On the computational modeling of English relative clauses

1 Introduction

Relative clauses have been the subject of much research in modern Generative Grammar.^[1] These constructions are of particular interest because the head noun of the relative clause appears to be doubly licensed. In (1)a, resp. (1)b, the relative clause head noun man appears to obtain both grammatical case and a theta-role in two distinct positions (assuming that there is only one head noun man); i.e., as an object (resp. subject) of the relative clause verb saw (resp. loves) and as an object of the matrix verb like.

Analyses of relative clauses in the Generative Grammar tradition have attempted to explain the structure of relative clauses and clarify how a relative N is licensed. Analyses can be loosely categorized into matching analyses, in which there are two separate relative nouns that have the same reference, and head promotion/raising analyses in which there is only one relative noun that undergoes movement. In an operator movement analysis, like that in (2)a (Chomsky 1977, Chomsky and Lasnik 1995), a relative operator is base generated in the relative clause and raises to the specifier of the CP. It then gets its interpretation by being associated with an external noun, expressed through coindexation here. In another account, shown in (2)b, there are two separate relative nouns that have the same reference, and the lower noun is deleted under identity (cf. Citko 2001). Both of these types of analyses in (2)a–b have been referred to as matching analyses, as there are two separate relative nouns. In a head promotion/raising account, the nominal head of a relative clause undergoes movement outside of the clause, as in (2)c (Brame 1968, Schachter 1973, Vergnaud 1974, Kayne 1994, Borsley 1997, Bianchi 2000, etc.). Unlike a matching analysis, there is only one relative noun which undergoes movement, and it is basically licensed in two positions.

The matching analysis does not face the problem of a single noun receiving case and a theta-role in two positions, as it makes use of separate but co-indexed nouns. On the other hand, a raising analysis does not require a separate matching/coindexation operation. A thorough comparison of the various approaches, and their variants, is beyond the scope of this article,^[2] but we adopt a version of the raising/promotion account in which new NPs with the same core noun lexeme can be formed through Internal Merge (IM), obviating the need for a separate matching operation. At the same time, we avoid the problem of a single noun receiving multiple theta-role and case assignments, through the use of separate D heads.

English relative clauses pose a non-trivial problem as they vary with respect to the content of the head and edge of the CP, as summarized in Table 1. None of the standard English relative clauses permit which/who that;^[3] there being a well-known ban on doubly filled COMP (cf. Chomsky and Lasnik 1977, among others). Object relatives permit an empty COMP (indicated by Ø), but subject-relative clauses do not.

This article presents a computational model of relative clauses based on linguistic proposals in the Minimalist Program (MP)^[4] framework (Chomsky 1995, 2001).^[5] We have a full computer implementation of the theory, verified across all core examples presented in this article.^[6] The detailed step-by-step derivations computed by the program are too lengthy for inclusion in the body of this article; they may be found in the online Appendix, thus permitting the reader to verify the accuracy of our claims.^[7] These derivations should also prove helpful to both linguists and engineers who wish to understand how the components of the theory interact in full detail. To our knowledge, this is the first computer implementation in the MP framework to accurately generate the complete set of basic subject and object English relative clause constructions, while also accounting for the usage of which, that, and who(m) in relative clauses.

2 The basic model

In this section, we briefly summarize the theoretical aspects underlying our account.

We implement a revised version of Gallego’s (2006) relative clause analysis, which builds on work by Pesetsky and Torrego (2001) (henceforth P&T). P&T propose that nominative case results from a checked uT feature (uT = uninterpretable T) on a head D. The head T locally c-commands the subject DP and checks the DP’s uT feature, resulting in nominative Case. Embedded C also possesses a uT feature, which can be checked in two ways. One way is by raising T to the edge of C and T checks the uT on C. An alternative way is by raising the subject DP to the edge of CP, in which case the already checked uT on D of the subject checks uT on C. When checked by T, the uT feature on embedded C is pronounced as that (e.g., Mary thinks that Sue will buy the book; P&T 2001, 373). When a nominative subject raises to the edge of CP to check the uT feature on C (e.g., Mary thinks Sue will buy the book), there is no pronunciation of that.

Although in principle, two methods for checking the uT feature on C are available, P&T utilize economy to account for that-trace effects and the English subject/object wh-movement asymmetry.^[22] In principle, multiple Agree operations are possible in this system. Abstractly, in (5)a, uF1 and uF2 on X are checked by Y and W, respectively. In (5)b, Z checks both uF1 and uF2 at once instead. Economy dictates that we prefer a single operation (over multiple operations) and, therefore, (5)b over (5)a.

Note that the preference for a single Agree relation over a multiple Agree relation does not make any predictions about the presence of that in cases where both are possible, as in (6)a. Note that P&T assume that in constructions in which there is wh-movement out of an embedded clause, there is a uWh feature in a non-interrogative C that hosts a wh-phrase. The uT feature on C can be checked by T, (6)b, in which case that is pronounced. The uT feature can also be checked by the subject, (6)c in which case that is not pronounced. Therefore, that is optional, and there is no preference for or against that.

Gallego extends P&T’s proposal to relative clauses, i.e., that that is the pronunciation of uT in C. In addition, Gallego assumes that a relative clause C has a uRel feature that is checked by a relative DP containing a corresponding iRel (i = interpretable) feature. Economy, following P&T, comes into play if both uT and uRel on C can be checked by a single goal. Gallego’s analysis is noteworthy in that it attempts to provide a unified account of relative clause formation and the distribution of which/who(m)/that/Ø.

According to Gallego, in (7)a, who man originates in the subject position of the clause, from where it moves to the relative CP edge, followed by further movement of man to a higher position in the CP. Assume the subject relative D who contains both an iRel feature and nominative case. Applying economy, who checks both uT and uRel on C via a single Agree relation, as shown in (7)b. There is no pronunciation of that crucially because who, not T, checks uT on C. Gallego proposes that uT and uRel have EPP subfeatures, a complication that we do not adopt and that forces who man to raise to the edge of the CP. Gallego also proposes that there is an extra projection, referred to as cP, in the left periphery that ‘introduces a subject of predication (Gallego 2006, 157)’. This c has uPhi features with EPP subfeatures. The uPhi probe for matching phi-features that are interpretable and the uPhi find iPhi on man in (7)a–b. The EPP sub-feature of uPhi forces man to raise to the edge of the cP. Example (7)a with that is blocked by economy: pronunciation of that would require uT on C to be checked by T, and uRel on C to be checked by who, separately. However, economy dictates who man checks both uT and uRel features on C simultaneously.

An issue is that Gallego’s analysis requires an extra cP projection in the left periphery. It is also not entirely clear why c can attract N from inside of a relative D and not the head of the DP itself, viz. D.

In (8)a, Gallego assumes the subject boy contains a null D and, following Chomsky (2001), that a null D must remain in situ. Furthermore, the uRel on C (conveniently) lacks an EPP sub-feature so that uRel on C is checked by iRel on null D without triggering movement. The uT’s EPP sub-feature then causes T to raise to C and be pronounced as that. (Note that this analysis also implies that the relative DP boy does not move to Spec-T either, as it has a null D.)

This analysis has two potential problems. First, it requires a stipulation that a relative DP with a null D cannot move. Furthermore, there is lexical proliferation for C containing uRel. As uRel typically has an EPP sub-feature, this must be modified for relatives containing a null D, as they do not move in Gallego’s account. Therefore, C with uRel must come in two versions: one with an EPP subfeature (as in (7)b) and one without an EPP sub-feature (as in (8)b).

Gallego’s analysis is also unable to account for the ill-formedness of (9)a; it has difficulty accounting for doubly filled Comp effects. As the structure (9)b indicates, T should be able to check uT on C, resulting in the pronunciation of that. Because the relative DP is an object, it does not have nominative case, and thus, it is unable to check uT on C. Hence, that must be pronounced, as in (9)a. But (9)a is ungrammatical in standard English.

We adopt a modified version of Gallego’s core proposals about uT feature checking on a relative C and about economy. While we follow Gallego’s insights regarding uT and uRel feature checking, we omit the extra cP projection and we do not utilize EPP subfeatures. We are able to account for the distribution of the relative D and a noun in the examples above, including the ban on *who that in (7). Also contrary to Gallego, we have no stipulation that a DP with a null D is unable to move. Our analysis, to be discussed below, is able to account for the ill-formedness of (9)a, and we also extend this analysis to account for headless relatives (which Gallego does not investigate) and genitive relatives, as well as other related relative clause types. Note that we assume the judgments of standard English about relative clauses; in particular, no doubly filled COMP. However, there are varieties of English that permit a doubly filled Comp, suggesting there may be some dialectical variation in whether or not a relative D can check a uT feature. We discuss this in detail in Section 5.

Suppose all relative D heads check a uRel feature. We assume there is variation in whether or not a relative D may also check a uT feature on C. When relative D can check both a uRel and uT feature, pronunciation of that (only when uT on C is checked by T) is blocked due to economy. Only when relative D is unable to check uT on C, then T can (raise and) check uT on C and that can be pronounced. Finally, we use an unvalued D feature to trigger extraction of the relative noun, termed “relabeling” in the study by Cecchetto and Donati (2015).

Consider sentence (10)a and its subject relative counterpart in (10)b.

(10)a has the core structure shown in Figure 1, typically assumed in Minimalist syntax.^[23] Root tell selects for an internal argument, the story, and transitive v* combines with the phrase headed by tell to form a basic verb phrase. Case-Agreement proceeds by minimal c-command. For example, v* c-commands and values accusative Case on the internal argument. v* also provides for an external argument (EA) position in its specifier, occupied by the boy. T_past selects for v*P and c-commands the EA, valuing nominative Case. In English, T_past also provides for a surface subject position that must be filled, the so-called EPP property. In Figure 1b, the boy raises to the edge of TP. Only the highest copy is pronounced, and unpronounced copies are indicated by strikethrough. As part of Case-Agreement, T_past picks up number and person feature values associated with the EA, resulting in English subject–verb agreement. The heads T_past, v*, and the root tell combine at Spellout to form told. (Note that we indicate C as c, C_rel as c_rel, and the relative determiner D_rel as d_rel in our diagrams.)

Figure 1

Example of syntactic structure for the boy told the story.

Example (10)b has the same underlying core as (10)a, with two crucial featural differences that will drive relativization. We assume rel to be a formal feature marking the DP that undergoes relativization, which is the EA headed by who_rel in Figure 2. The clausal head C_rel attracts this EA (containing rel) to its edge. We crucially assume the noun boy has an unchecked D feature (uD), indicated by !D, normally checked through Merge with a determiner D. We assume all (and only) relative Ds lack the ability to check uD. Thus, boy may subsequently emerge from sentential structure to head a new NP, and its unchecked D-feature will be checked by the (regular) determiner the, as shown in Figure 3.^[24] As only the highest copy may be pronounced, vertical lines in Figure 3 are used to pick out possible pronounced elements of the frontier of the structure.^[25]

Figure 2

Relative clause structure for the boy who told the story.

Figure 3

DP structure for the boy who told the story.

To summarize, uD on N, if left unchecked, enables N to (raise and) relabel a relative clause. N then gets its uD feature checked by a higher D in a regular sentence. The feature-checking details regarding uD, uT, and uRel are summarized in Table 2.

A reviewer asks how examples such as (11) in which the relative book on syntax, not a simple head, can be accounted for under this relabeling proposal. As the PP on syntax is an adjunct, the relevant structure is 〈book, {on, syntax}〉, where book and the PP on syntax are pair-Merged, as indicated by the angle brackets. Since pair-Merge is asymmetric, the adjunct on syntax is essentially invisible, and book on syntax is treated exactly the same as the single-head book; thus, it can relabel.^[26]

Relativization productively occurs with external and internal arguments, and even oblique, i.e., non-core, arguments, as will be illustrated in the following sections. In each case, the mechanism is the same, i.e., a relative determiner (D_rel) heading the argument to be relativized is attracted by a relative complementizer (C_rel). There is no theta role clash (or theta criterion violation) with this movement-based account as we assume theta roles are hosted in D.^[27] In Figure 3, external the (not boy) bears the theta role assigned to the entire DP when it is Merged as an argument in a higher clause, and the lowest copy of who _rel (not boy) bears the theta role assigned to the EA of tell. As the and who _rel are distinct, there is no theta problem.

We next summarize the algorithm used to derive the structure in Figure 1. Assume all sentences involve a selection of heads from the Lexicon to feed Merge. A head may bear both formal features, e.g., D and Case on nominals (discussed previously), and unvalued phi-features (person, number in English) on T and v*. Unvalued formal features must be valued in the course of a derivation (or else the derivation will not converge). Heads may also bear interpretable features, e.g., Q on wh-words and intrinsic phi-features on nominals, e.g., first-person-singular on I/me. A head that probes for matching values gets only one opportunity to value its unvalued formal features, viz. when it is first Merged. If a head H merges with a phrase YP, as in HP = {H, YP}, YP is the c-command search domain for H’s formal features. Once HP is merged with another head or phrase, H is inactivated as a probe and cannot search again. As this policy is strict, leftover unvalued features on H will crash the computation, and no convergent structure will be produced.

As the algorithm selects only the first head of a sequence for Merge, heads selected from the Lexicon are sequenced precisely for proper assembly.^[28] For (10)a, the sequence of heads that derives the structure shown in Figure 1 is given in (12)a.

Sequence (12)a is read from left to right with the algorithm selecting the appropriate Merge action based on the current state, i.e., the SO constructed so far and the first input head.^[29] In most cases, there will be only one possible Merge action per state. Non-determinism, i.e., more than one possible Merge action, is limited solely to linguistic choice points; e.g., the option to pied-pipe a preposition with a DP in English or the T-to-C option described in this article, both producing derivations that separately converge.^[30] Let us sketch the steps for Figure 1: step (i) Merge combines story and the, forming a DP; (ii) tell, the next head in the list, merges with the DP formed in (i), we obtain {tell, {the, story}} (a VP); (iii) the next head, v*, merges with the VP from (ii), forming {v*, VP}; (iv) the sub-list [the, boy] initiates a sub-computation producing {the, boy}, which replaces [the, boy] in the list of heads, (v) the v* phrase in (iii) Merges with {the, boy}, the EA, forming {EA, {v*, VP}} (a v*P); (vi) the head T_past Merges with the v*P from (v), forming {T_past, v*P}; (vii) English T has an EF which triggers IM for {T_past, v*P}. By minimal search, EA, being the highest accessible DP, is raised, forming {EA, {T_past, v*P}}. In step (viii), the last head, C, Merges to head the clause. Note there is no ambiguity as to which sub-phrase must label the merged structure at each step. Therefore, the derivation is deterministic (and efficient in this sense). Minimal search itself is implemented using a stack to maximize the efficiency of the search. Phrases with unvalued features (or rel) are placed onto a stack when merged initially. When IM is triggered or a head probes to value unvalued features, generally only the top stack element is consulted. For IM, the top stack element is extracted, i.e., raised. As a goal, the top stack element features must be used (to satisfy the probe). Hence, minimal search typically involves no search at all, and minimal c-command naturally results.^[31] The derivation of Figure 3 proceeds similarly with the sequence of heads in (12)b. One crucial difference between (12)a and (12)b is that C_rel in (12)b possesses EF, triggering IM after the equivalent of step (viii), and the EA {who_rel, boy} raises (in a similar fashion to wh-phrase fronting triggered by C_Q).

The system that we implemented is based on the feature-driven Merge model of Chomsky (2000, 2001, 2008, and other work).^[32] In this work, Chomsky assumes there is a one-time selection of items from the Lexicon to form an LA. Merge of Lexical Items is recursively applied to form an aggregate SO. An SO can be selected and Merged from the LA (EM), or it can be Merged from within the current SO; this is the process of movement (IM). The term Workspace refers to the LA and SO at any given stage. For a convergent derivation, the Workspace must consist solely of a single SO, with formal features eliminated. Any remaining uninterpretable features in the SO, or leftover LA items, will crash the derivation.

Multiple threads of derivation are in principle possible if there are multiple possible operations, i.e., choice points, at any given point in the derivation. An example of a theoretical choice point that we use is the possibility of uT on C being checked either by movement of T (resulting in pronunciation of that) or by nominative case on the subject (in which that is not pronounced). In such cases, e.g., “the man (that) John saw,” the model correctly generates two different structures starting from the same LA. Another linguistic choice point will permit the option of pied-piping for cases like “the man to who/whom I talked” and “the man who/whom I talked to.” Note that we assume that who and whom are inflectional variants of the same word who. Again, two different structures will be generated from the same LA. The model we describe has only linguistic choice points predicted by the theory; there are no temporary ambiguities attributable solely to the algorithm or data structures required. In this sense, our model is maximally efficient with respect to the theory.

Assuming we begin, as does Chomsky, with a one-time LA, our LA is selected in order, purely for computational efficiency.^[33] As the LA is ordered as a queue, the current SO has the choice of EM with the first item in the sequence, or ignoring the LA, the choice of IM, i.e., selecting a sub-SO from within itself. Based on the current SO and the head currently first in line in the LA, our machine will correctly select the right operation one step at a time to converge on the intended SO. (In the case of non-convergence, the machine will end up in a state with no possible continuation, call this a crash.) Lexical items selected from the LA may have unvalued and valued features. In the case of an LA head with an unvalued feature, when it is first Merged to the current SO, it must probe the existing SO for a matching valued feature. For efficiency, we assume all required probing for valued features can be accomplished during this first Merge time; i.e., no second chances are permitted nor needed.^[34]

Our model also incorporates an operation of Last Resort that enables an unlicensed relative head to move to the edge of a phase. If heads with remaining unvalued features are not to crash the derivation, the phrases they head must move to the edge of the Phase to save and keep the derivation going. This Last Resort operation happens automatically. A general remark about feature-driven movement is in order at this point: a head with an EF licenses movement to its phrase edge. Without it, movement is not permitted. Hence, for Last Resort to operate, either we must assume all Phases have an optional EF, or movement is generally licensed to all Phase edges.^[35]

The model that we created is complete in the sense that all convergent derivations are grammatical and all grammatical sentences in this article are generated. For a summary of the basic operations of our model, please see the Appendix.

3 Derivations of basic relative clauses

Our model crucially accounts for the (im)possibility of that in a variety of relative clauses. Consider (13), in which that can be either pronounced or unpronounced.

Snapshots of the derivation of (13) with that are shown in Figure 4. In Figure 4a, TP is the current SO, and C_rel is about to be Merged from the LA. In Figure 4b, C_rel has been Merged, and its unvalued features uRel and uT have been checked by D_rel and T, respectively. uT on C_rel, checked by T, results in pronunciation of that. As C_rel possesses an EF, the DP {D_rel, book} raises to the edge of CP. We assume D_rel cannot check the D feature on the noun (in this case, book), freeing book to raise as shown in Figure 4c. Book is a head and therefore labels{book, CP}. Finally, the external D is merged, checking uD on book. Note that the diagram correctly indicates Case (shown as !case) is currently unvalued on the external D head the. Its Case will be valued via probe-goal agreement when the relative clause is integrated into a larger environment, as in “They like the book that I read.”

Figure 4

Derivation of the book that I read.

The corresponding derivation of (13) without that is given in Figure 5 – in this case, the option of uT being checked by the subject (instead of T) is taken, so that is not pronounced. The remainder of the derivation, as illustrated in Figure 5a and b, is the same as in the case with that, described earlier.

Figure 5

Derivation of the book Ø I read.

Example (14) contains a covert D_rel within a PP headed by to. The two licit derivations are shown in Figures 6 and 7. We assume talk to is a verb-particle construction, where to is a particle and Case is valued by v*.^[36] In this case, pied-piping is generally blocked, as *the man to that I talked and *the man to I talked are ill-formed. One explanation for the lack of pied-piping here is that to followed by an empty category disallows pied-piping (Chomsky 2001, 28).

Figure 6

Derivation of the man that I talked to.

Figure 7

Derivation of the man Ø I talked to.

Consider the case of the subject relative in (15)a–b.

In the previous examples, i.e., (13) and (14), D_rel is covert. (15)b can be explained if covert D_rel generally cannot check uT on C_rel. Then the only available option is for T to raise to check uT on C, obligatorily pronounced as that in (15)a, and illustrated in Figure 8.^[37] The covert/overt distinction neatly divides uT (on C_rel) valuation; in short, covert D_rel cannot check uT and overt D_rel can. Thus, the wh-relative counterpart of (15)b, i.e., the boy who called Mary, is available.

Figure 8

Derivation of the boy that called Mary.

Our model can also account for long-distance subject relative clauses such as (16)a.

D_rel boy raises from the subject of embedded verb call out to the matrix CP. Since it passes through the edge of the embedded CP, there is no violation of the PIC. D_rel will check the uRel feature on C_rel at the matrix CP. However, in our theory, the uT feature on C_rel cannot be checked by D_rel, leaving it to be checked either by movement of the matrix subject to C, as in Figure 9, without the higher that, or by T-to-C, pronounced as the higher that, as in Figure 10. In the case of the embedded (non-relative) C, viz., C_e, the lower that is predicted to be obligatory because D_rel from D_rel boy cannot check C_e’s uT feature as it passes through the edge of the embedded CP. One of the authors of this article finds (16)b, which lacks that in the embedded clause, to be ill-formed. The other author finds (16)b perfectly acceptable (both authors are native speakers of English). This suggests for those who find (16)b fine, D_rel can check the uT feature of an embedded non-relative C, and for other speakers, D_rel can never check a uT feature.

Figure 9

Derivation of the boy John thinks that called Mary.

Figure 10

Derivation of the boy that John thinks that called Mary.

We next consider why a wh-relativizer (e.g., which and who) cannot co-occur with that in an object relative clause (17)a–d, nor in a subject relative clause (17)e–f.

Our proposal is that which _rel and who _rel are relative Ds that may value uT on C_rel.^[38] Economy then forces uT on C_rel to always be checked by a relative wh-determiner when present. This is summarized in Table 3, which states that it is more economical for a single goal to value multiple uFs on a probe than it is for multiple goals to value the uFs. Basically, the fewer Agree operations required, the better.^[39]

In the derivation of (17)a shown in Figure 11, a single Agree relation between C_rel and which _rel results in simultaneous valuation of both uT and uRel on C_rel. Economy blocks the option in which uRel and uT are separately checked (by which _rel (or who _rel ) and nominative Case on the subject, respectively). Hence, (17)b, which would require checking of uT on C_rel by T, is blocked. Similarly, the derivation of (17)c, shown in Figure 12, results from a single Agree relation between C_rel and who _rel, and likewise, (17)d is blocked by economy.

Figure 11

Derivation of the book which I read.

Figure 12

Derivation of the man who(m) John saw.

Next, consider the case of who _rel in subject relative clauses as shown in (17)e-f. Again, a single Agree relation between C_rel and who _rel licenses (17)e, as depicted in Figure 13, and (17)f is blocked by economy.

Figure 13

Derivation of the man who loves Mary.

Related constructions with pied-piping can also be accounted for. Notably, pied-piping of P is optional as shown in (18)a–b, which contain whom _rel , the object equivalent of who _rel . To account for this, we assume that C_rel may Agree with a relative DP contained within a PP, and the EF on C_rel can attract either the relative DP itself or the containing PP. Pied-piping obtains in the latter case.^[40]

The derivation of (18)a is given in Figure 14. Note we assume who _rel may also be pronounced as whom at Spell-Out. For some speakers, the form of who _rel can be sensitive to Case. For example, whom = who + Accusative. C_rel agrees with the relative DP headed by who _rel., and uT and uRel on C_rel are simultaneously valued. Economy blocks the option of T separately checking uT on C_rel, and (18)c is ruled out. The EF of C_rel attracts the relative DP to the edge of CP, leaving to stranded. Example (18)b is analyzed in Figure 15. This is identical to Figure 14 except that the entire containing PP is raised to the edge of CP. Similarly, (18)d with that is ruled out by economy.

Figure 14

Derivation of the man who(m) I talked to.

Figure 15

Derivation of the man to who(m) I talked.

Wh-adverbials such as when can also be relativized, as in (19)a–b, from an anonymous reviewer. Note that when and where are adverbials, not determiners. We must extend the rel feature to wh-adverbials, i.e., when _rel and where _rel exist in the Lexicon. This raises a possible acquisition question as not all determiners have a relative counterpart.^[41]

As when _rel has an iRel feature and can check uT on C_rel, our model straightforwardly accounts for (19)a, as shown in Figure 16. We assume that when _rel time initially adjoins at the TP level (as it is a temporal modifier).^[42] Furthermore, we assume that when _rel checks both uT and uRel simultaneously on C_rel, so economy blocks (19)b with that. Finally, the relative wh-adverbial when _rel cannot value the uD of time (as is the case with all relative Ds); hence, time raises and its uD is valued via Merge with external the.^{[43] [44]}

Figure 16

Derivation of the time when I got drunk.

Relatives can also occur in non-finite clauses, as in (20)a–b.^[45] Note that Sag (1997) indicates (20)b as being ill-formed; however, we find it grammatical. Pied-piping seems subject to dialectal variation.^[46]

Relevant structures for (20)a–b are given in Figure 17. Note that we employ a non-finite T (Tinf) and a null subject (PRO). We assume a dyadic in that takes complement and specifier arguments.

Figure 17

Derivation of the baker in who to place your trust/the baker who to place your trust in.

Another type of non-finite relative clause can occur with an optional for as in (21)a–b.

Assume that Tinf (as with tensed T) and for are both capable of checking the uT feature on C_rel. For (21)a, as shown in Figure 18, Tinf raises and checks the uT on C_rel. The noun person raises and relabels the clause as a nominal. For (21)b, as shown in Figure 19, we assume that the complementizer for raises and checks the uT feature on C_rel. Since for is closer to C_rel than Tinf, Tinf does not raise given minimal search. The relative DP raises to the edge of CP, and then, person raises to relabel.

Figure 18

Derivation of the person to visit.

Figure 19

Derivation of the person for us to visit.

Our analysis also extends to the case of headless relatives, examples shown in (22)a–b. Headless relatives appear not to support that for C_rel.

Assume that headless relatives contain pro_n, a form of pro occurring in relative clauses. We can co-opt our uRel and uT on C_rel analysis by assuming that pro_n also has a uD feature, just as with the overt Ns so far.^[47]

Figure 20 illustrates the derivation of (22)a. Suppose a relative determiner what _rel, like who _rel and which _rel previously, agrees with C_rel. In particular, permit what _rel to simultaneously value uT and uRel on C_rel. By economy, the option of checking uT on C_rel separately via T is blocked, and (22)b is ruled out. Note that we permit pro_n to undergo movement before Merging with an external null D. (We do not need to stipulate a difference between covert and overt relative N with respect to movement.) This null D values uD on pro_n, cf. null D_rel, which cannot value uD. Finally, we must also assume that pro_n is limited in distribution to co-occur with relative determiners only, as *the what I read is ill-formed.

Figure 20

Derivation of what I read.

We next turn to subject headless relative clauses, accounted for in parallel fashion.

This is similar to the case of (22)a–b, except that the relative DP originates in the subject position here. The derivation of (23)a is shown in Figure 21.

Figure 21

Derivation of what annoys John.

We have developed an analysis of the distribution of who/whom/which/what and a null D_rel in English. The relative determiner who occurs with human nouns, with the object variant whom occasionally used in some varieties of English.^[48] Relative D which can be used with non-human NPs. A reviewer notes nothing in our syntactic analysis blocks *the man which arrived. We assume semantic feature matching for determiner-noun combinations is also involved, e.g., -human for which and +human for who. We assume that the appropriate relative pronoun is selected from the lexicon, so which _rel occurs with a non-human relative noun and who _rel occurs with a human relative noun. (But see also Note 3.) Otherwise, these relative Ds are identical. We have also seen that what can be used with a null NP complement.

4 Comparative and genitive relatives

Hale (2003) implemented a Minimalist Grammar that covers a variety of relative clauses from Keenan and Hawkins (1987) involving subject and object relatives, passivization, comparatives, and genitives. Although Hale covers a wide range of relative clause constructions, the reasons for the uses of the relative determiners which, who, what, and for restrictions on their use with that are not accounted for. Our model also accounts for all of the relative clause examples from Keenan and Hawkins (1987, 63), notably genitive relatives, as well as other related constructions.

The examples in (24) from Keenan and Hawkins (1987, 63) are essentially identical to examples that we have discussed earlier (Hale models (24)a, b, c, and a version of d).^[49] (24)a is a subject relative (Figure 8), (24)b–c are object relatives (Figures 11 and 12). (24)d–e contain relative nouns that originate as the object of a preposition (as in Figures 14 and 15).^[50] See the Appendix for complete derivations of these particular examples.^[51]

We next discuss some examples from Keenan and Hawkins that require some revisions to our core model.^[52]

In example (25), boy originates from a relative DP object of the comparative than.^[53]

As shown in Figure 22, the relative who _rel boy raises and remerges with C_rel, checking uRel on C_rel. The head boy with unvalued uD raises out of C_rel P, then relabels and Merges with external the (which checks unvalued uD on boy).

Figure 22

Derivation of the boy who Mike writes better than.

Next, we consider (26), from Keenan and Hawkins, which contains a genitive subject relative.

Figure 23 analyzes (26) as follows: the possessive subject DP who _rel girl ‘s friend raises from the edge of v*P to the surface subject position at the edge of TP. This is followed by raising to the edge of C_relP (who _rel checks uRel on C_rel). The head girl raises and relabels the structure. We need to assume that although who _rel is embedded in the specifier of the possessive DP, its Rel feature is visible to C_rel and Agree (who _rel , C_rel) results in raising of the entire DP.^[54]

Figure 23

Derivation of the girl whose friends bought the cake.

Example (27) is similar to (26) except that the genitive relative originates as an object. As shown in Figure 24, the genitive relative raises to the edge of C_rel P, and the head man then further raises and relabels.^[55]

Figure 24

Derivation of the man whose house Patrick bought.

Example (28) is similar to those shown previously in Figures 22 and 23 except that it is a passive construction (see the Appendix for the complete derivation).

Note that in addition to these examples from Keenan and Hawkins, our model is also able to generate related relative clause constructions with the relative contained within a PP complement headed by of. Examples (29)–(31)a correspond to the genitive relatives (26)–(28) except that the relative pronoun originates in a PP complement headed by of.^[56]

The structure of (29)a is shown in Figure 25. The relative DP who _rel girl originates in a PP of-phrase that is the complement of friends, embedded within the subject. After the subject moves to the TP edge, the relative DP who _rel girl moves to the C_rel P edge to check the uRel feature, and head girl moves out and relabels. Example (30)a is similar except that it involves a relative object, and (31)a involves a passivized relative object.

Figure 25

Derivation of the girl who friends of bought the cake.

We next turn to deeply embedded genitive relatives, such as in (32).

The structure of the relative DP whose person ‘s mother’s friend’s sister’s dog’s appearance is shown in Figure 26. In our implementation, we must assume that the relative feature of deeply embedded who _rel percolates up onto the highest ’s, so C_rel is able to attract the entire DP to check its uRel feature.^[58] See the Appendix for further examples of embedded relatives.

Figure 26

Embedded relative: the person whose mother’s friend’s sister’s dog’s appearance had offended the audience.

5 Other varieties of English

We have focused on an analysis that accounts for the structures of basic relative clauses in modern standard English. Although the relative clauses’ heads in (33)a–c are unavailable in standard modern English, they do occur in older stages of English and in some modern dialects.

Old and Middle English allow a doubly filled CP. Examples (34)a–b are from Old English. Se is a demonstrative pronoun, although it is translated as a wh-pronoun (Ringe and Taylor 2014, 467).

Examples of which that are also attested in Middle English, as shown in (35)a–b and (36).

Zero subject relatives may also occur. Examples (37)a–c are cited by Bauer (1994).

Belfast English also has zero subject relatives, as in (38)a–b.

Finally, the following two examples are from Black English Vernacular/African American English.

In our analysis so far, we have assumed the Lexicon contains who _rel , which _rel , when _rel , and what _rel , all of which are able to value uT on C_rel. It is certainly plausible that this property could vary over individual lexical items. Thus, certain varieties of English which _rel and who _rel may lack this ability, thereby permitting uT on C_rel to be checked separately by T or nominative Case on a subject, crucially licensing the pronunciation of that in the former case. Another point of variation concerns null D_rel; we proposed earlier that null D_rel, unlike overt D_rel, is unable to value uT on C_rel, but it appears that in some dialects null D_rel may behave like overt D_rel, permitting zero subject relatives, e.g., as in Belfast and African American English. To summarize, a relative D must contain a core Rel feature (by definition). However, the ability to value uT on C_rel may vary diachronically and/or synchronically. To summarize, this minor change in lexical feature specification can account for the data described above and is not a problem for our computer implementation in principle.

6 Conclusion

We have built our theory and verified implementation based on the insights of Gallego’s (2006) analysis of relative clauses. Gallego, in turn, has built on the insights of P&T (2001). The fact that this refinement is possible is a sign that the MP is a viable research program. Our account makes use of a relative complementizer (C_rel) with separate unvalued Rel (relative) and T (Tense) features. Rel is a construction-specific formal feature, distinguishing relatives from normal clauses. Rel and T together are subject to economic considerations, i.e., simultaneous valuation (where possible). Our verified analyses improve upon Gallego in the following ways: a) there is no need for an extra projection in the left periphery, b) there is no stipulation that a null D cannot move, c) there is no need for two types of C, one with an EPP feature, and one without, and d) we are able to account for the absence of which that in standard English. The additional stipulations of our model are that: i) a relative D cannot check a uD feature on N, in order to trigger extraction of the relative noun for relabeling, and ii) the null D_rel cannot generally check a uT feature, although other relative Ds, such as which _rel /who _rel /whom _rel /what _rel /when _rel , can. A natural question arises: is our three-feature system, Rel, T and D, minimal, i.e., parameter-efficient? As, in our theory, movement is driven, both EF and something akin to our unvalued D are required to initiate raising and relabeling of the relative clause into a nominal. Finally, a minimum of two features, such as Rel and T, are needed in order to exploit economy. Economy simplifies operational complexity, enabling multiple features to be valued in one operation. More broadly, in the MP framework, the functional category T selects for verbal phrase structure and further projects phrase structure (with a surface subject position).^[60] In Chomsky (2008), non-selectional properties of T, e.g., phi-features, the ability to value nominative Case and Tense, do not appear in T’s lexical entry, but instead are transmitted from phase head C.

Overall, we have developed a detailed and logically consistent feature-driven theory of English relative clauses in the MP framework. We have also built a computer-implemented derivational system capable of converging on the correct analyses starting from an initial LA queue. The implementation confirms that our theory is both complete and detailed enough to constitute an (automatic) computer program. The interested reader is referred to the Appendix, which contains step-by-step computer-generated derivations, too detailed to be included in the main body of the article. The Appendix includes all the English relative clause examples discussed in the article (and others). The program is able to correctly select the precise Merge operation at each step (without human intervention), based on the state of the current SO and the first available item in the LA.^[61] Moreover, our implementation permits us to verify that the model does not generate spurious analyses – unpredicted by the theory – for all example sentences.

We summarize the core relative D facts in Table 4.

Finally, we believe our analysis can be extended to account for data in other dialects and languages, assuming limited variation in determiner heads with respect to the ability to value uT on C_rel. There are also a variety of other relative clause types that remain for future work.^[62]

Abbreviations

C

complementizer

COMP

complementizer

cP

(extra) complementizer phrase (above the normal CP)

CP

complementizer phrase

C_Q

interrogative (Question) complementizer

C_rel

relative C

C_relP

relative CP

D

determiner

DP

determiner phrase

D_rel

relative determiner

EA

external argument

ECM

exceptional case marking

EF

edge feature

EM

external merge

EPP

extended projection principle

H

head

HPSG

head-drive phrase structure grammar

IM

internal merge

iPhi

interpretable phi-features (person, number, gender)

LA

lexical array

MG

minimalist grammar

MP

minimalist program

N

noun

NP

noun phrase

Op

operator

phi-features

person, number, and gender features

POSS

possessive head ’s

PP

prepositional phrase

pro

a pronoun that is not pronounced which is associated with Case positions.

PRO

a pronoun that is not pronounced which is associated with non-Case positions

pro_n

a nominal pro

Q

question

rel

relative feature

SO

syntactic object

T

tense, a feature and a functional head

TP

tense phrase

T_Past

past tense

uF

unvalued/uninterpretable feature

uPhi

unvalued/uninterpretable phi-features (person, number, gender)

uRel

unvalued relative feature

iRel

interpretable relative feature

uT

unvalued/uninterpretable T

v

verb

V

verb

v*

transitive verbal head

VP

verb phrase

YP

a phrase with the head Y