Based on the above definition of MS, which is a general algorithm incorporated in both Agree and Labeling, Ke (2019, to appear[a]) gives an MS-based definition for Agree (MS-Agree):

Below, I give an example to illustrate the implementation of MS-Agree. Be in (5) can agree with a man, or more accurately, the determiner a, the head of a man. This is a case of long-distance agreement.6 The steps of MS-Agree are shown in (6).

A few notes should in place before we move on. (i) MS as a general SA defined in (3) always searches downward, and never searches upward. (ii) MS-Agree is split into two components, MS and valuation. This split can also be found in a broad ranges of previous studies, including Arregi & Nevins (2012), Bhatt & Walkow (2013), Deal (2015), Smith (2017), Kučerová (2018), and Bjorkman & Zeijlstra (2019). It is worth mentioning that this split is adopted here not due to a stipulation. Instead, it is a natural consequence of the MS defined in (3), as there is no principled way for a search algorithm to do the job of valuation. (iii) MS-Agree determines which syntactic object will be returned by the search algorithm, but it does not determine which syntactic object will undergo movement to the specifier position of the probing head (Bobaljik & Wurmbrand 2005), consistent with Chomsky’s (2015) Labeling-based account of movement. (iv) The SD and ST in MS for Agree are independently assigned by Agree (Ke to appear(a)), and this is a unique feature of the definition of MS. Previous definitions of Agree do not provide this option of assigning the values of the SD and ST; however, this is now a natural consequence of the SA: a SA must have the information of what to search for and which domain to search into, although the ST and SD may not be explicitly defined in a relevant theory. The ST is the unvalued feature (uFs) on a head that triggers MS. MS-Agree then is to look for a head with the ST inside the SD. Crucially, it is this unique feature that the SD and ST are independently assigned by Agree, together with other assumptions, enables us to analyze apparent upward agreement as downward MS-based Agree. Below I would like to explain how the SD and ST are determined for MS-Agree. In brief, I assume that the sister of the trigger will by default be taken as the SD. When the search into this SD fails, then the next built phase above the trigger could be taken as the new SD, a pattern that has been observed in cyclic agreement (Béjar & Rezac 2009) and the Delayed Valuation analysis (Carstens 2016).

The SD of MS for Agree is determined in accordance with the purpose of Agree. Agree connects two heads, one carrying unvalued features and the other carrying matching valued features. In order for two heads in an agreement relation to be connected to each other syntactically, they must form a syntactic relation at a certain stage of derivation. That is, they must be contained in the same root set or under a single node in a syntactic tree at a certain stage of derivation. Given a head X with an unvalued feature uF, represented as X_[uF], in order to value the uF on X by another head Y with a corresponding valued feature vF, represented as Y_[vF], there are three logically possible situations for X to be connected to Y at a certain point of the derivation, with regard to the c-command relations between X and Y:

All three options are utilized in natural language. Downward (long-distance) Agree, e.g., where the matrix verb agrees with an embedded nominal for noun classes in Tsez (Polinsky & Potsdam 2001) is an instance of (7a). Upward Agree in negative concord (Zeijlstra 2012), inflection doubling/parasitic participles (Wurmbrand 2012a) and multiple case licensing (Hiraiwa 2001) are instances of (7b). And Ke (2019, ch. 3) argues that reflexive binding is an instance of (7c).7 Due to space limitations, we will set (7c) aside for the discussion below.

Regular downward Agree in (7a) such as long-distance Agree in Tsez observed by Polinsky & Potsdam (2001) composes a strong argument for downward Agree. MS-Agree, building upon a downward search algorithm, can easily implement downward agreement. The searching of the target which is buried deep in the root structure can be accomplished by MS-Agree in a way similar to what we have seen in the there-construction in (5). What is potentially challenging for MS-Agree are cases of upward agreement in (7b) that provide crucial support for an Upward Agree analysis. Below I will provide an analysis of apparent upward agreement as a special case of downward MS-Agree.

We have mentioned that there are three logically possible configurations in which a head X with an unvalued feature can be related to and agree with another head Y with a corresponding valued feature, as listed in (7), and the focus of this paper would be the second configuration based on which Upward Agree is proposed. The structure of the second configuration is shown in (8) (The dots in the tree diagram indicate optional additional structure):

The upward agreement configuration in (8) does raise a problem to the classical probing-based Agree operation. We have mentioned that negative concord, inflection doubling/parasitic participle, and Multiple Agree as instances of the upward agreement configuration in (8) provide strong evidence for the existence of Upward Agree. To illustrate, below I quote one example from each of these constructions, which is coupled with a corresponding syntactic analysis.8 Let us start with negative concord in Czech.

Zeijlstra (2004) assumes that n-words must be licensed by or agree with an element bearing an [ineg] feature. This element could be the negative marker ne (the first analysis in (9b)) or a null negative operator Op (the second analysis in (9b)), the latter of which bears an [ineg] feature and is projected at a position higher than TP. If the first analysis in (9b) is adopted, Upward Agree is needed to value the unvalued feature on the object nikomu, as the object is c-commanded by, not c-commands, ne (or nevolá), which bears an [ineg] feature. On the other hand, if we adopt the second analysis in (9b), all the syntactic objects bearing the [uneg] are c-commanded by the null negative operator with [ineg]. Classical probing-based Agree as defined in (1) cannot be applied to check these [uneg] features, thus calling for an alternative analysis, e.g., Upward Agree.

Zeijlstra (2012) defines Upward Agree as in (10).

I would like to briefly note that according to (10c), in the configuration where there are two c-commanding syntactic objects carrying matching interpretable features, α will agree with the one closer to it, causing an intervention/blocking effect to the structurally higher candidate. I will return to this point in Section 5 and show that this leads to incorrect empirical predictions.

Inflection doubling (parasitic participles) also calls for an analysis along the lines of Upward Agree. Wurmbrand (2012a) encodes morphological selection (e.g., a modal selects an infinitive verb) as feature agreement. She calls this type of feature agreement “Reverse Agree,” which shares with Zeijlstra’s (2012) Upward Agree analysis in its core assumption of upward probing direction. In the following example from Swedish, the parasitic participles are in boldface, and the auxiliaries that license the parasitic participles are underlined.

Wurmbrand (2012a) assumes that semantically vacuous parasitic participles carry an uninterpretable feature. Since a c-commanding auxiliary can function as a licenser, Wurmbrand (2012a) suggests that the auxiliary carries a corresponding interpretable feature that agrees with the parasitic participle it licenses. This is hence another case to which Reverse Agree/Upward Agree does provide an appealing analysis.

Let us now consider another case which has been previously suggested to be an instance of Upward Agree: multiple case licensing in Japanese. (12) illustrates that in Japanese raising-to-subject constructions, multiple DPs can be marked as nominative within an infinitival embedded clause.

If we assume that (i) nominative case assignment from the T head to the DPs in (12) is accomplished via agreement, (ii) T bears a valued [vCase] feature that is responsible for case assignment, and (iii) all DPs carrying unvalued [uCase] features must be valued by agreeing with T, (12) presents a problem to the standard probing-based Agree. The problem is that the DPs with the unvalued [uCase] feature do not c-command the T head which bears the valued [vCase] feature. To address this problem, one must stipulate that there is some unvalued feature on T, other than the case feature, that triggers the downward search aiming for DPs bearing corresponding valued features, and then case assignment is just a free rider of the agreement relation that has been established. One such choice is to assume that the unvalued ϕ-features on T initiate the search for DPs with corresponding valued ϕ-features, and agreement and case are just two sides of the same coin (e.g., Chomsky 1995). However, this analysis encounters a different problem. If Agree is defined as in (1), we would expect that probing will be terminated as soon as a DP with matching valued ϕ-features is found (due to the “closest c-command” requirement). The consequence is that T in (12) will probe for and agree with the subject DP only (as in the instances where only the subject acquires the nominative case), and therefore can assign case to that DP only. In other words, an intervention effect caused by the subject DP is predicted. Contrary to this prediction, no such intervention effects are observed in (12), because all the DPs are assigned case by the T head. As a result, Hiraiwa (2001) proposes the operation Multiple Agree, as defined in (13), to account for the absence of intervention effects in (12).

The Multiple Agree analysis assumes that the T head in multiple nominative case assignment bears a [+multiple] feature, and that this feature enables the probe to look for multiple matching goals that are locally available (see also Chomsky 2008: p. 142). Such an analysis therefore requires the T head to be ambiguous between either bearing a [+multiple] feature or not, depending on the construction.

To some extent, this approach, while empirically successful, requires ad hoc assumptions and cannot explain why Multiple Agree occurs. In addition, Multiple Agree introduces the concept of “simultaneity” in Agree, which is fundamentally incompatible with the idea of Minimal Search or probing that respect “closest c-command.” In contrast, an Upward Agree analysis of (12) does not need to assume simultaneity in Agree or to stipulate a T that bears a [+multiple] feature. This is because each DP carrying an unvalued case feature can independently search upward and agree with the valued case feature on T. No intervention effects are expected, in accordance with the data. Therefore, an Upward Agree seems simpler and less stipulative than the Multiple Agree analysis, as far as the multiple case-assignment in (12) is concerned.

In sum, we see that Upward Agree solves significant empirical problems faced by the classical probing-based Agree theory. It seems, Agree, at least in the cases discussed, should probe upward.

Aiming for an unified analysis of both upward and downward agreement, Bjorkman & Zeijlstra (2019) revise and extend this approach to regular long-distance downward agreement. The main modification is to split agreement to two components, checking via Upward Agree and feature valuation. Checking is exactly Upward Agree as defined previously by Zeijlstra (2012) shown in (10) above. It is to establish an accessibility relation between a c-commanding syntactic object with interpretable features and a c-commanded syntactic object with uninterpretable features. Accessibility established by Upward Agree is then a precondition for feature valuation, according to what I will call “Accessibility Condition”:

The Accessibility Condition in (14) suggests that as long as any uninterpretable feature of a syntactic object checks with a corresponding interpretable feature of another syntactic object, which puts these two syntactic objects in a checking relation, all the features on them are made accessible to each other for valuation purposes. This applies to all interpretable and uninterpretable features (as long as they have already been checked; see below).

However, the Accessibility Condition needs to work together with another hypothesis9:

Consequently, when a syntactic object α bearing uninterpretable feature uF1 checks with β bearing corresponding interpretable feature iF1, all the other features on α, for example, an interpretable feature iF2, could value corresponding uninterpretable features, uF2, on β, as long as uF2 have been checked. Bjorkman & Zeijlstra (2019) further allow the valuation relations to be disassociated from the checking relations: if a uF on α fails to be valued by an iF on a c-commanding syntactic object β, it can be valued instead by a uF on another syntactic object γ that is c-commanded by α, as long as (14) and (15) are met. This theoretical design indicates that Bjorkman & Zeijlstra’s (2019) approach allows both downward and upward valuation (Preminger & Polinsky 2015). The mechanism that unifies various types of agreement, as claimed by Bjorkman & Zeijlstra (2019), is therefore not the valuation component, but the checking (via upward probing) component.

As noted, Bjorkman & Zeijlstra’s (2019) analysis has yielded attractive analyses of various phenomena and is certain to inspire valuable additional work. However, Preminger (2013) and Preminger & Polinsky (2015) have discussed at length that this approach as a hybrid approach that resorts to both downward valuation and upward valuation is not successful in accounting for ϕ-agreement in general. Recently, Rudnev (2021) also provides empirical arguments against various predictions of Bjorkman & Zeijlstra’s (2019) analysis of ϕ-agreement in ergative-absolutive languages. I will not restate these counter-arguments here. The focus of this paper is instead to discuss a critical component of Bjorkman & Zeijlstra’s (2019) analysis that was rarely put under careful scrutiny: the probing direction. It is also worth noting that the direction of probing/checking is probably even more crucial than the direction of valuation, from the perspective of the system itself. This is because as long as checking relations could be established, valuation is simply making use of these checking relations, whatever direction of “feature transmission” it is. In fact, feature valuation is just feature copying between parts of a syntactic structure: feature valuation can function without the involvement of any concept of syntactic structural relations such as c-command relations. This is also consistent with the idea that feature valuation could be a non-syntactic operation or could occur not in syntax; instead, it could be in the postsyntactic morphology, a proposal by Arregi & Nevins (2012) that Bjorkman & Zeijlstra (2019) parallel their approach to in terms of the valuation component. Indeed, the original empirical data that have motivated Bjorkman & Zeijlstra’s (2019) system is exactly the checking/Upward Agree component, not the valuation component, as previously reviewed.

For inflection doubling and multiple case licensing, as indicated by the syntactic representations in the (b) part of examples in (11) and (12), these attested cases of Upward Agree are all phase-constrained. That is, the same minimal phase (the CPs in the examples) dominates both the valuee carrying the unvalued features and the valuer bearing the corresponding valued features. This gives us a hint on how to model these cases of Upward Agree with MS-Agree. As a reminder, the ST and SD for MS-Agree can be independently assigned. The ST will be the feature attributes of any features that trigger MS; for example, they could be ϕ-features for ϕ-agreement, Q-feature for questions, and Neg-feature for negative concord. The SD is usually the sister/co-member of the trigger. What are other possible SDs that can be determined in a principled way? Due to the fact that all the Upward Agree cases listed in (9) to (12) are generally phase-constrained, if MS can have the CP phase as the SD and searches downward from it, then we obtain the desired results.

For the negative concord in Czech (9a), with the first alternative analysis in (9b) provided by Zeijlstra (2012), only the object nikomu is involved in upward agreement. Depending on whether NegP is a part of the vP phase, the reanalysis of this case of upward agreement with MS-Agree will be slightly different. If NegP belongs to the vP phase (cf. Akahane 2006), the phase immediately above the object is NegP. To value the [uNeg] feature on the object nikomu, MS-Agree will take NegP as the SD and search down from there. The negative marker ne, bearing a matching [vNeg] feature, will be correctly returned. On the other hand, if NegP is assumed to be part of the CP phase (cf. Butler 2004), MS-Agree can be initiated when the vP phase is built but it fails to return a target. The derivation may proceed until the CP phase is built, which is allowed under Chomsky’s (2001) theory of Transfer: Tranfer of the current phase occurs after a higher phase is built. MS for Agree purposes can be initiated as long as unvalued features are not transferred, and the timing of Transfer is determined by Chomsky’s (2001) theory of Transfer (see also Footnote 13). Then another instance of MS with the CP as its SD will be initiated, returning the negative marker ne, as desired.10

With the second alternative analysis in (9b), the [uNeg] feature on the subject and the negative marker ne can be valued by conducting two independent searches probing downward from the CP phase. For the [uNeg] feature on the object, an analysis along the same lines as that for the object under the first alternative analysis can be provided: an MS taking the CP phase as the SD will find the negative operator below CP and successfully establish an agreement relation between the object and the negative operator.11

More generally, I assume that in the above cases of Upward Agree, the SD is not the sister/co-member of the valuee. By contrast, if we still want to find the valuer by downward search, the SD in cases of Upward Agree must be sets that include the NegP/TP (in 9), the AuxP (in 11), and the TP (in 12). Therefore, as long as these examples are concerned, it could be either the vP or CP that is assigned as the SD of MS for these cases.12 MS then searches downward until the head with the ST is found.

We have seen that taking vP and CP as the SD can give us a sound empirical account for the attested upward agreement phenomena reviewed above. An immediate question is whether there is a theoretical reason why vP and CP, rather than other syntactic objects, should be assigned as the SD of MS here. A reasonable conjecture is that generally, the phase status of vP and CP may be relevant. Again, I essentially adopt Chomsky’s (2001) theory of phases with a slight revision: vP and CP are phases, and the complement of the lower phase head is transferred when a higher phase is built.13 As a consequence of this theory of phases, if a valuee remains unvalued in the phase that is transferred, like in the apparent upward agreement cases, the valuee will be rendered inaccessible for future MS-Agree. This will either cause the derivation to crash or lead to agreement failures (Preminger 2014). Note that MS is not obligatorily initiated to save the unvalued features from being transferred. Instead, the idea is that if the unvalued features are to be valued, the point when they are to be transferred is the last chance for MS to be initiated to value them. To put it another way, in order to value unvalued features (which is not obligatory), MS must be applied to find a target in the currently built root structure, which is a phase. The [uneg], the unvalued feature associated with the participle morpheme, and the unvalued feature connected to the nominative case morpheme are all uninterpretable to the interfaces. Therefore, MS takes the next higher phase dominating the valuee and looks for a valuer. This is the last chance for the unvalued features to be valued by a valuer if the valuee is inside the Transfer domain, i.e., the lower phase head complement. What if an unvalued feature is located in the edge of the lower phase, and thus it will not be transferred until the next two higher phases (instead of the next higher phase) are built? The assumption is, as a general mechanism, MS should be triggered when the next higher phase is built. The advantage of this approach is that MS then can be blind to, and not be complicated by, the specific syntactic position of its trigger.14

Another question that is relevant here is: why not initiate MS after each application of Merge above the syntactic object with unvalued features? This will be in effect making the analysis similar to Upward Agree. There are two reasons speaking against this option. Firstly, such approach will always return a c-commanding target closer to the trigger, and thus predict an intervention effect caused by a closer target to all other competing targets higher up. This prediction concerning intervention effects is the same as that of Upward Agree. Empirical counter-evidence will be discussed in the next two sections. Secondly, from the theoretical perspective, such an approach will result in an inefficient mechanism, as it requires MS to be initiated frequently, and most of the searches will fail without returning a target.

If the phase status of vP and CP is relevant here, given that the heads with unvalued features are in the c-command domain of the valuers, we can formalize the locality constraint in upward agreement by assuming that the next built phase as the root structure is taken as the SD for the relevant MS, with additional constraints imposed by Chomsky’s (2001) theory of phases:

With the assumption in (16), the cases of upward agreement can be perfectly captured by MS-Agree, as discussed above. Likewise, in (11), the unvalued feature on the verb bearing the parasitic participle can be valued by the auxiliary hade ‘had’ by downward searching from the CP. For multiple case assignment in Japanese (12), the unvalued case feature on the DPs can also be valued by the T head through multiple independent searches with SD = CP. Note that under the current analysis, multiple case assignment in Japanese does not require a [+multiple] feature or resort to a simultaneity approach in probing; instead, each instance of case assignment will be implemented by an MS searching downward from the next higher phase.

Therefore, MS-Agree which employs a downward search algorithm provides neat solutions to apparent cases of Upward Agree, with the assumption in (16).16 This gives rise to an important question: since these cases of upward agreement are not standard ϕ-features, should they be treated as non-syntactic concord and thus be treated differently from regular ϕ-feature agreement? If this is the case, then we should not try to account for upward agreement and downward agreement with a single mechanism, and it is even misleading to do so (Preminger & Polinsky 2015). Bjorkman & Zeijlstra (2019) address this question by pointing out that treating concord phenomena such as negative concord and inflection doubling as non-syntactic would fail to explain their locality constraints. If these phenomena are syntactic in nature, then there is no reason in principle why these phenomena of concord should be treated separately from ϕ-feature agreement.

To provide an even stronger argument, however, I will discuss in the next two sections cases where upward ϕ-feature agreement is detected. The discussion of cyclic agreement will help us refine the current MS-Agree analysis by specifying the timing of search into the sister of the trigger or the next higher phase. A principled mechanism will be developed to determine when the sister of the trigger or the next higher phase must be taken as the SD: MS will always start from taking the sister of the trigger as the SD; only when the search fails, MS will take the next built phase above the trigger as its SD and search into it (see Section 4). This will address the question as to when and why MS searches into the next built phase, further validating the assumption in (16). Additionally, the discussion of complementizer agreement in Lubukusu will shed light on a critical empirical diagnostic that can tease apart the predictions of MS-Agree and Upward Agree. Overall, I argue that MS-Agree with the assumption in (16) also offers a neat and simple analysis to upward ϕ-feature agreement, in addition to instances of concord. These upward ϕ-feature agreement phenomena, however, cannot be fully captured by the Upward Agree analysis.

A phenomenon that is critical to the current purpose is the subject–complementizer (S–C) ϕ-feature agreement in Lubukusu, a Bantu language. S–C agreement in Lubukusu is pertinent to the current discussion because it is, at least appears to be, an instance of long-distance upward agreement. As Preminger & Polinsky (2015) point out, the most convincing evidence for upward (ϕ-feature) Agree is long-distance Upward Agree21 that crosses a finite TP (or a CP) clause boundary, which generally excludes covert movement; namely, a head with unvalued features triggers agreement with a target in a higher TP where the target receives its case or θ-role. This is because, due to derivational opacity (the derivational history cannot always be known), we can neither justify nor falsify Upward Agree if at least in some circumstances there is covert movement of the trigger to a higher position c-commanding the target; it is also quite unlikely that we can completely exclude the possibility that the target is in fact raised from a lower position c-commanded by the trigger in an earlier derivation stage. In both of these cases, the trigger c-commands the target at certain point of the derivation, an agreement pattern that can be handled with downward Agree. However, with long-distance Upward Agree, covert movement of the trigger that crosses a finite TP, as an instance of head movement, is widely considered unlikely. Raising of the target to a position in a higher TP where it receives its case or θ-role, as an instance of A-movement, cannot be easily justified either. Therefore, long-distance Upward Agree cannot be readily formalized as instances of downward Agree, and thus it is strongly in favor of Upward Agree.

More importantly, as we have mentioned in the discussion of cyclic agreement, local Upward Agree can usually be captured by the Spec–head relation, which can in turn be formalized as downward Agree if Chomsky’s (1995, 2000) Labeling Theory or a theory of projection is assumed, although we have argued that these assumptions complicate and are not well compatible with the more recent formalization of the Labeling Theory (Chomsky 2013, 2015).

Unfortunately, examples of long-distance Upward Agree are extremely rare in the literature. Preminger & Polinsky (2015) thus take it as an unattested agreement pattern in human languages.

However, at least at the surface form, S–C agreement in Lubukusu is an instance of long-distance upward agreement, as the embedded C head agrees with the immediately superordinate subject. Preminger & Polinsky (2015) are aware of this type of upward agreement, but following some previous analyses of S–C agreement in Lubukusu, e.g., Diercks (2013), they assume that S–C agreement in Lubukusu can be successfully explained by an analysis that does not resort to Upward Agree. I argue below that such an non-Agree analysis encounters many difficulties and is not tenable; on the other hand, MS-Agree gives us a much simpler analysis that is free of these problems. More important, S–C agreement provides a testing ground for MS-Agree versus Upward Agree.

Diercks (2013) argues convincingly that in Lubukusu an embedded C agrees only with the subject, not the object, of the immediately superordinate clause in full ϕ-agreement, in terms of noun class agreement. Exemplified in (27), the embedded C head -li agrees with the matrix subject (ba-ba-)ndu, rather than with the object Alfredi, although the latter is structurally closer to the embedded C.

Further evidence shows that (27) is not a surface reflection of an agreement between the logophoric center of the embedded CP (i.e., the “source,” see Sells 1987) and the lower C. (28a) indicates that a non-logophor subject can agree with the lower C head; on the other hand, (28b) suggests that the non-subject logophor, Sammy, cannot trigger agreement with the lower C. Token together, it is clear that the subject of the higher clause rather than the logophor of the embedded CP agrees with the C head in the lower CP.

It should also be noted that S–C agreement is subject to locality constraints. A C head must agree with a subject that is right in the immediately superordinate clause, not with subjects in any higher clause, as illustrated by (29).

Diercks (2013) claims that such subject-orientation in Agree in examples such as (27) can be explained if we assume a null operator in SpecCP which agrees with C -li through a Spec–head relation. This null operator is a subject-oriented anaphor, akin to the reflexive clitic se in French (Safir 2004). This reflexive raises to adjoin to a higher T where it is bound by the matrix subject (cf. Chomsky 1986), as shown below:

This analysis correctly captures the lack of intervention effects with regard to the object Alfredi. However, a potential drawback of Diercks’s analysis is that a null reflexive is positioned in every embedded CP that agrees, yet they make no semantic (or phonological) contribution to their local CP. As acknowledged by Diercks (2010), these reflexive operators are not logophors or elements that are related to any thematic roles, and they receive no identifiable thematic interpretation themselves. To make their status even more dubious, the null reflexives are required to undergo covert movement to the T head in the superordinate clause, which is a crucial aspect of the analysis to account for the subject-orientation effects in S–C agreement, but this assumption is essentially unfalsifiable, as it is a null element going through a covert movement.

There are still other drawbacks of Diercks’s (2013) analysis. Diercks has to assume two distinct agreement relations, a subject–reflexive and a null reflexive–C dependency. The subject–reflexive binding dependency has been argued not to be a primitive operation, but one that is reducible to Agree (e.g., Hicks 2009 and Reuland 2011; see Ke 2019 ch. 3 for a review of various approaches to reduce reflexive binding to Agree). An alternative analysis that can directly analyze S–C agreement as a case of Agree is thus simpler (and preferable). In addition, the null reflexive-C agreement requires the reflexive to be involved in ϕ-feature agreement, an agreement that has been shown to be impossible or unattested (so called “anaphor (anti-)agreement effects,” cf. Preminger 2018, Rizzi 1990; Woolford 1999; but see Rudnev 2020 for arguments of an exceptional case of agreeing anaphors).

The above problems can be avoided if we assume a direct agreement relation between C and the superordinate subject. With a direct Agree analysis, we do not need to assume a null reflexive, a hypothesis that does not have empirical basis. The analysis is therefore significantly simplified. In fact, Diercks (2010) considered such a possibility. Nevertheless, Diercks (2010) ends up not adopting a direct Agree analysis, mainly due to the lack of intervention effects when there is an indirect object intervening between the agreeing subject and C. (27), repeated below in (31a), shows that the indirect object ‘Alfred’ cannot agree with the embedded C. (31b) is a sketch of the relevant aspect of the structure of (31a).

This is a problem if we assume Upward Agree (e.g., Zeijlstra 2012; Bjorkman & Zeijlstra 2019), which Diercks (2010) does. An Upward Agree analysis will incorrectly predict that in (31), the embedded C must agree with the object, which is structurally closer than the subject to the embedded C. However, if we adopt MS-Agree instead of the Upward Agree approach, this major obstacle for the direct Agree analysis is naturally removed. With the MS-Agree analysis, we no longer predict an intervention effect caused by the indirect object, as MS starts its search from the next higher phase, namely, the vP in (31b), and the vP-internal subject rather than the indirect object is returned; that is, the search is top–down in the sense of tree representations.

In fact, I argue that “subject-orientation” in Lubukusu can in fact be derived by MS-Agree defined previously in (4) with an independently assigned SD, as in the second cycle of cyclic agreement (21). Instead of being mediated by a null reflexive, I assume that the embedded C can directly agree with the matrix subject if the next built phase is taken as the SD.

To make more concrete the MS-Agree account of subject-orientation in S–C agreement in Lubukusu, consider again the structure under discussion:

As a reminder, I assume that MS observes Chomsky’s (2001) Phase Impenetrability Condition; namely, a phase head complement is transferred and is not accessible to MS after a higher phase head enters the derivation. Therefore, when the matrix v head merges in, the complement of the embedded C will be transferred, indicated by the dots in (32). The lexical array for the matrix vP phase includes the vP-internal subject. Now the crucial step is: an MS is conducted with ST = [uϕ] and SD = the phase that is built so far, i.e., the matrix vP. This MS first finds the vP-internal subject ba-ba-ndu (more accurately its D head), which causes intervention to the object Alfredi. The subject-orientation phenomenon in Lubukusu is therefore explained: it is also a natural consequence of downward search from vP.

Taking the next built phase as the SD can derive all the cases of upward agreement we have discussed, including the subject-orientation effect in Lubukusu, and this is consistent with Carstens’s (2016) Delayed Valuation analysis for Lubukusu S–C agreement. In order to account for Diercks’s (2010, 2013) observation regarding S–C agreement in Lubukusu, Carstens (2016) proposes that the valuation of C can be delayed up to the point of cyclic Transfer, for example, when a higher phase head merges in. Delayed Valuation is initiated only when no target exists in the c-command domain of the trigger. The empirical examination of downward and upward agreement phenomena across languages in this paper supports this overall proposal.

However, a side effect of the Delayed Valuation approach is that it allows the indirect object in the superordinate clause above C to agree with C in Lubukusu S—C agreement, and thus would miss the subject-orientation effect if without an additional mechanism to preclude the indirect object from agreeing with C. Carstens (2016) therefore resorts to the activation condition to prevent the indirect object from agreeing with C: because the indirect object receives an inherent dative case, which renders it inactive and inert to agreement. Such an analysis then needs to explain that, in Lubukusu, (i) why dative DPs can be involved in an agreement relation in some other cases, and (ii) why a subject DP is not rendered inactive after it has been involved in an agreement relation with the C head in the subordinate clause and can still be involved in a ϕ-feature agreement relation with its local T head. Similarly, in West Germanic, the subject can agree with both the unvalued ϕ-features on its local T and C heads: an argument needs to be made to explain why subjects, which agree with T already, are not turned to be inactive but can further agree with C. Carstens’s (2016) solutions to both of these exceptional cases, although intriguing and having the potential to account for some other important phenomena, lead to considerable theoretical complications to the operation Agree (see Carsten 2016 Section 3.6 for relevant discussion). In principle, if the Delayed Valuation approach is adopted, whenever an intervention effect is observed, a reason has to be found in order to exclude from agreement a competing target which is either in the c-command domain of the probing head or in a higher phase but does not agree with it.

MS-Agree, however, makes a prediction different from Carsten’s Delayed Valuation approach. Subject-orientation in Lubukusu, which is due to the lack of intervention effect from the dative object, is a direct consequence of downward search: the higher target (the subject) is found by downward MS before the lower target (the object) is reached, not the other way around. In addition, MS-Agree accounts for intervention effects in downward and upward agreement with the same downward search algorithm, whereas the Delayed Valuation approach, on the one hand, will probably need to use downward search to derive intervention effects in downward agreement, and on the other hand, may resort to activation condition or other mechanisms to exclude any intervening potential candidates in upward agreement.

The differences between the MS-Agree analysis and another prominent analysis of S–C agreement in Lubukusu is also worth noting. Diercks, van Koppen & Putnam (2020) proposes that the agreeing C head, which bears interpretable but unvalued anaphoric features, moves to adjoin to a higher vP (see also Carstens 2016). This higher copy of C head (specifically Force⁰) will then probe for the subject in the superordinate vP. The lower copy of the C head, rather than the higher copy, is then spelled out (the valued features hence must pass down from the higher copy to the lower copy before the spelling-out). MS-Agree, on the other hand, distinguishes itself by not making such an assumption regarding the movement of the C head as an adjunct to the vP.

Note that in Lubukusu, only the second cycle MS-Agree, not the first cycle MS-Agree, is relevant. One may wonder why this is the case. A conjecture is, following Carstens (2016), the CP periphery in Lubukusu has the following structure, where Force, Interrogative (Int), and Finite (Fin) are phase heads (Rizzi 1997, 2001).

When the agreeing C_Force -li enters the derivation, FinP has been transferred, rendering the lower subject inaccessible for C_Force. Due to space limitations, interested readers are referred to Ke (2019: pp. 85–87) for relevant discussion on details of this hypothesized analysis and its potential alternatives.

To summarize, the current MS-Agree analysis of S–C agreement in Lubukusu does not assume (i) the existence of a null reflexive, nor (ii) covert movement of the null reflexive, nor (iii) agreement between the reflexive and the embedded C head. In short, it does not run into any of the problems that we identified above for Diercks’s (2013) indirect Agree analysis. In addition, compared to Diercks’s (2013) analysis, the current MS-Agree analysis is simpler and more intuitive, because now S–C agreement is established directly by MS-Agree, whereas Diercks needs to assume two distinct agreement relations, subject-reflexive and reflexive-C agreement.

We have seen that the MS-Agree analysis of S–C agreement in Lubukusu provides critical evidence for downward MS for Agree, which accurately capture the intervention effects caused by the structurally higher subject to the object. In this subsection, I will discuss two pieces of evidence for Upward Agree offered by Baker (2008), who proposes that both downward Agree and upward Agree exist in natural languages. I argue that closer scrutiny reveals a contradiction in the interpretation of the data regarding upward agreement.

Baker (2008) supported an Upward Agree analysis besides downward Agree based on ϕ-feature agreement on adjectives in Italian (examples are taken from Cinque 1990). The following example indicates that the structurally lower DP i sostenitori ‘the supporters,’ rather than the structurally higher DP, the null matrix subject, agrees with the adjective infelici ‘unhappy.’ The critical aspect of the structure is represented in (34b), where F_A is a functional agreeing head for predicative adjectives. In terms of (34b), F_A agrees with NP2 rather than NP1.

Note that Baker (2008) does not assume that NP2 is originally generated inside the AdjP in (34b) due to independent reasons. Therefore, F_A can only probe upward to agree with NP2. Apparently, NP2 seems to block agreement between NP1 and F_A because it intervenes between them, consistent with the prediction of intervention effects by an Upward Agree analysis.

In Footnote 21, Baker (2008) mentions another case in Icelandic to support this type of intervention effects. “[I]n the Icelandic version of ‘The women(nom) consider Mary(dat) to be cold,’ ‘cold’ must be default masculine singular, not feminine plural in agreement with ‘the women’ (Sigurðsson, personal communication).” (p. 48) This intervention effect even occurs when “the subject of its predication has quirky case and hence does not trigger agreement on the adjective itself.” (ibid.) It must be noted that what Icelandic reveals is not as predicted by Upward Agree. When the local subject of the adjective predication has quirky case, it should be inaccessible for agreement. Consequently, if Upward Agree is the operation involved. the quirky subject can no longer be an intervener; and this should render the higher, matrix (vP-internal) subject, ‘the women,’ available for agreement, unless the matrix subject is prevented from agreeing with F_A due to other reasons.

Indeed, Phase Theory may be the underlying mechanism that prohibits the matrix subject from agreeing with F_A. The idea is that F_A is a phase head, and it is transferred when a higher phase head, the matrix F_V, enters in the derivation. As a consequence, the matrix subject is no longer accessible to F_A as the latter has been transferred when the former enters the derivation. The same reasoning can also explain why in the Italian example (34), the matrix subject is not available for agreement with the embedded F_A. In sum, upon closer examination, previously acknowledged as intervention effects in support of Upward Agree may be a by-product of independent restrictions due to Phase Theory. Therefore, they do not constitute counterexamples to MS-Agree: MS-Agree, also constrained by the theory of phases, makes the same predictions as Upward Agree as far as these data are concerned.