Chapter 6: Transformations (I)

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6.1. The English Auxiliary System Revisited

In Chapter 4, we took a look at the English auxiliary system and saw that the auxiliary is an optional element of a sentence which, if it occurs, may select one or more of the options included in the following rule, PSR9:

(1) PSR-9: The Auxiliary Rule

According to this rule, the infinitival auxiliary, to, and the modal auxiliaries (will, could, must, etc.) are in complementary distribution. They cannot co-occur (*for John to will go, *for John will to go). The infinitival auxiliary and modal auxiliary, however, may each co-occur with a perfective or a progressive aspect, or with both, in the order given.

We also observed that the Infinitival auxiliary differs from the other auxiliary elements in two important ways. First, the auxiliary to can only be used in a subordinate clause whereas a sentence without to may occur as a main clause or a subordinate clause. Secondly, a clause with to does not contain any marking for Tense, whereas one without to must. That is, a clause is tenseless if infinitival:

(2) a. For John to sing . . . .
b. For John to have sung . . . .
c. For John to be singing . . . .
d. For John to have been singing . . . .

But if not infinitival, a clause or sentence is necessarily marked for either Present or Past Tense:

(3) a. John sings/sang.
b. John will/would sing.
c. John has/had sung.
d. John is/was singing.
e. John will/would have sung.
f. John will/would be singing.
g. John has/had been singing.
h. John will/would have been singing.

Note that Tense, when it shows up on a sentence or clause, may show up in different positions depending on what other elements a given sentence has. Thus, if a sentence contains no auxiliary at all, Tense shows up on the verb (as in (3a)). If it contains one auxiliary (a modal, have, or be), then the Tense shows up on this auxiliary (as in (3b, c, d), respectively). If it contains two or more auxiliaries, Tense always shows up on the leftmost auxiliary (as in (3e, f, g, and h)). The following sentences are ungrammatical:

(4) a. *John will sings.
b. *John have sang.
c. *John be sings.
d. *John have is singing.
e. *John will had been singing.
f. *John will have was singing.

Furthermore, note that each sentence can contain at most one marking for Tense:

(5) a. *John would sang.
b. *John is sings.
c. *John has is singing.
d. *John would had was sang.

How can we incorporate this piece of our knowledge--which is clearly systematic and therefore rule-governed--into our Grammar? Let us just concentrate on the part of PSR9 that deals with tensed S's. A tensed S contains a sub-string of the following form:

(6) (Modal) (Perf) (Prog) V . . . .

The descriptive generalization appears to be that Tense must appear on the leftmost element chosen from (6). The problem we are facing is how we can express this generalization by a rule of some sort, thus capturing the generalization that the distribution of Tense is systematically rule-governed. Our Grammar contains two components: a PSG and a Lexicon. Since all verbs and auxiliaries (save to) are capable of bearing Tense, the question of which of them should bear Tense in a given sentence cannot be answered by a lexical marking on any of these elements. We must then look to the PSG component for an answer. For example, consider only the tensed part of PSR9, as in (7):

(7) Aux ----> (Modal) (Perf) (Prog)

Recall that a PSR is a general statement of constituency for phrases or sentences in a given language. The rule (7) says what kind of things an English auxiliary may consist of and in what order. Suppose we use the notation [+Tns] to indicate that a given element bears Tense, the tensed Aux in English may take any of the following forms:

(8) a. Aux ----> Prog

[+Tns]

b Aux ----> Perf (Prog)

[+Tns]

c. Aux ----> Modal (Perf) (Prog)

[+Tns]

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Note that while each of these rules is an adequate description of a given grammatical realization of (7), we cannot combine these sub-rules into one like (7) itself. For example, we cannot abbreviate all of (8) with the rule (9):

(9) Aux ----> (Modal) (Perf) (Prog)

[+Tns} [+Tns] [+Tns]

Because this rule incorrectly allows cases where more than one element shows up with Tense, and where Tense shows up on the non-leftmost element in Aux. Since we cannot collapse the cases in (8) into one general rule like (7), we miss an important generalization about the structure of Aux, that it contains three optional constituents in the order given in (7).

The problem is in fact more serious when we consider sentences containing no Aux, in which case the main verb must bear Tense. We could modify the VP rule PSR3 in such a way as to allow for verbs to bear Tense, but it's not going to do the work we need done:

(10) VP ----> V . . . .

[+Tns]

This rule fails to capture the fact that the V bears Tense just in case the VP is not preceded by any Auxiliary element.

We might continue to pursue the strategy represented by (8) and (10), but it is clear at least that, whatever result we come up with, it will necessarily cost our Grammar much of the simplicity and generality it has otherwise displayed.

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6.2. Affix Hopping

The important generalization that has presented a problem for us is that the Tense morpheme in English seems to "migrate" depending on the kind of elements available in the Aux+VP complex of a sentence. There is a very simple way to capture the descriptive generalization, first suggested by Chomsky in his little 1957 monograph Syntactic Structures. Chomsky argues that natural language grammar contains two types of rules: Phrase Structure Rules (PSRs) of the type we have been assuming, and Transformational Rules (or Transformations). First, he proposes that Tense, an element of inflectional morphology, should be recognized as a separate lexical category (a "word") and be admitted as a leftmost daughter of the category Aux for a tensed sentence:1

(11) Aux ----> Tns (Modal) (Perf) (Prog)

The constituent Tns in turn may consist of the Past or the Non-Past (Present) Tense morpheme, which we shall represent with the suffixes {-es} and {-ed}, respectively. The minor PSR we need is (12), and our Lexicon needs to contain the two entries in (13):

(12)

(13) a. Present ----> {-es}
b. Past ----> {-ed}

Note that by positing Tense morphemes as constituents of the Aux, we are analyzing an inflected verb, like finishes and finished, as two separate items: the uninflected stem of the verb (i.e., finish), and the Tense suffix. By listing these morphemes as independent units in the Lexicon, we now only need to list the root (uninflected) form of each verb. (As for how each root form combined with a suffix is to be pronounced, we assume that this will be taken care of by principles of English morphology, which lies outside the scope of this course.2).

With this proposal, a sentence like John would be singing will be generated in the form of the following P-marker (assuming that the root form of would is will):

(14)

And he arrived suddenly yesterday has the P-marker (15) (irrelevant details omitted):

(15)

Other P-markers can be generated, giving terminal strings like:

(16) a. John -es have sung three times.
b. They -es be playing in the bathroom.
c. Mary -es will have been singing.
d. Bill -ed believe that I -ed shall try the dish.

Note that none of the P-markers and terminal strings in (14)-(16) correspond directly to the form the sentences are actually pronounced or heard. Chomsky proposed that the actual forms are obtained by a rule of transformation, called Affix Hopping, which attaches an affix (a bound form) to the very first element that follows it within the Aux+VP complex. The rule of Affix Hopping is a set of instructions which says that if you scan a P-marker or terminal string and encounter an affix immediately followed by an auxiliary or verbal element, attach the affix to the immediately following element. as a suffix of the latter. If we now apply this transformation to (14)-(16), we obtain the following:

(17) a. John will+ed be singing.
b. He arrive+ed suddenly yesterday.
c. John have+es sung three times.
d. They be+es playing in the bathroom.
e. Mary will+es have been singing.
f. Bill belive+ed that I shall+ed try the dish.

(Note that Affix Hopping applied two times to yield (17f). Once the Tense morpheme is placed in its proper location, appropriate morpho-phonemic rules will turn these sentences into their surface form:

(18) a. John would be singing.
b. He arrived suddenly yesterday.
c. John has sung three times.
d. They are playing in the bathroom.
e. Mary will have been singing.
f. Bill believed that I should try the dish.

Summarizing, what Chomsky proposed is, first, to look under the surface of English syntax, by detaching Tense affixes from their hosts, and place them in the beginning of the Aux+VP complex, and then invoke a transformational rule to place the affix onto whichever auxiliary or verbal element follows it. This provides a very simple and straightforward way to guarantee that the Tense morpheme for each sentence is realized on the correct element within the sentence. Notice how all possibilities illustrated in (3), and only these possibilities, are generated by exactly this single rule of Affix Hopping, and there is no need to complicate our PSRs as in (8)-(10) and to run into the problem of not being able to collapse the sub-rules of the PSG. Most importantly, the proposal to look below the surface and the postulation of Affix Hopping enable us to capture the linguistically significant generalization that in English, Tense morphology seems to migrate, settling on whichever element follows it in a P-marker generated by the PSRs including the new Aux rule (11).

The idea that Tense belongs to the Aux constituent also captures the fact that Tense is not an inherent part of a verb (unlike derivational affixes, e.g., -ize), but an element that modifies the sentence as a whole. This is because Tense is not generated as part of a verb in the grammar, but as a constituent of Aux outside the whole VP. Since it is a bound morpheme, it cannot surface as an independent word. Therefore it must, with the help of Affix Hopping, cling to an appropriate host and be supported by it.

It should be noted that Affix Hopping is not an ad hoc rule proposed for the sole purpose of accounting for the distribution of Tense morphology in English. For example, recall that the Perfective Aspect in English involves the auxiliary have and a requirement that the verbal element following it must take the form of a past participle (symbolized by {-en}, and the Progressive Aspect requires the following verb to appear in the form of a present participle (symbolized by {-ing}). Furthermore, if both the Perfective and the Progressive Aspects appear, then the past participle morpheme {-en} must be realized on the auxiliary be, but not on the verb. In other words, the {-en}, {-ing} morphemes must also be realized on the first auxiliary or verb immediately following it. We can capture these requirements straightforwardly by assuming that the Perfective Aspect consists of the free word have and an affix {-en} that will be subject to Affix Hopping. And the Progressive consists of the free word be plus an affix that will undergo Affix Hopping.

(19) a. Perf ----> have -en
b. Prog ----> be -ing

Under these assumptions, the appropriate P-marker for John would be singing is (20), prior to the application of Affix Hopping:

(20)

And Mary will have been singing has the P-marker:

(21)

The result of applying Affix Hopping to these structures will yield:

(22) a. John will+ed be sing+ing.
b. Mary will+es have be+en sing+ing.

And the appropriate morphophonemic rules of English will turn these into their surface forms.

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6.3. Deep Structure, Surface Structure, and Transformations

According to Chomsky's proposal, then, a grammar consists of a Lexicon and two types of rules: PSRs and Transformations. PSRs generate P-markers by successively expanding phrasal categories into sequences of their constituents until every node is specified in terms of lexical (word) categories (until we have reached the "terminal nodes"). Then appropriate lexical items are inserted into a given P-marker, giving substance to the P-marker as a representation of a sentence. The results of applying the PSRs and Lexical Insertion do not necessarily correspond to what is directly observed on the surface, however. They may still be somewhat abstract. Such abstract structures may be subject to alteration by Transformations, such as the Affix Hopping rule, which map them into P-markers that are closer to their observed surface forms. The (abstract) P-markers generated by the PSRs and Lexical Insertion are called the Deep Structures of sentences. Transformations operate on P-markers and map them to (relatively more concrete) P-markers, called their Surface Structures. The organization of a Transformational-Generative Grammar is as follows:

(23)

Note that a transformational rule differs from a PSR in fundamental ways. A PSR always takes the form of specifying what any given phrasal constituent consists of:

(24) X ----> Y Z W

The rule is "context-free": it says that any constituent of category X may consist of the daughters Y, Z, W in that order. By applying various PSRs, we generate P-markers. In deciding whether a given constituent should be further expanded, we simply examine whether that constituent appears on the left-hand side of any PSR. Any category appearing on the left-hand side of the arrow of a PSR must be rewritten as a sequence of its daughter(s). It does not matter where that category occurs in a sentence. (For example, the rule NP ---> (Det) N .... applies to rewrite NP as N, Det-N, etc., regardless where NP occurs (as subject of S, object, or object of a preposition, etc.).

A transformation, on the other hand, is "context-sensitive". It does not generate P-markers by successively expanding given phrasal categories. Rather it operates on P-markers generated by the Base Component and modifies them. The rule Affix Hopping, for example, might be formulated as follows (with the arrow "==>" indicating a change effected by a transformation):

(25) Aff X ==> X+Aff

[+V]

Let's use the feature [+V] as a cover term to refer to verbs and auxiliaries (both of which are "verbal" elements--auxiliaries are traditionally auxiliary verbs, while verbs are main verbs). The rule (25) says that if you scan a given P-marker and encounter a string of an Affix immediately followed by a verbal (verb or auxiliary) element, then attach the affix to the verbal element as its suffix. (The "+" indicates a "morpheme" boundary, not a word boundary. Thus X+Affix is one single word.) We can also formulate a transformation in the following manner, in terms of a Structural Description (SD), a Structural Change (SC), and optionally one or more conditions:

(26) Affix Hopping

SD: Aff X
1 2
SC: ¯ 2+1
Condition: 2 = [+V]

This rule says that any string (within a given P-marker) that satisfies the SD will undergo the change described by the SC (become a string or P-marker that satisfies the SC). The Condition gives more information about the SD that triggers the application of the rule.

Clearly, according to either formulation (25) or (26), the Affix Hopping transformation is a context-sensitive rule. It cannot apply, for example, if the affix is not

immediately followed by a [+V] element.

Thus, according to the organization indicated in (23), the derivation of a sentence proceeds as follows. First, PSRs apply to generate abstract P-markers to which Lexical Insertion occurs, resulting in d-structures, or deep P-markers. Transformations operate on the d-structures and map them to more concrete structures. When all the transformations have applied, the result is an s-structure, or surface P-marker. Since a d-structure may be modified by more than one transformation, the result of applying a given transformation is an intermediate structure, unless the transformation is the last apply, in which case the result is an s-structure. (We shall use the capitalized terms D-Structure and S-Structure to refer to the levels of syntactic representation in our grammar, and occasionally use the lower-case "d-structure" or "s-structure" to refer to an actual P-marker at the D-Structure or S-Structure levels, respectively.

We have seen an example of the Transformational Component. In the rest of this Chapter we shall introduce a few other transformations and show why it is desirable for our Grammar to incorporate these transformations.

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6.4. Auxiliary Inversion

Consider the following sentences:

(27) a. Will John see Bill tomorrow?
b. Would you have helped me this afternoon?
c. Has he flied out today?
d. Have you been telling these lies to them?
e. Was the woman singing in the bath?
f. Will you be joining us?

These sentences are questions, more specifically "yes/no questions", differing from the ordinary declarative sentences that have been the subject of our study so far. Each of these sentences starts with an element of the Auxiliary system, followed by a subject, other auxiliary elements, and the VP, in that order.

None of these sentences are directly generatable by our Grammar as it has been formulated. There is only one rule in our PSG that allows us to generate a sentence that begins with something other than the subject, i.e., the rule S' ----> Comp S, but these sentences each start with an auxiliary element, not with a Complementizer. What can we do about our Grammar to allow it to account for these sentences?

One possibility is to increase the inventory of the Complementizer, and say that auxiliaries like any modal, have and be may be used as a Complementizer and be inserted under Comp in a P-marker generated by our PSG. A slightly different possibility is to revise our S' rule as:

(28)

However, neither of these possibilities is satisfactory. For one thing, listing auxiliaries both as members of Modal, Perf, or Prog, and as members of Comp in the Lexicon is undesirable because we are duplicating the lexical listing for what are clearly the same items, for no other reason than to accommodate the sentences in (27). In other words, such a move would be ad hoc and not independently motivated. Even if we take the strategy of revising the S' rule as (28), a problem arises as to how we can ensure that only one Aux element can appear before S--recall that our Aux rule says that an Aux may contain several elements (Modal, Perf, and Prog). We would have to further complicate the rule (28) by listing all the three possibilities together with Comp in (28), again in an ad hoc way. But most importantly, whether we pursue the first or the second possibility, we miss an important generalization about the sentences under consideration. Note that in each of these sentences, if an auxiliary, say a Modal, appears before S, then that element must be missing from S. Similarly, a sentence that starts with the auxiliary have or be cannot also contain have or be between the verb and the subject. The following sentences are ungrammatical:

(29) a. *Will John will see Bill tomorrow?
b. *Would you would have helped me this afternoon?
c. *Has he has flied out today?
d. *Have you have been telling these lies to them?
e. *Was the woman was singing in the bath?
f. *Will you will be joining us?

If the sentences do not start with an auxiliary, as in the following examples, they are of course grammatical:

(30) a. John will see Bill tomorrow.
b. You would have helped me this afternoon.
c. He has flied out today.
d. You have been telling these lies to them.
e. The woman was singing in the bath.
f. You will be joining us.

That is, a given auxiliary can occur before the subject just in case it is missing from the position after the subject, and an auxiliary must be missing from the internal position just in case it is found in sentence-initial position. The obvious generalization is that in each of (27) an auxiliary element has been "moved" to the sentence-initial position to form a yes/no question; that is, the sentences in (27) are somehow derived from those in (30), respectively, by moving an auxiliary element to the sentence-initial position. We cannot express this generalization by base-generating each of (30) with one set of rules, and each of (27) with another. (That would treat the two sets of sentences as if they were not related to each other whatsoever.) However, the generalization can be expressed quite straightforwardly if we invoke a transformation, call it Subject Auxiliary Inversion (SAI), which operates on the P-markers of (30a-f) and map them to P-markers representing (27) by moving the first auxiliary element in each of (30) to the sentence-initial position. You can see that this is exactly what happens in these sentences. The sentences in (30) may each contain one or more auxiliary element, and if you move the first auxiliary element in each case leftward across the subject, you get the desired result indicated in (27). The effect on (30a-b) is shown in (31):

(31)

Note incidentally that in each of the yes/no questions, the inverted auxiliary is inflected with Tense already. Since we have assumed, with Chomsky, that Tense is base-generated by our PSG as a daughter of Aux, dissociated initially from the other Aux elements, the d-structures underlying the sentences in (27) are, strictly speaking, not the ones in (30), but rather more abstract P-markers (having the form before Affix Hopping takes place). Thus the d-structure of (27b), for example, is actually (32):

(32)

This structure is subject to both Affix Hopping, which needs to apply twice to this structure, and SAI, which moves the inflected auxiliary to the left of the subject NP. For present purposes, we can assume that these two rules may be ordered in either way. Suppose Affix Hopping applies before SAI, then from (32) we first get (33) as the result of applying Affix Hopping.

(33)

To this intermediate structure, the SAI rule applies, moving the inflected modal (will+ed) across the subject, resulting in the s-structure (27b). (We shall assume without justification that the moved category is attached to the S node as its daughter.) Similar sentences may be derived in the same way.

On the other hand, we might assume that SAI applies before Affix Hopping. Since the inverted auxiliary has Tense with it, we must make sure that SAI moves both the Tns constituent and the first Aux immediately following it to the front of the sentence. In other words, SAI applies to (32) and preposes the substring Tns+Modal, resulting in the intermediate structure (34). (We again assume that the inverted auxiliary elements are immediately dominated by S after they are fronted.)

(34)

After Affix Hopping applies to this structure, the s-structure (27b) is obtained.

For the moment, it seems that either the order "Affix Hopping > SAI" or the order "SAI > Affix Hopping" will do. As we shall see below, however, in other cases the order is not free.

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6.5. Do Support

Such questions are illustrated by the examples in (35):

(35) a. Ý Do you know that Bill married his ex-wife again?
b. Does she love him still?
c. Did he propose to her this time?

These sentences differ from the other yes/no questions we have seen in that each question starts with an inflected form of the element do, instead of an auxiliary element like a modal, the perfective have, or the progressive be. In fact, none of these sentences contain any Auxiliary element after the subject either. If we consider the following declarative sentences, from which we assume they are derived ("transformed"), we see that these are cases where the Tense affix has hopped onto the main verb, there being no other auxiliary element for it to hop to.

(36) a. You know that Bill married his ex-wife again.
b. She loves him still.
c. He proposed to her this time.

Note that the occurrence of do, does, did in (35) is entirely triggered by the process of yes/no question formation. Furthermore, the Tense affix that occurs with the main verbs in (36) now shows up on the do, does, did in (35), in sentence initial position. The D-Structure representations of these declarative sentences are as in (37), considering only the terminal strings:

(37) a. You -es know that Bill marry+ed his ex-wife again.
b. She -es love him still.
c. He -ed propose to her this time.

Let us see how we can derive the yes/no questions in (35) from the affirmatives in (37). First, SAI must apply to move certain auxiliary elements to the left of the subject. Since the only Auxiliary element in each case is a Tns affix, SAI moves that affix to sentence-initial position, resulting in the following intermediate structures:

(38) a. -es you know that Bill -ed marry his ex-wife again?
b. -es she love him still?
c. -ed he propose to her this time?

Now, each of these sentences has (at least) one Tns affix, which must undergo Affix Hopping, so that the affix will have a host to cling to. Applying Affix Hopping to the sequence -ed marry in (38a) is no problem, and the correct result marry+ed will be obtained. However, we cannot apply Affix Hopping to the sentence-initial Tns affixes. In fact, we must prevent Affix Hopping from applying to these affixes, because if the affixes were to hop to the first following verbal elements, that would simply undo the effect of SAI, and we are back to the same old declarative sentences! We must somehow constrain Affix Hopping so that it will not move an affix across a following subject NP. We cannot, however, simply require Affix Hopping not to apply in these cases and leave the sentences as they are in (38), with the affixes "stranded", because by definition affixes are bound forms; they must cling to some lexical element (an auxiliary verb or a main verb). How can we rescue these affixes from being stranded? The answer is that a transformational rule, called Do Support, inserts the dummy verb, do, immediately after the Tns affix to "support" the affix in each case, to act as a host for the affix to hop to, and to prevent it from being stranded:3

(39) a. -es do you know that Bill -ed marry his ex-wife again?
b. -es do she love him still?
c. -ed do he propose to her this time?

Note that Do Support must be constrained in such a way as to apply only as a Last Resort, to rescue a sentence with an otherwise stranded affix. For example, if the Tns affix is already followed by an auxiliary or verbal element so that Affix Hopping can apply, an unmotivated application of Do Support would result in ungrammaticality. The following sentences do not allow a dummy (auxiliary) do:

(40) a. John would talk to her in the morning.
b. *John did will talk to her in the morning.

(41) a. They are all streaking in the rain.
b. *They do be streaking in the rain.

(42) a. Bill has broken many promises.
b. *Bill does have broken many promises.

The ungrammaticality of the (b) sentences can be explained if we assume that Do Support is a "last resort" rule. Since it is not called for to prevent affix-stranding, it cannot apply. Similarly, the following sentences are grammatical, in which a dummy do has been inserted between Tns and the main verb:4

(43) a. *You do know that Bill married his ex-wife again.
b. *She does love him still.
c. *He did propose to her this time.

Returning to (39), we see that, with do inserted into these sentences, Affix Hopping can now apply, yielding the following:

(44) a. do+es you know that Bill -ed marry his ex-wife again?
b. do+es she love him still?
c. do+ed he propose to her this time?

which, of course, will be morphophonemically realized as the surface structures in (35).

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6.6. Summary

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We have seen that our description of English syntax can be much simplified if our Grammar contains a Transformational Component in addition to the Base Component with a PSG and a Lexicon, as depicted in (23), and if we look at sentences at two different levels of representation: an abstract level called Deep Structure, and a more concrete level called Surface Structure. These two levels are related by transformations, such as Affix Hopping, Subject Auxiliary Inversion, and Do Support. We have also seen that the transformational rules apply sequentially, one after another, each mapping a P-marker into another and that, in order to obtain the correct results, the rules must apply in a correct order. Thus, a question like did you see John? is derived by first applying SAI, Do Support, and Affix Hopping in that order. First, the Base Component (with the PSG and the Lexicon) generates the d-structure (45):

(45)

SAI applies, mapping it to the following intermediate structure:

(46)

To this Do Support must apply, yielding (47):

(47)

After Affix Hopping applies, the surface structure (48) is obtained:

(48)

Therefore, in order to obtain the correct results, we must apply the transformations in the following order: SAI > Do Support > Affix Hopping. Recall that, while discussing yes/no questions that do not involve Do Support in Section 6.4, we noted that either the order Affix Hopping > SAI or the order SAI > Affix Hopping would give us the desired results . However, in order to derive the sentences involving Do Support, we must apply SAI before Do Support, and Affix Hopping after it. This means that we must not apply Affix Hopping before letting SAI have a chance to apply. If Affix Hopping were to apply to (45) before SAI, the string You see+ed Bill would result. If SAI were to apply to this output, we would get *Saw you Bill?, which is of course ungrammatical in English.

Note that while some Transformations are obligatory, others are optional. Do Support is obligatory (when its application is motivated), and so is Affix Hopping; otherwise an affix would be stranded. On the other hand, SAI is optional, so it need not apply to a d-structure like (45). If one chooses not to apply SAI, Do Support would have no occasion to apply. And (45) will directly undergo Affix Hopping, yielding the surface sentence You saw Bill.

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Homework 6

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(1) Examine the following sentences:

a. Mary will not talk to Bill.
b. Mary must not be talking to Bill.
c. Mary has not been talking to Bill.
d. Mary is not talking to Bill.
e. *Mary will have not talked to Bill.
f. *Mary not will talk to Bill.
g. *Mary has been not talking to Bill.
h. *Mary must be not talking to Bill.
i. *Mary must be talking not to Bill.
j. *Mary must be talking to Bill not.
k. *Mary not talked to Bill.
l. Mary did not talk to Bill.
m. *Mary did talk not to Bill.
n. *John talked not to Bill.

Assume that these negative sentences are derived from their affirmative counterparts by a transformation called Negative Placement, which places the morpheme not into an appropriate position.

(i) Describe the Negative Placement rule, indicating how it can correctly obtain the correct negative sentences (in conjunction with the other Transformations we have posited in this chapter).

(ii) Give the D-Structure P-marker of the sentence Mary did not talk to Bill, and indicate how the s-structure is obtained (name the transformations that apply to them in succession and describe what happens when each given transformation applies).

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(2) For each of the following sentences:

(a) Could the little boy have been crying?
(b) Did you explain the problem to him?

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(i) provide an appropriate d-structure (with a tree diagram) and

(ii) indicate what transformations are involved in deriving their surface forms. Name the transformations in the order they apply, and for each transformation, indicate what it does, by showing the intermediate structure or surface structure (with a terminal string--not a tree) that it yields.

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(3)

(i) Explain the following contrasts:
a. Do you have any wool?
b. *Have you any wool? (*in American English)
c. Have you brought any wool?
d. *Do you have brought any wool?

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(ii) Explain the following contrasts:

a. John did a good job.
b. *John did not a good job.
c. John did not do a good job.
d. John has done a good job.
e. *John does not have done a good job.

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1 A tenseless Aux would have the form defined by Aux ----> Inf. (Perf) (Prog). This case and the case represented by (11) can be collapsed into the following rule:

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Note that every S must contain either Inf or Tns as its Aux, because an S is necessarily either tensed or tenseless. This formulation, which takes Tns as a constituent of Aux, means that every S contains an Aux, which is necessarily either tenseless or tensed, containing Inf or Tns. Hence we need to revise our PSR1 so that the Aux constituent is obligatorily chosen: S ----> NP Aux VP, not S ---> NP (Aux) VP. Note also that Modal as an option is available only when Tns is chosen instead of Inf.

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2 For example, English morpho-phonemic rules provide that the Past Tense morpheme takes the phonemic form of /Id/ if the stem ends with /t/ or /d/; otherwise it takes the form of /t/ if the stem ends with a voiceless consonant; otherwise it takes the form of /d/. The morpho-phonemics of irregular verbs like had, has, was, went, etc. would be directly specified in the Lexicon. But at the syntactic level we still can consider them as consisting of a root form plus a suffix, e.g., have + {-ed}, go + {-ed}, etc. The fact that go + {-ed} is pronounced as went is provided by the morphological-lexical component of the Grammar.

3 The dummy, or auxiliary, use of do should be distinguished from the main verb do. The main verb do means "to perform, act, execute, or carry out", etc., but the dummy verb is devoid of semantic content. Its sole existence is to serve the grammatical function of a place holder to which a Tns affix can be attached. In the sentence Did he do the job? the sentence-initial did is used as an auxiliary (dummy), and the sentence-internal do is the main verb.

4 These sentences are ungrammatical with the dummy do, did, does each pronounced with normal (reduced) stress. They are grammatical only if they are emphatically stressed. We exclude emphatic sentences from consideration.

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