The distribution of φ-probes in the inflectional structure

Subject-verb agreement in φ-features has been treated as a relation between the subject and some functional category in the clausal spine (Infl, Agr, T). I argue that such severing of the φ-probe from the verb is problematic for agreement patterns in Bantu languages and argue for a tighter connection between them. The crucial argument is the lack of consistent association of functional heads with agreement features, observed e.g. in compound tenses and aspectual-verb constructions in Bantu languages. The number and positions of φ-probes in clausal structure are derived from the number and size of head-chains containing a verb.

1. Introduction.The so called subject-verb agreement has been for a long time analyzed as a relation between the subject and some functional head in the clausal spine (for example Infl 0 /T 0 (Chomsky, 1981) or AgrS 0 (Pollock, 1989)).Its common realization as an affix on the verb is, under this view, due to syntactic or postsyntacting conflation of the agreeing head with the verb.I call this approach, where the ϕ-probe is a property of a functional head, the Infl-origin approach, schematized in (1).An alternative view, suggested in Iatridou (1990), is that the verb itself is the agreeing head -the Verb-origin approach (2). (1) Infl-origin of ϕ-probes (2) Verb-origin of ϕ-probes

Infl
Even though the Infl-origin approach is widely accepted and certainly not unmotivated, I argue in this paper that it faces a major difficulty in accounting for subject agreement in Bantu languages.
The crucial aspect of subject agreement in Bantu is the lack of consistent association of ϕ-probes with specific functional heads.This can be seen in multi-verb constructions, such as compound tenses (section 2) and aspectual verb constructions (section 4), where a single functional head, e.g.Asp, agrees with the subject in one syntactic context but not in another.It thus becomes dubious that the agreement probe is introduced in the structure by that functional head, as the Inflorigin approach has it.Interestingly, this problem goes away under the Verb-origin approach: the number of agreement probes always matches the number of verbs (lexical or auxiliary) in the clause, irrespective of the type of inflectional material around it.Building on this observation, I propose a version of the Verb-origin approach (section 3).First, I assume that a verb carries a category feature iV, while functional heads in its extended projection have a matching uV feature, which is checked against the closest iV during the derivation (Svenonius, 1994;Chomsky, 1995;Julien, 2002;Cowper, 2010;Adger, 2003, a.o.).Subject agreement probes are claimed to be a property of iV, not uV -they are introduced in the structure by a verb.The actual probing position is, however, higher than the verb that introduced the probe.I model this as feature percolation of the ϕ-probe, which cooccurs with uV checking, as shown in (3).
(3) Proposal: Verb-origin & ϕ-percolation under V-checking a. ϕ-probe introduced by V Infl [uV] b. ϕ-probing from Infl In (3), V and Infl are in a V-checking relation, which I argue is the vehicle for ϕ-percolation (cf.Grimshaw's (2000) feature percolation within an extended projection).Probing takes place from the highest position in the V-chain (a sequence of heads in a V-checking relation), i.e. from Infl in (3).The Verb-origin approach directly captures the generalization that the number of agreement probes in the Bantu clause always correlates with the number of verbal elements.Together with the feature percolation mechanism, it also accounts for the apparent inconsistency is associating ϕ-probes with specific functional heads, allowing variability in ϕ-probe positions: the variability depends on the presence of additional verbal elements (auxiliary and aspectual verbs), and their position in the structure.Finally, I discuss how the present proposal relates to other existing approaches to multiple agreement in Bantu languages in section 5.
2. Inconsistent loci of ϕ in simple vs compound tenses.A characteristic feature of multi-verb constructions (e.g.compound tenses) in Bantu languages is that every verb in such as construction is fully inflected for subject agreement (unlike the pattern we often find in Indo-European languages, for instance, where only the highest verb is fully inflected, while the participle either doesn't agree or agrees partially).This phenomenon is illustrated in (4) with Ndebele, Kilega and Swahili.1  Each construction involves the main, lexical, verb and one or more auxiliary verbs: the default be in a compound tense (4-a), an aspectual auxiliary, e.g.kili 'still do' (4-b), or both the default and an aspectual an aspectual auxiliary (4-c).Irrespective of the type of auxiliary, every verb in the clause is fully inflected for subject agreement.
Existing accounts of the multiple agreement pattern in Bantu all assume the Infl-origin approach (though they differ in further details), that is, multiple instances of subject agreement correlate with multiple functional heads bearing a ϕ-probe (Kinyalolo, 1991;Carstens, 2001Carstens, , 2005;;Henderson, 2006;Baker & Willie, 2010;Baker, 2008, a.o.).Consider, for instance, the Swahili compound tense in (5).In addition to a ϕ-probe on T, the lower Asp Perf has a ϕ-probe, as well.The probe on T corresponds to the agreement prefix on the auxiliary kuwa, while the probe on Asp Perf is realized as an agreement prefix on the main verb. (5) A-li-kuwa 3sg-PST-AUX a-me-fariki.3sg-PERF-die 'He had died.' (Swahili; Nurse, 2008) The assumption that Asp Perf introduces an extra ϕ-probe in the structure is unproblematic for languages in which perfect aspect is systematically expressed as a compound tense, as is the case in English (6).
(6) a.She has left.b.She had left.c.She will have left.
If a particular functional head, e.g Asp Perf , systematically requires an auxiliary verb, and both the main verb and the auxiliary agree with the subject, then the hypothesis that Asp introduces the extra ϕ-probe can correctly capture the distribution of agreement.Importantly, however, so can the V-origin approach: if Asp Perf always cooccurs with an auxiliary, then the construction always contains two verbs, one for each agreement probe.In order to decide between the Inflorigin approach and the Verb-origin approach on empirical grounds, we need to identify a case in which the functional head in question does not systematically cooccur with an auxiliary.The Infl-origin approach predicts that the extra ϕ-probe is present whenever the relevant functional heads in present in the structure, regardless of whether it requires an auxilairy verb.The Verborigin approach makes the opposite prediction: the number of ϕ-probes will track the presence of an extra verb and be insensitive to the particular functional heads.Compound tenses in Bantu languages show this type of inconsistent association of functional heads and auxiliaries, allowing us to test these prediction.As discussed below, the facts support the Verb-origin approach.
Unlike the Past Perfect tense in Swahili (5), the Present Perfect is a simple (synthetic) tense.As we see in (7), there is no auxiliary verb, and the main verb (preceded by the perfect aspect prefix) is marked with a single subject agreement prefix.

T Pres ϕ
This distribution of default auxiliaries (called the overflow pattern of auxiliary use in Bjorkman (2011)), is characterized by the lack of consistent association of periphrastic expression with a specific inflectional head.2In this case, Asp Perf triggers periphrasis in the context of a past tense, but not in the context of a present tense.The same pattern is found in other Bantu languages and with other types of inflectional heads.I illustrated below with progressive tenses in Kinande (Bjorkman, 2011) and prospective tenses in Ndebele (Pietraszko, 2017).

Past Prospective
In all three languages, some aspectual head (perfect, progressive or prospective) triggers the appearance of an auxiliary verb in the past tense, but not in the present tense.Crucially, the inconsistent association with an auxiliary verb correlates with similarly inconsistent association of that inflectional head with an extra agreement probe -all of the synthetic tenses above have only one agreement prefix, despite the presence of the relevant aspectual inflection.Instead, the number of agreement prefixes correlates systematically with the number of verbal elements.
Before we move on, let me reject a possible analysis in the Infl-origin spirit.There is something special about the present tense in these languages: it has no overt exponent and it doesn't require (or allow) an auxiliary when combing with an aspectual inflection.It is, then, unmarked in the morphological and syntactic sense (see Bjorkman (2011) and Pietraszko (2017) for accounts of overflow periphrasis in terms of syntactic unmarkedness of certain inflectional heads).It is perhaps plausible that the present tense T is unmarked in yet another way, namely in having no ϕ-probe.The sole agreement prefix in the present tenses in ( 5)-( 9) would be the one contributed by the aspectual head.This analysis would, however, incorrectly predict that in the absence of the aspectual head, i.e. in the simple present, the verb is not inflected for subject agreement.This prediction is wrong, as shown in ( 10) and ( 11).

T Pres ϕ
As shown in ( 12), Asp is either not projected in Simple Present or is syntactically inert, pointing back to the assumption that T, even when unmarked, bears an agreement probe.
We conclude, then, that the extra agreement probe in compound tenses is not introduced by a specific aspectual head (as predicted by the Infl-origin approach), as its appearance does not correlate with the presence of that head in the structure.Instead, it correlates directly with the number of verbs.
3. Proposal: Verb-origin and feature percolation.In this section, I propose a formal implementation of the generalization that the number of agreement probes in Bantu compound tenses correlates with the number of verbs, rather than with particular inflectional heads.
First, I assume that a verb and functional heads in its extended projection are related by feature checking (Svenonius 1994, Chomsky 1995, Julien 2002, Adger 2003, Cowper 2010, Pietraszko 2017 a.o.).Verbs bear a category feature iV, while functional heads have a matching uV, checked against the closest iV.In a simple tense, the lexical verb is the only bearer of iV, therefore all functional heads establish a checking relation with the main verb, forming a single V-chain (13).Compound tenses, on the other hand, contain a higher verb -the auxiliary -which is a more local iV goal to some higher head(s) ( 14). 4 As a result, two V-chains are formed: one between the main verb and the heads below the auxiliary, and one between the auxiliary and the heads c-commanding it.Voice [uV] Asp [uV] T [uV] (14) Compound tense The claim put forth here is that subject agreement probes are introduced in the structure by elements with iV, i.e. lexical and auxiliary verbs, and not by elements with uV -functional heads.I further propose that the ϕ-probe undergoes feature percolation under V-checking; that is, from its original position on a verb to the top-most head in the V-chain, and it is that percolated position in which the probe becomes active and enters in an Agree relation with a DP.This proposal is schematized in (15) below. ( This proposal directly captures the generalization that agreement probes correlate with the number of verbs (lexical and auxiliary), and makes no independent claims about which functional heads should appear in such a structure.This latter correlation is indirect: it depends on how particular inflectional heads interact with periphrasis, which in turn determines the number of agreement probes.Let us see how this analysis derives the apparent inconsistent distribution of ϕ-probes in Bantu simple and compound tenses.
Recall that Past Perfect in Swahili is periphrastic, it contains an auxiliary verb (5), while Present Perfect is synthetic (7).In the periphrastic Past Perfect, the tense inflection is realized on the auxiliary, while the perfect aspect prefix is on the main verb.I assume, therefore, that the auxiliary is adjoined to T, as shown in (16).V-checking proceeds as follows: Voice and Asp check their uV against the main verb -the only iV they c-command, forming the V-chain Asp, Voice, V .T has a more local iV goal -the auxiliary verb.Therefore, it forms a separate V-chain with the auxiliary: T, V-aux ( 16). ( 16) Given that there are two verbs in the structure of ( 16), two ϕ-probes are introduced.In each case, the probe percolates to the highest head in its head chain: to Asp Perf and to T, deriving the effect of an extra probe on Asp in the Past Perfect.Crucially, the presence of an agreement probe on Asp Perf is Swahili is not a lexical property of that head.Rather, it is a consequence of the presence of an auxiliary in this tense, which in turn makes Asp Perf the highest head of a V-chain.
As predicted, ϕ-probing does not take place from Asp Perf , if it is not the higher head in the chain.This is precisely the case in Present Perfect -a context in which perfect aspect does not trigger auxiliary insertion in T (17).Given that the main verb is the only iV goal in that structure, all functional heads, including T, enter a checking relation with the main verb, forming one V-chain: T, Asp, Voice, V .The highest head in this V-chain is T, not Asp Perf , and so the sole agreement probe in this structure is located in T after percolation.
This account derives the apparent inconsistent association of Asp Perf with a ϕ-probe which, in the proposed analysis, falls out from an independent property of Asp Perf -its inconsistent cooccurrence with an auxiliary verb.Moreover, the analysis straightforwardly captures the observation made in the previous section that T appears to be an agreeing head in all tenses (even if its feature is [pres]) -assuming that T is the highest head with a uV feature in the clause, it will always be a probing position, whether the probe percolates there from an auxiliary or the main verb.The same derivation applies to progressive tenses in Kinande and prospective tenses in Ndebele.Even though these constructions involve different aspectual heads, they share the relevant property with Asp Perf in Swahili: they do not systematically trigger an auxiliary in T. This inconsistency gives rise to the apparent inconsistent association of these heads with a ϕ-probe.They host one (after percolation) in periphrastic constructions, but not in synthetic ones.In section 4, I present further advantages of this account observed in aspectual verb constructions in Ndebele.Before that, let me discuss the feature-percolation aspect of the proposal.
While the claim that ϕ-probes are introduced by verbs in Bantu is empirically supported, the feature-percolation aspect of the proposal requires additional discussion.Admittedly, the generalization that the number of agreement probes correlates with the number of verbs in derived by the Verb-origin approach without percolation.The reason for introducing feature percolation in the account is to integrate the V-origin approach with well established theoretical claims about ϕ-agreement.
Let us look at a simple tense, with a single subject agreement probe.If that agreement is morphologically realized on the verb, what is the motivation for locating the feature on a higher head (T/Infl)?One reason has been the observation that in English (and some other languages that informed the first proposals in syntactic theory), tense and agreement are related: tensed (finite) clauses show subject agreement, while tenseless ones do not.This correlation is, however, absent in Bantu languages, where full subject agreement is found irrespective of the presence of tense features. 6Another, theoretical, motivation for relating agreement and T is the proposal that T is a nominative case assigner, and case and agreement are outcomes of the same syntactic relation (George & Kornfilt, 1981;Chomsky, 2000Chomsky, , 2001)).Under this hypothesis, if the subject is assigned nominative case by T, ϕ-agreement must be a relation between the subject and T, as well.However, the hypothesized case-agreement relation does not stand crosslinguistic scrutiny, as argued in Preminger (2011Preminger ( , 2014)); Kornfilt & Preminger (2015); Levin & Preminger (2015) and specifically for Bantu in Carstens (2001).And even if true otherwise, it is far from obvious that the case-agreement relation would be of relevance for Bantu languages, in which case phenomena are systematically absent, both morphologically and syntactically (Carstens, 2001(Carstens, , 2005;;Baker, 2008;Diercks, 2012). 7onetheless, there are reasons to think that, even in Bantu languages, subject agreement probes are higher than the verbs introducing them.The first motivation for this claim is maintaining a principled mapping between structural order of heads and affix order.Prefixal material in Bantu languages reflects the syntactic structure directly (rather than in the mirror order), i.e. object agreement follows an aspectual prefix, which in turn follows the tense marker.Subject agreement prefixes are typically the leftmost prefix, suggesting the probe is at least as high as T. Second, a theory in which subject agreement is a relation between the subject DP and the verb itself would require a radical reformulation of locality constraints on agreement.Whether such reformulation would indeed be possible also not obvious.For instance, agreement between V and a transitive subject would require a directionality constraint on Agree according to which the verb may agree only with a c-commanding DP, not with a c-commanded DP (to prevent agreement with the object instead).While upward directionality of Agree has been proposed for Bantu languages (Baker, 2008;Carstens, 2005, a.o.), such a theory would incorrectly predict intervention by applied objects, which, as schematized in ( 18), a more local agreement goal to V than an external argument.( 18) In the absence of such upward intervention effects, parametrizing directionality of Agree does not solve the locality problem.On the other hand, the attested locality effects of subject agreement follow from Relativized Minimality (Rizzi, 1990) if the probe is in T (or some other position that c-commands all arguments).In summary, this section presented a Verb-origin account of the distribution of subject agreement probe is the Bantu clause, according to which ϕ-probes are introduced in the structure by verbal elements (lexical and auxiliary verbs).The main argument for this claim was a direct correlation between the number of ϕ-probes and the number of verbs.Crucially, this correlation which cannot be derived by the alternative Infl-origin approach, according to which ϕ-probes are properties of particular functional heads, due to the lack of consistent association of such heads with ϕ-probes.In the next section, I discuss further instances of variable and apparently inconsistent positions of ϕ-probes in aspectual verb constructions in Ndebele, and show that the proposed account derives them without further modifications.
4. Variable ϕ-probe positions in aspectual verb constructions.In addition to the default auxiliaray be (used in compound tenses), Ndebele makes use of auxiliary verbs with specific aspectual meanings (corresponding to adverbs in Indo-European languages).I will show in this section that aspectual auxiliaries, like default auxiliaries and lexical verbs, introduce a ϕ-probe, giving rise to multiple agreement markers in aspectual verb constructions.
Ndebele has only a handful of aspectual auxiliaries (Pietraszko, 2017).Here, I will use two of them as examples: the auxiliaries se 'already' ( 19) and lokhe 'still' (20).I analyze aspectual auxiliaries such as lokhe and se as functional verbs in the sense of (Cinque, 1999, et.seq.) (see also Wurmbrand (2004); Grano (2012); Pietraszko (2017)) -they are verbal elements occupying functional positions in the clausal spine.Functional heads realized by functional verbs (rather than affixes) have an iV feature, instead of the usual uV feature.Following previous work, I assume that the auxiliary se 'already' is a realization of Asp Perf (cf.Cinque's hypothesis that the adverb 'already' is a specifier of the perfect aspect head), while the auxiliary lokhe 'still' occupies the Asp Prog position (some evidence will be given below; for full argumentation see Pietraszko (2017)).Furthermore, note that the form of the the main verb covaries with the aspectual auxiliary: the complement of the progressive auxiliary lokhe is a progressive participle (19), while the complement of the perfect auxiliary se is a perfect participle (20).I adopt the analysis of this dependency as assignment of inflectional features by the functional verb to the lexical verb, as shown in (21) (Adger, 2003;Wurmbrand, 2011;Bjorkman, 2011;Pietraszko, 2017).
Perf A characteristic property of functional verbs is that they occupy fixed positions in the clausal spine, which in turn is determined by a (possibly universal) functional hierarchy.While the uni-versality of Cinque's hierarchy remains controversial, there is strong crosslinguistic evidence for the relative order of the perfect aspect and progressive aspect: the progressive is a lower inflectional category than the perfect (Iatridou et al., 2003;Pancheva, 2003;Harwood, 2013Harwood, , 2014;;Ramchand & Svenonius, 2014;Aelbrecht & Harwood, 2015).The perfect auxiliary se is thus predicted to precede the progressive auxiliary lokhe when the two cooccur ( 22).As we see in (23), this is indeed the case.Let us move on to the distribution of agreement probes in aspectual verb constructions.The observation is that, just like in compound tenses, there is full agreement on every verbal element.Like in Swahili, T appears to always be an agreeing head, as evident from simple tenses (without a specific aspectual inflection) (24).Consider now the appearance of a progressive auxiliary in a present tense clause, as in (25), where both the aspectual auxiliary and the main verb show ϕ-agreement.The aspectual auxiliary is located in Asp Prog and the agreement prefix on it is likely the realization of the probe on T. The ϕprobe on the main verb must, then, correspond to some lower head, such as Voice.The Infl-origin approach requires a postulation of a ϕ-probe on Voice in Ndebele, in addition to a ϕ-probe on T, in order to account for the distribution of agreements in this construction (25).

T Pres ϕ
However, Voice is not systematically a ϕ-probe bearer in the language.We've seen that in the absence of the aspectual auxiliary, i.e. in simple present, Voice does not host an independent agree-T would form a V-chain with the main verb, whose ϕ-probe would then percolate all the way to T, instead of Voice.This is precisely the case in simple tenses.We thus derive the apparent inconsistent association of Voice with a ϕ-probe in Ndebele.
Finally, the present account predicts a ϕ-probe on Asp Prog exactly in the contexts in which the immediately c-commanding head is a verb, as in ( 26).This structure contains three verbal elements: the main verb and two aspectual auxiliaries (28).The higher auxiliary is the closest iV goal for checking by T, forming the V-chain T,V-Aux(se) , while the uV on Voice is checked against the lexical verb, forming the V-chain Voice,V .The intermediate verb in Asp Prog is in a position where it is not targeted by uV-probing, and so it forms a trivial, one-head, chain by itself.After feature percolation, the ϕ-probes introduced by each verb end up on the highest head of their respective V-chains, deriving agreement on Voice, Asp Prog and T.
The derivation of ( 26) Asp [iV,ϕ] lokhe The complex aspectual verb constructions reveal even more clearly the inadequacy the Infl-origin approach to subject agreement probes in Bantu languages.This type of approach needs to stipulate i) two incarnations of the relevant functional heads (with and without a ϕ-probe) and ii) the syntactic contexts in which these incarnations appear.Such stipulations would need to be reproduced every time we discover a new functional auxiliary or a combination of auxiliaries.Unlike the account proposed in this paper, the Infl-origin approach makes no predictions about the distribution of agreement probes, entirely missing the generalization that an agreement prefix occurs on the highest head of every head-chain containing a verb.
5. Other existing accounts.In this section, I briefly discuss some other exiting accounts of multiple agreement in Bantu.It is often assumed that the subject agreement prefix in Bantu heads its own phase, AgrP, projected above TP.In multi-verb constructions, the clausal structure would then contain lower instances of AgrP, projected from heads like Asp in compound tenses etc.That is, instead of analyzing ϕ-probes as properties of some functional heads, the AgrP view treats them as immediately projected from these heads.As such, this account does not solve the problem of inconsistent association of functional heads with ϕ-probes.The burden of explana-tion would simply be shifted to deriving the correct distribution of AgrPs in various constructions.For instance, it would need to account for why AspP projects AgrP in (28) but not in (27).
According to another analysis of multiple agreement in Bantu, proposed by Henderson (2006), there is only one subject agreement probe in the clause, on T. Agreement prefixes on the lower verbs arise due to ϕ-concord -copying of ϕ-features from T onto lower concord bearing elements (roughly, verbs).The key to explanation lies in the precise definition of a concord bearing element.Quite clearly, the affix is not copied onto V itself as it may be separated from the verb stem by higher inflectional morphology (as in perfect participles in Swahili, for instance).Thus, a precise implementation of the concord analysis requires making reference to particular functional heads which in some contexts (but not in others) copy the ϕ-features from T. The characterization of these context would ultimately reduce to counting verbal elements in the clause.
Finally, Baker & Willie (2010) propose that, in Ibibio, every functional head in the clause comes with a subject-agreement probe.This is evident from multiple exponents of subject agreement in simple tenses (with only one verb).Even so, not every functional head is preceded by an agreement prefix, which Baker & Willie (2010) claim is due to phonological processes.It appears, however, that this interesting pattern of multiple agreement in Ibibio is not replicated in Bantu languages.Recall the adverbial meaning 'still' expressed in Ndebele by the progressive auxiliary lokhe.There is an option to express this same meaning by means of a prefix on the lexical verb (29).Crucially, when Asp Prog is realized as a functional verb, a lower agreement prefix is required, whereas its non-verbal incarnation precludes the extra agreement (29-b).It is unclear how this contrast would be derived under Baker & Willie's idea that every head comes with a ϕ-probe -here, we see the same head appearing with a ϕ-probe inconsistently.This is exactly the pattern expected under the present account: unlike (29-a), (29-b) contains only one iV, therefore all functional heads form a V-chain with the lexical verb, resulting in a single ϕprobe in T. Note that the ban on the lower agreement prefix in (29-b) is not a phonological confound.The same string is grammatical in that position if it is an object marker (30).
(30) Ba-∅-sa-ngi-bona.3pl-PRES-still-1sg.o-see'They are still looking at me' Finally, let me point out that the present account is compatible with the view that only one of the probes agrees with the subject DP, while the lower heads agree with T itself (Bhatt, 2005;Baker & Willie, 2010), instead of entering an independent Agree relations with the subject (Kinyalolo, 1991;Carstens, 2001;Baker, 2008, a.o.).

Conclusion.
I argued that complete severing of ϕ-probes from the verb, as in the Infl-origin approach, fails to capture their distribution in the Bantu clause, due to inconsistent association of functional heads with ϕ-probes.I proposed that ϕ-probes are not a property of individual functional heads, but rather of V-chains, which comprise a verb and a sequence of functional heads.
The size of a V-chain may vary, depending on the syntactic context, in particular, on the number and positions of auxiliary verbs.While the number of ϕ-probes is determined by the number of verbs, their exact probing position is determined derivationally, via feature percolation to the highest head of the chain.Unlike the Infl-origin approach, this account derives the attested variability of ϕ-probe positions in the Bantu clause, observed in compound tenses and aspectual verb constructions. 3 Ngi-∅-za-pheka.1sg-PRES-PROSP-cook 'I am going to cook' Present Prospective b.Ngi-a-ye 1sg-PST-AUX ngi-za-pheka.1sg-PROSP-cook 'I was going to cook' 5 Asp Perf se 'already' [ Asp Prog lokhe 'still' [ Voice ... ]]]] /u-phekile.2sg-cook.PROG/2sg-cook.PERF s *lokhe < se