that the basic structure of a declarative all-new sentence as in (1) is (4) (for a transitive verbal predicate): (4) Igbo clause structure: CP The VP is head-initial; the structurally highest argument (here, the external/agent argument of the transitive verb) undergoes obligatory EPP-movement to SpecT. The main verb raises cyclically to Asp. Furthermore, the structurally highest verb (the V+v+Asp complex or, if present, an auxiliary) raises to T to pick up the inflection (but see Déchaine 1993 for a different view on verb movement). Verb movement to T is motivated by the observation that only the finite verb precedes negation in a sentence with negative polarity, viz., the main verb if no auxiliary is present, and the auxiliary otherwise. EPP-movement of the subject is evident from the fact that the subject must precede the finite verb (and thus also negation, aspect markers, etc.).

Focus ex-situ involves movement
In this subsection we argue that focus ex-situ involves movement of the focused XP to the left periphery of the clause in Igbo. Furthermore, we briefly exemplify a subject/non-subject asymmetry with ex-situ focus. 3 As was shown in (2b) and (3b) for direct objects, ex-situ focus involves fronting of the focused XP to the left edge of the clause, where it must be followed by the focus marker kà (see Amaechi and Georgi 2019 for arguments that kà is a focus marker). The same holds for all other non-subjects, viz., for focus fronting of indirect objects (IO) and adjuncts (ADJ), see (5). We illustrate this here with question formation, but exactly the same pattern holds for fronting of non-wh-XPs that are focused.

ADJ question
We assume that the fronting of the focused XP is brought about by movement in the syntax because the dependency is island-sensitive, exhibits reconstruction as well as cyclicity effects, and licenses parasitic gaps; these properties are the hallmarks of (Ā-)movement dependencies. (6) and (7) illustrate sensitivity to strong islands, viz. adjunct and complex noun phrase (CNP) islands. 4 non-wh-focus, we use question formation in this section (assuming that wh-words are inherently focused, see Horvath 1986;Rochemont 1986;Tuller 1986;Sabel 2000;Haida 2007, andAboh 2007 for a different view). Furthermore, the evidence from cyclicity effects, viz., the tonal reflex of movement, is new and is not discussed in Amaechi and Georgi (2019). 4 In the adjunct island examples throughout this paper, the verb in the embedded temporal clause is nominalized (nominalizing prefix à-). This nominalization happens in certain aspects as well as in some embedded clauses, though in the latter case it is not entirely clear what the conditions for its occurrence are. For example, it does not surface in all temporal embedded clauses. This nominalizing prefix is also absent whenever the preceding subject is a clitic pronoun. Crucially, the adjunct island effect we report here is independent of the form of the verb (nominalized or not), since it also arises in temporal adjunct clauses that do not trigger nominalization of the verb. Note that several tone changes occur in (6b) and (7b) (as well as in other examples in this paper) compared to their declarative counterparts (6a) and (7a): First, the final low tone of a subject DP becomes high when another element moves across it; this happens e. g. to Uche in (6b) and (7b), but not to proper names such as Ada and Obi here and in other wh-ex-situ examples in this paper since these names already end in a high tone underlyingly, so the effect is not visible. Second, Ā-movement of a subject, as e. g. subject relativization in (7b) triggers downstep on the verb hù 'see' (and harmonizing affixes), which otherwise surfaces with low tones. Another regular tonal change can be observed on the pronominal subject pronoun ȯ throughout this paper: it bears a high tone in an affirmative sentence, but a low tone in negative clauses. For more dis- Note that the ungrammaticality of (6b) and (7b) is not due to the distance spanned by the dependency because long-distance focus fronting as such is possible in Igbo, see (8) for long fronting of a wh-direct object. Thus, the ungrammaticality is indeed due to the crossing of an island boundary.  The examples in (9) and (10) show that the fronted XP reconstructs e. g. for Principle C and variable binding. In (9b) we see that the matrix clause 3sg pronoun cannot be coreferent with the fronted wh-word, just like in the baseline example (9a), where coreference with both R-expressions is excluded by Principle C. In (10) the variable contained inside the fronted wh-XP can be bound by the universally quantified subject of the embedded clause, as indicated by the possibility of pair-list answer in (10b) (note: 'to like' is expressed in Igbo as 'to see with the eye'). An alternative analysis in terms of quantifier raising (QR) of the universally quantified XP is excluded because this would involve long-distance QR, which is generally not available. Thus, the focus fronted XP in Igbo can be interpreted in the position of the gap, which follows if the XP has undergone movement and has thus left a lower copy/trace, which is accessible for interpretation at LF.
Moreover, movement dependencies in Igbo exhibit cyclicity effects. One of these effects is tonal: the final tone bearing unit on the subject DP becomes a high tone when an XP is moved across it (Goldsmith 1976;Nwachukwu 1976;Manfredi 2018 In the declarative sentence, the subject Úchè, a proper name, ends in a low tone, see (11a). If the direct object undergoes focus fronting to the left periphery and thereby crosses the subject, the final tone of the subject obligatorily becomes high, see (11b). In long-distance focus fronting, this tonal reflex can be observed in every CP that is crossed by movement, see (8b), where the tonal change affects both the embedded subject Ézè and the matrix subject Úchè. Crucially, this tonal reflex does not arise in Ā-dependencies that do not involve movement but rather base-generation (topicalization), and it does not arise under A-movement; thus, it only tracks Ā-movement. See Amaechi (2020: ch.4) for the relevant data and more cyclicity effects in Igbo.
Finally, (12) shows that focus fronting a constituent from the matrix clause can license a parasitic gap (pg) in an adjunct clause (Amaechi and Georgi 2019: 18 These findings provide evidence that movement is involved in focus fronting in Igbo. Another property of Igbo focus fronting that will play a role in what follows is the observation that only one XP can undergo focus fronting in the language. This is illustrated in (13) for multiple questions. Even though there are several whwords in the sentence, only one of them can occur in the ex-situ left-peripheral position. Fronting more than one (regardless of their linear order and the position of the focus marker kà) results in ungrammaticality. Hence, the wh-words that do not front stay in-situ. Note that Igbo does not exhibit superiority effects in focus fronting, and hence any of the multiple wh-XPs can in principle front, as long as it is just one that undergoes movement. Àdá Ada n'-Àbá P-Aba 'Obi saw Ada in Aba.' declarative 5 Note that to prize is expressed by an inherent complement verb construction in Igbo that literally means 'agree to mouth something'. Syntactically, 'mouth' is the (inherent) complement (direct object) of the verb, while 'something' is an applied argument (i. e. an indirect object) that linearly precedes the direct object, just like indirect objects in double object constructions do in the language. Crucially, indirect objects, including applied ones, behave exactly like direct objects with respect to Ā-movement in Igbo. They can undergo Ā-movement such as focus fronting, Ā-movement of indirect objects also leaves a gap, and they are also pronominalized by the accusative form of the personal pronoun. To summarize, exactly one focused XP in Igbo must move to the left periphery of the clause (unless there is no focused XP in the structure, of course). In Amaechi and Georgi (2019) we argue that this position is the specifier of FocP (SpecFoc) in a split CP-system. Given this assumption, the structure of ex-situ focus looks as follows (exemplified for an ex-situ direct object): The focused XP moves from its base position inside the vP to the specifier of FocP; this movement is driven by the probe-feature [ * Foc * ]↑, which is satisfied (and hence deleted/deactivated) as soon as there is an XP in SpecFoc. Put dif-ferently, [ * Foc * ]↑ probes upwards, viz. it seeks a focus XP that c-commands it, which is the case when an XP is in SpecFoc. The head of FocP, viz., Foc 0 is realized as kà (the focus marker) if an overt (viz., pronounced) XP occupies Spec-Foc; otherwise Foc 0 remains silent (Ø). The motivation for the sensitivity of Foc 0 spell-out to the overtness of the XP in SpecFoc will be introduced in Subsection 2.3. So far, we have only considered examples with non-subject XPs in the ex-situ strategy. This is because subject focus differs slightly from non-subject focus with respect to the availability of in-situ vs. ex-situ focus in Igbo. Focused subjects, like focused non-subjects, can occur in-situ, i. e. without the focus marker, see (15a). 6 However, it is impossible to add kà to the subject if the subject is focused (in the minimal clause), see (15b). Since with non-subjects kà can only attach to exsitu focus XPs, this suggests that subjects cannot be focused ex-situ in Igbo but have to stay in their canonical position SpecT. In fact, Amaechi and Georgi (2019) provide further arguments for this view, e. g. from another tonal reflex of movement. Before we can illustrate this, note that the restriction to focus in-situ for subjects only holds for clause-bound Ā-dependencies. Long-distance subject focus is possible, and in this case the subject is also followed by the focus marker kà, just like any other ex-situ focus XP, see (15d) based on (15c). (15d) also shows that under long subject movement, we see a tonal effect on the verb in the clause in which the subject originates: its tones (underlyingly low, see (15c)) surface with downstep. Amaechi (2020) shows that this tonal reflex only arises in movement dependencies (focus fronting) but not in base-generation Ā-dependencies (topicalization). Crucially, this tonal reflex is absent when the subject of the minimal clause is focused: the tones on the verb stay low, see (15a). This is a fur-6 In fact, the possibility of using in-situ subject focus is limited. In-situ subject focus is possible for wh-subjects and non-wh-subjects preceded by a focus-sensitive particle like 'only'. However, in-situ focus is not available for 'bare' focused subjects that are neither wh-words nor accompanied by a focus-sensitive particle as e. g. in an answer to a subject question "Who came?" -"John came". This answer would be ungrammatical in Igbo, even with stress on the subject; Igbo does not (primarily) use phonetic cues to indicate focus. No such restrictions hold for in-situ focus on non-subjects. This is in line with Fiedler et al.'s (2010) generalization that subject focus -unlike non-subject focus -must be marked in West African languages (and beyond). In Igbo this involves some morpho-syntactic indication of focus, e. g. wh-morphology, the occurrence of the focus marker (generally unavailable for in-situ focus, however) or the presence of a focussensitive particle. Otherwise, the string is morpho-syntactically indistinguishable from a declarative clause (as in the answer "John came." above.). The only way to express focus on a "bare" subjects (in the minimal clause) is to use a cleft structure ("It is John who came.").
ther argument for the claim that local subjects can only be focused in-situ in Igbo. 7 Amaechi and Georgi (2019) attribute the immobility of local subjects to an antilocality constraint on movement; see the paper for a detailed analysis.
Due to the restrictions on subjects with respect to the availability of the exsitu/in-situ strategy, and given that it is not totally clear whether focused matrix subjects undergo movement to SpecFoc (see Footnote 8), we will only consider non-subjects in what follows when we compare focus ex-situ and focus in-situ. See Fiedler et al. (2010); Zimmermann (2011); Zimmermann and Onea (2011) for more subject/non-subject splits in focus marking similar to that found in Igbo and 7 Note that, as illustrated e. g. in (7b), local subject relativization -unlike local subject focus fronting -also triggers the tonal reflex of movement on the verb of the relative clause. This shows that the reflex is not per se restricted to long subject extraction. As for the difference between local subject relativization vs. focus fronting, we have argued in Amaechi and Georgi (2019) that local subject relativization can exceptionally move to the C-domain of the minimal clause since this movement is required for interpretation (lambda abstraction). See the aforementioned paper for details and a formal implementation of this difference in local subject Ā-movement. 8 Island-sensitivity cannot be used to test for movement in local subject focus fronting: The distance spanned by the putative movement from SpecT (the canonical subject position) to SpecFoc is too short to cross e. g. an adjunct or a complex NP-island. Subextraction of a conjunct from a coordinated subject is possible, but only with a resumptive pronoun instead of a gap, and in this case the subject is also followed by the focus marker, unlike when the entire subject is locally focused. pg-licensing is also not informative for subjects since the pg must not be c-commanded by the true gap (Engdahl 1983), which is, however, the case if the Ā-moved XP is a subject. See Amaechi and Georgi (2019) for other potential movement diagnostics (e. g., D-linked wh-phrases, fragment answers), most of which can, however, not be applied in Igbo for independent reasons (because the constructions do not exist in the first place or they do not exhibit a distinction between ex-situ/in-situ focus XPs in general, not even with non-subjects). reasons for the split. Such splits seems to be wide-spread cross-linguistically and they always go in one direction (special behavior of subjects compared to nonsubjects).

Foc-in-situ involves syntactic movement
We now turn to the syntax of focus in-situ. There are two basic views on the nature of focus in-situ in the literature (see Bayer and Cheng 2017 for a recent overview on analyses of wh-/focus in-situ). First, in-situ XPs may be literally in-situ, i. e., they do not undergo (focus) movement in the syntax at all and are located in the same position they occupy when they are not focused (i. e., in an all-new declarative clause). Under this view, the in-situ element is interpreted either by moving to their scope position at LF (May 1985) or without LF-movement via unselective binding (Pesetsky 1987). The second view is that focused XPs do undergo movement to the ex-situ focus position (here: SpecFoc) in the syntax, but are pronounced in their base position. In the latter case, the difference between ex-situ and in-situ focus thus obtains in the PF-component: either the topmost copy of the movement chain (the one in SpecFoc) is pronounced, leading to focus ex-situ on the surface, or the lowest copy of the chain (base position of the XP) is phonologically realized, resulting in an in-situ focus XP on the surface (see Nissenbaum 2000; Bobaljik 2002). In this subsection we argue that the second view is appropriate for focus in-situ in Igbo, i. e., the optionality between focus ex-situ and in-situ arises at PF. In the syntax, one focus XP has to move to SpecFoc. Evidence for this claim comes from the observation that focus in-situ in Igbo (illustrated here again with wh-words) exhibits (Ā-)movement properties: it is island-sensitive, can license parasitic gaps and does not induce Beck intervention effects. The parasitic gap data also argue against LF-movement.
First, consider (16). It shows that an in-situ wh-word cannot occur inside an island (here, an adjunct island). This follows if there is syntactic movement involved, which is blocked by islands. (16) Island-sensitivity of wh-in-situ: Second, wh-in-situ can license a parasitic gap (pg), see (17). Pgs are only licensed by Ā-movement in the narrow syntax, but not by LF-Ā-movement (Engdahl 1983; see Branan and Sulemana 2019 for the same effect with wh-in-situ in Bùlì). Hence, (17) does not only provide evidence that the (apparent) in-situ wh-word has undergone Ā-movement, but also that this movement has happened in the narrow syntax, and not at LF. This argues against the alternative approach to wh-in-situ mentioned above, where the in-situ wh-element does not move in the syntax, but rather at LF. 9 Finally, (18) illustrates that negation (and also focus-sensitive particles) can intervene between an in-situ wh-word and its putative landing site in SpecFoc. If the wh-word were indeed in its base position in the syntax, it would be c-commanded by negation and should thus induce a Beck intervention effect (Beck 1996(Beck , 2006Kotek 2017a,b; see e. g. Kobele and Torrence 2006 for such effects with wh-in-situ in Asante Twi). These intervention effects are suspended by syntactic movement of the wh-element across the potential intervenor (though LF-movement alone does not safe the intervention effect). Hence, the wh-in-situ element in Igbo also behaves as if it has undergone syntactic movement in this respect. We can thus conclude that focus in-situ is only apparent in the sense that the focused XP undergoes movement to SpecFoc in the syntax, but the lowest copy of the chain is pronounced (cf. Bobaljik 2002). At this point it becomes clear why we formulated the conditions on the realization of the focus head Foc 0 with reference to the overtness of the XP in SpecFoc in Section 2.2: recall that elements that are focused in-situ (on the surface) cannot co-occur with the focus marker kà. If Foc 0 were always realized as kà when an XP occupies its specifier, it should also surface with (apparent) focus in-situ given that we have argued that there is also movement of the focused XP to SpecFoc in these sentences. What seems to matter for the realization of Foc 0 is whether the XP in SpecFoc is overt or not. If the XP in SpecFoc is pronounced, then Foc 0 is also pronounced, viz., kà surfaces; if, however, the XP in SpecFoc remains unpronounced (focus in-situ) then Foc 0 remains silent, too.
Recall that only one focus XP can move to SpecFoc in Igbo (see (13)). We thus predict that in multiple questions, all but one wh-XP are in fact in-situ in the syntax, i. e. do not undergo movement to SpecFoc in the syntax (and since there are no superiority effects in Igbo, see (13), in principle any of the wh-words in a multiple question can move, as long as just one of them does). Thus, we propose that there are two types of wh-in-situ elements in Igbo: true (unmoved) ones as in multiple questions, and apparent in-situ ones that have in fact undergone movement but are pronounced in their base position, as in simple questions. Evidence for this split of in-situ wh-elements comes from the following observations. First, true wh-in-situ elements in multiple questions are not sensitive to islands, see (19): the wh-word gí nī 'what' is inside an adjunct island, but the sentence is grammatical. 10 The reason is that it has not undergone wh-movement at all. The sole ex-situ focus position SpecFoc in the matrix clause is visibly occupied by ònyé 'who', the direct object of the matrix verb. Hence, gí nī can (and in fact must) stay in its base position. 11 Compare this with (16b) where the sole wh-element cannot be inside the adjunct island because it has to move to matrix SpecFoc, since there is no other wh-element that can do this. Second, we consider evidence for two types of wh-in-situ elements from pglicensing in multiple questions. Look at the question in (20); both objects of the ditransitive matrix verb are wh-pronouns, with the direct object in the ex-situ position and the indirect object in-situ. It is not possible in this configuration to have a pg licensed by each of the wh-words. The reason is that pgs require a syntactically moved antecedent. But the wh-word representing the indirect object is truly in-situ, i. e. it has not undergone movement at all in the syntax -the sole landing site is visibly occupied by the wh-direct object. Hence, licensing of pg 1 fails (the linear order of objects in Igbo is indirect object ≻ direct object). Compare this pg-licensing behavior of a truly in-situ wh-element with that of an apparent in-situ wh-element (moved but pronounced in-situ) in a simple question as in (17b): the apparent wh-in-situ element can license a pg -unlike the truly insitu one in (20) -since it can move to the ex-situ focus position SpecFoc. This account of the grammaticality difference between (20) and (17b) further predicts that (20) becomes grammatical if pg 1 representing the (truly in-situ) indirect object is replaced by an overt pronoun; pg 2 should be licensed since its antecedent is the ex-situ wh-direct object. Indeed, this sentence is grammatical in Igbo, see (21).

(21)
Gínī what Hence, the generalization for Igbo is that in a sentence in which one or more XPs are focused, exactly one XP must undergo movement to SpecFoc in the syntax (though it may be pronounced in its base position). This restriction to the movement of one focused XP can be formalized in an optimality-theoretic approach with ranked and violable constraints (cf. Prince and Smolensky 1993). 12 We need the following constraints: Movement must be feature-driven (result in discharge of a probe feature) c. ranking: LR ≫ Foc-Crit Foc-Crit basically demands that focused XPs must occupy SpecFoc and hence must move from their vP-internal position to the left periphery. This holds for all focused XPs in the clause. In order to restrict the XPs that move to SpecFoc to exactly one, Foc-Crit interacts with the constraint LR. LR says that every movement step must result in the checking of a feature. Recall from Section 2.2 that the focus head Foc 0 bears a probe feature that probes upwards and is discharged as soon as it finds an XP in SpecFoc. Thus, this probe feature [ * Foc * ]↑ is deleted after the first focus XP moved to SpecFoc. Any further focus XP that intends to move to Spec-Foc (to satisfy Foc-Crit) violates LR because it does not result in feature checking (given that the sole focus movement related probe feature has been discharged by the first instance of focus movement). Since LR outranks Foc-Crit, we derive the restriction that only one focus XP moves to SpecFoc; any potential other focus XPs in the clause stay in-situ, in violation of Foc-Crit. The immobility of local subjects with respect to focus movement can be integrated into this analysis by a high-ranked anti-locality constraint à la Erlewine (2016) that prohibits movement steps that are too short as defined in (24): (24) Spec-to-Spec anti-locality (SSAL, Erlewine 2016: 431): Ā-movement of a phrase from the Specifier of XP must cross a maximal projection other than XP Movement of a focused subject XP from its canonical position SpecT (due to Igbo's obligatory EPP-feature on T) to SpecFoc would be too local in this sense as it does not cross a phrase other than TP, see the tree in (14). If SSAL outranks in particular Foc-Crit, see (25), subjects will not undergo focus movement to the local SpecFoc, in violation of Foc-Crit.
(25) Constraint ranking (extended): SSAL ≫ LR ≫ Foc-Crit This brief sketch of the analysis illustrates one way of modeling the requirement that exactly one focus XP must move to SpecFoc in the syntax in Igbo. The forinterested reader is referred to Amaechi and Georgi (2019) for a detailed OT-analysis, including, for example, relativization and long-distance focus movement. malization of this generalization will, however, not be important in what follows, only the empirical pattern will be immediately relevant.

Interim summary
We have argued in Section 2 that the optionality between focus ex-situ and focus in-situ in Igbo does not arise in the syntax: if there is at least one focus XP present in the structure, exactly one focus XPs must undergo movement to left-peripheral focus position (SpecFoc) in the syntax. We find true syntactic focus in-situ only if there are multiple focused XPs; all but the one XP that moves to SpecFoc in the syntax stay in their base positions. The optionality between focus ex-situ and in-situ arises at PF, viz., what is variable is which of the copies in the focus movement chain is pronounced: either the topmost copy, viz., the one in SpecFoc, is pronounced, which leads to focus ex-situ on the surface; or the lowest copy of the chain (XP's base position) is pronounced, which results in (apparent) focus in-situ on the surface.

Factors that govern copy deletion / spell-out
If the ex-situ / in-situ distinction is a matter of PF, the next question is whether we can identify any factors that govern the choice between the pronunciation of the topmost copy vs. the lowest copy in the focus movement chain. In this section we show that -in line with previous mainly semantic studies of ex-situ vs. in-situ focus -semantic/pragmatic consideration, viz., the type of focus to be expressed, is the main factor involved in the choice. This PF-LF interaction suggests that these two modules can interact.

Focus types and the structure-meaning correlation
Focus is a means to highlight that there are contextually salient alternatives that are relevant for the interpretation of an utterance (Rooth 1985, Rooth 1992Krifka 2008). Different types of focus have been identified in the literature; these arise if additional semantic and pragmatic factors come into play, see Zimmermann and Onea (2011). A common distinction is between identificational focus (or contrastive focus) vs. new information focus (Rochemont 1986;É. Kiss 1998;Aboh 2007), but more fine-grained distinctions have been argued for, e. g. in Dik (1997) and more recently in Bazalgette (2015). Bazalgette adopts a four-way distinction between simple focus (only triggers alternatives), implicational focus (comes with a cancelable implicature of contrast, exclusivity or unexpectedness), pragmatic focus that is associated with a presupposition (e. g. existence, exhaustivity) and focus that has an effect on the truth-conditions of the utterance (scalar, exhaustive or exclusive readings). Crucially for present purposes, É. Kiss (1998); Vallduví and Vilkuna (1998) claim that there is a correlation between focus realization (the morpho-syntactic strategy used to encode focus) and focus interpretation (the focus type) based on studies of focus in Hungarian, Finnish and Catalan: whereas in-situ focus encodes new information focus (viz., the simple presence of alternatives), ex-situ focus is used to express additional semantic and pragmatic meaning components (exhaustivity, contrast, etc.). Thus, morpho-syntactic complexity correlates with complexity in meaning. Hartmann and Zimmermann (2007); Zimmermann (2011)  More concretely, the idea is that ex-situ foci always come with an additional meaning component. We tested (some of) the contexts listed in Bazalgette (2015) and discussed / exemplified in van der Wal (2016) to check whether this general tendency also holds in Igbo.

The meaning-structure interaction in Igbo
In this subsection we will investigate whether there is a correlation between focus type and focus position (ex-situ/in-situ) along the lines of the Meaning-Structure Mapping Hypothesis in (26). We will not illustrate each focus type here, but restrict ourselves to a few illustrative examples that test whether ex-situ focus is indeed associated with additional meaning components such as contrast, exhaustivity, etc. For a comprehensive overview of (term) focus types, see Bazalgette (2015); van der Wal (2016).
13 See Zimmermann (2011: 1192) for a critical discussion of the Meaning-Structure Mapping Hypothesis especially with respect to contrastive focus. He adopts a somewhat weaker version of the hypothesis, viz., the Focus-Marking Implication, based on ideas in Skopeteas and Fanselow 2009.
As we have already shown in (3), in-situ focus in Igbo can be used to express new information focus as in an answer to questions such as in (2). It is not excluded to use the ex-situ strategy in the answers (see (27)), but in-situ focus is the preferred option in this context, as expected under the Meaning-Structure Mapping Hypothesis.

DO ex-situ focus
Contrastive focus can also be expressed both by focus in-situ and ex-situ, but this time with a preference for the ex-situ strategy; see (28) and (29)  n'-áhíá P-market 'Obi saw Ada at the market but Uche saw Ugo at the market.'

DO ex-situ focus
Moreover, the ex-situ strategy expresses exhaustivity, viz., it indicates that the predicate holds solely for the mentioned alternative but for none of the other contextually salient alternatives. That ex-situ focus induces exhaustivity is evident from the following observations: 14 (i) Focus ex-situ is incompatible with the particles also and even (É. Kiss 1998), while they can co-occur with focus in-situ (new information focus in answers to questions), see (30). Note that (30b) is not unacceptable because the focus-sensitive particle cannot attach to an ex-situ focus, as a reviewer suggests; it is indeed out because focus ex-situ induces exhaustivity (and the additive particle is incompatible with that semantically), since (30c), without the focus-sensitive particle but with an additional alternative in an afterthought is also unacceptable. (ii) In the focused conjoined XPs test (Szabolcsi 1981) we compare a pair of sentences in which one contains a focused conjoined XP and the other sentence contains a focused non-conjoined XP which is identical to one of the conjuncts of the focused XP in the first sentence. If the sentence with the coordination entails the sentence without coordination, focus is not (obligatorily) exhaustive. (31) and (32) illustrate the test for focus in-situ (e. g. in an answer to an object question) and focus ex-situ in Igbo. 14 We illustrate exhaustivity tests here with ex-situ focus XPs that are not wh-elements. However, the same holds for content questions: ex-situ wh-elements induce exhaustivity, while in-situ ones don't. Since focused subjects cannot undergo local Ā-movement, i. e. they have to remain in-situ, wh-subjects in a matrix question do not have an exhaustive interpretation, as expected. See Amaechi (2020) for further applications of exhaustivity tests in Igbo, e. g. in it-clefts. (31a) entails (31b), but this does not hold for (32a) and (32b). This shows that only ex-situ focus expresses exhaustivity.
Ex-situ focus is also compatible with an exclusive meaning component in Igbo: one can add the co-text "and not Y" to a sentence with an ex-situ focused XP, which explicitly excludes an alternative (Chafe 1976). This is, however, not possible with in-situ focus, see (33) (where the verb is focused; ex-situ verb focus requires nominalization in Igbo): (33) Context: Before going out, you ask your son to prepare fufu for dinner. When you came back in the evening the fufu is ready and you want to know how he prepared it: by pounding or by stirring. You ask your daughter, who was at home with your son, how he did it. She answers: In addition, ex-situ focus in Igbo can induce an implicature, e. g., in the interpretation of numerals that in-situ focus does not induce: It has been noted that numerals, which are in principle ambiguous between an exact amount reading and an "at least this amount" (upward entailing) reading, can only have the exact amount reading under (exhaustive) focus, see among others van Rooij and Schulz (2004) for discussion. In Igbo, we observe that in-situ focus can have the upward entailing "at least" reading, while ex-situ focus only has the exact amount reading, see (34) The loss of the "at least" reading under focus is assumed to be the result of a conversational implicature. Thus, ex-situ focus is associated with this additional pragmatic component, while in-situ focus is not.
The above examples illustrate that there is in fact a (non-perfect) correlation between the focus strategy used and the expressed focus type in Igbo in accordance with the Meaning-Structure Mapping Hypothesis: in-situ focus expresses solely information focus; ex-situ focus is (often) associated with additional meaning components (such as contrast, exhaustivity, implicatures) that are not available with in-situ focus. Thus, meaning has an influence on the choice of the focus realization strategy, which we argued to be a matter of PF rather than syntax. We will discuss the consequences of these findings for the architecture of grammar in the following subsection.

Consequences for the architecture of grammar
To summarize our findings, we can say that the (apparent) optionality between in-situ and ex-situ focus is not a syntactic effect but is rather determined at PF (realization of the topmost vs. the lowest copy in the syntactic movement chain). The choice of the copy that is to be pronounced is influenced by a semantic/pragmatic factor, viz., focus type. We thus see an interaction between the two non-syntactic components PF (phonological form) and (roughly) LF (logical form). In a commonly assumed model of grammar in the Extended Standard Theory (Chomsky 1973) and its descendants, PF and LF are separate post-syntactic modules, see (35). This model is called the Y-model or T-model (Chomsky and Lasnik 1977) because the two modules PF and LF branch off from syntax: In this model, syntactic processes can feed or bleed (i. e., can influence) PF and LF-processes (pronunciation and interpretation), but not vice-versa, since PF and LF come too late to have an effect on syntax. Moreover, PF and LF do not interact since they constitute separate branches; they can both be sensitive to the output of syntax, but not to each other. Interestingly, the Igbo focus optionality poses a challenge for this view: apparently, PF is sensitive to LF in the language in that the choice of chain copy that is to be pronounced is determined by semantic/pragmatic factors. Such an interaction is unexpected under the Ymodel.
Does that mean that we have to give up the Y-model? Not necessarily. In a study of head-and A-movement dependencies that also seem to exhibit a PF/LFinteraction similar to the one in Igbo, Bobaljik (2002) provides a solution to the puzzle (building on previous work in a similar spirit, e. g., Brody 1995). First, he adopts a single output syntax based on the copy theory of movement. This means that there is no distinction anymore between overt movement (movement in the narrow syntax which can feed PF, viz., ex-situ constructions) and covert movement (movement at LF which cannot feed PF and thus results in in-situ constructions) as in the pre-copy theory (trace) era. Rather, movement is always syntactic; a movement chain involves several copies and PF and LF decide which of these copies they interpret (phonetically or semantically), with potential mismatches between the two post-syntactic modules. If PF chooses to privilege a higher copy in a chain than LF, we get reconstruction effects (an XP is interpreted in a lower position than where it surfaces); if, on the other hand, LF interprets a higher copy than PF, we get in-situ effects (an XP is interpreted in a higher position than where it surfaces). This intuition is precisely what we have argued to be the case in Igbo (apparent) focus in-situ: there is a movement chain in the syntax (with its scope position being the highest copy), but the lowest copy of it is pronounced at PF. This assumption still does not predict an interaction of PF and LF, of course. The second assumption Bobaljik makes to enforce such an interaction is the economy constraint in (36): Minimize Mismatch (Bobaljik 2002: 251): (To the extent possible) privilege the same copy at PF and LF.
This constraint requires LF and PF to operate in parallel, i. e. to interpret the same copy because this is the most economical option (only one copy needs to be considered in both modules). Mismatches of the kind outlined above (reconstruction effects, in-situ effects) are not excluded, but they are dispreferred by (36) and must thus be triggered by other (more important) constraints. Minimize Mismatch describes an interaction of PF and LF; they have to "talk" to each other to evaluate this constraint. We believe that the Igbo PF/LFinteraction can also be modeled in Bobaljik's (2002) framework given the economy condition in (36): If the lowest copy in the focus movement chain is interpreted (and this position is associated with information focus), then (36) strongly favors the pronunciation of the same copy, which results in focus in-situ. If, however, an additional meaning component (e. g. exhaustivity, contrast, etc.) is to be expressed, the highest copy in the chain is interpreted at PF (a position associated with such meaning components); given the Minimize Mismatch condition, this highest copy is also privileged at PF, viz., it is pronounced. The economy condition is not absolute, it can be overwritten by other constraints, as Bobaljik has pointed out. And in fact, there is no strict one-to-one correlation between interpretation (focus type) and focus marking strategy, see Zimmermann and Onea (2011);Zimmermann (2011). Such exceptions to Minimize Mismatch can also be modeled in an optimality-theoretic analysis with ranked and violable constraints. We leave it for future research to identify such interacting constraints and to model the interactions. What is crucial for present purposes is that the Igbo facts are in conflict at least with the initial version of the Y-model because PF and LF seem to interact, which the model excludes. It is, however, possible to reconcile the data with Bobaljik's (2002) revision of the model that is based on a single output syntax and the economy condition Minimize Mismatch, which postulates the required interaction between PF and LF. In particular, it demands isomorphism between PF and LF in terms of the choice of the privileged copy, which is precisely what we see in Igbo (and many other languages). Note however, that the constraint Minimize Mismatch is still not in line with the Y-model in a strict sense: it postulates an interaction between two modules that should not interact because the LF and the PF-branch are strictly separated in the model. This raises the question whether the Y-model can be upheld in its present form given that we have evidence for a PF-/LF-interaction from head movement, A-movement (e. g. Bobaljik 2002) and Ā-movement (e. g. from the Igbo data in this paper).
On a final note, we would like to highlight the difference of the current study of focus marking in Igbo to similar previous studies that center around the Meaning-Structure Mapping Hypothesis (see (26)). As this hypothesis expresses, scholars (in particular semanticists) working on focus types (see the references above) have noted quite a while ago that there is a correlation between the focus position (ex-situ vs. in-situ) and focus type, with the more semantically/pragmatically complex types preferably expressed ex-situ and information focus expressed insitu. In this sense, the Igbo facts are not surprising and support the hypothesis. However, in previous work on this topic, the syntax of focus in-situ has not been studied in any detail, i. e., the syntactic status of focus in-situ (moved with pronunciation of the lower copy or unmoved) remains largely unclear. In the discussions of focus type and focus positions in the literature, focus in-situ is usually talked about as if it were 'real' focus in-situ, viz., the focused XP does not undergo syntactic movement at all. But often no tests are applied to support this view, though see Keupdjio (2020) for a recent study on Medumba (Grassfields Bantu): he shows that focus in-situ has not undergone movement in the syntax (and we find a similar split as in Igbo regarding the interpretation between focus in-situ and ex-situ). Now, imagine this were indeed the case in the languages discussed in the semantic literature on the topic, viz., focus ex-situ involves syntactic movement, while focus in-situ does not involve syntactic movement at all, the focus XP stays in its base position. Furthermore, the structurally highest copy is pronounced in each case, viz., the highest copy in the ex-situ scenario and the sole copy in the in-situ scenario. In this case, we have a syntactic difference between the ex-situ and the in-situ strategy. The interpretative component (semantics, pragmatics) can be sensitive to this syntactic difference because in the Y-model syntax feeds LF. A high copy (that is the topmost one among a number of other copies in a focus movement chain) is then associated with additional meaning components (exhaustivity, contrast, etc.), while a focus chain that consists of only one element (a trivial chain, since no movement has applied and hence no copies have been created) is interpreted as information focus. In such a scenario, no interaction between PF and LF is necessary, because the difference is already present in the syntax, which feeds both PF and LF. A real problem arises if there is no syntactic difference between focus ex-situ and in-situ, which we claim to be the case in Igbo. Still, the Meaning-Structure Mapping Hypothesis seems to hold. To achieve this, communication between PF and LF is necessary, such that the pronunciation of a copy (in a chain) is affected by its interpretation (focus type). Thus, a problem for the Y-model only arises if there is no syntactic difference between focus ex-situ and in-situ in that there is movement to a dedicated focus position in both cases. This is how the Igbo facts are different and potentially more informative about the architecture of grammar than languages in which focus ex-situ and in-situ differ syntactically.

Conclusion
In this paper we have presented a study of an (apparent) optionality between focus ex-situ and in-situ in Igbo (Benue-Congo, Nigeria). We have argued that the optionality does not arise in the syntax; in this component both strategies involve focus movement (of exactly one focus XP) to the left periphery of the clause. Instead, the optionality emerges at PF: either the topmost copy or the copy at the bottom of the focus movement chain is pronounced. The choice is not completely optional, however. It is influenced by the semantics/pragmatics, i. e., the focus type that is to be expressed along the lines of the Meaning-Structure Mapping Hypothesis: information focus is preferably expressed with the in-situ strategy, while additional (pragmatic) meaning components, e. g., exhaustivity are preferably realized by the ex-situ strategy. Igbo differs from other languages with a similar correlation between focus type and focus realization strategy in that it requires an interaction between PF and LF. This is the case because there is no syntactic difference between the ex-situ and the in-situ strategy in Igbo (unlike, presumably, in some of the other languages discussed in the literature on focus types -though the syntactic properties of focus in-situ in these languages remains to be investigated). Hence, syntax cannot mediate between PF and LF in this case. A direct interaction between PF and LF is, however, challenging for the standard Y-model of grammar where PF and LF branch off from syntax and are separate branches. We have shown that Bobaljik's (2002) Single Output Syntax combined with the economy constraint Minimize Mismatch provides a partial solution to the problem, though an interaction between LF and PF is still required (for the evaluation of the economy constraint), and hence, a strict version of the Y-model cannot be upheld.