[This draft corresponds roughly to P.K.'s lectures of January 29 & 31, 1996, on Head Principles and Headed Constructions. There are some slight differences in the formulation of some of the constructions from the handout we used in class - nothing major, but you might like to compare this outline with that handout.]

We want to review and expand our treatment of some of the main constructions of English considered last semester. In particular, there are two important families of constructions which share the property of including exactly one daughter marked 'comp head'. While these two families of constructions differ from each other in important respects, they are alike in being headed, that is, having a head daughter and one or more non-head daughters. Along with the detailed specification of the constructions in each of the two families, we will be concerned below with three general principles governing all such headed constructions.

The first family is typified by what we called last semester the Phrasal Verb Phrase (PVP) construction and will now call the V-Comp (Verb [Plus] Complement(s)) construction. The abstract construction inherited by each member of this family is called the Head-Complement (H-Comp) construction. ("Family" is not a technical term; a loose metaphor of 'common inheritance' is intended.) Each construction in this family consists of a lexical head followed by either (a) all its non-subject complements (e.g., V-Comp: ate the pizza) or (b) all its complements (e.g., Inverted Clause: Did Rex eat the pizza? NB, here Did, not eat is the head in that we will treat all auxiliary verbs as ordinary raising verbs which take a single verbal complement; that is, a phrase like was eating is treated as structurally parallel to a phrase like began eating.

The second family is typified by the Determination construction of last semester, which we rename the Specifier-NP (Spec-NP) construction. The abstract construction inherited by all the members of this family is called the Specifier [Plus] Headed-Phrase (Spec-XP) construction. Each construction in this family consists of a right daughter which is 'role head' and a left daughter marked 'role spec'. The right (head) daughter is not specified with respect to lexicality. Generally speaking, a construct of the H-Comp family, can - but need not - serve as the right (head) daughter of a construct of the Spec-XP family. Those familiar with X-bar theory will recognize in this interaction the standard X-bar configuration:

CG, unlike approaches including the X-bar theory, does not hold that this configuration always obtains. CG does not countenance empty categories and also does not assume binary branching (in particular, not of H-Comp structures). CG sees a configuration such as the following (essentially the same as the one above, but with different labels) as a frequently occurring, but not exceptionless, pattern of English.

In theories of the GB family, on the other hand, the subject of a sentence like Mud is soft, will contain empty categories since mud is the only audible thing available to fill the terminal constitutents Spec X, Xo, and X".

Head Principles:

  Many of the constructions in most, possibly all, languages are headed, a fact which reflects the pervasiveness of the valence requirements of individual lexical items. However, probably no language entirely lacks headless constructions. (Coordinated structures (Sue and the cat) present a possibly universal example of non-headed structures.) By noting those principles which govern all headed constructions we capture the generalizations inherent in these constructions. We would like it to turn out that our head principles are universal and that the abstract constructions, H-Comp and Spec-XP, represent broad typological properties of English.

At the same time, by abstracting and stating separately the headedness principles, we simplify the formal representation of the constructions. As you will recall, the diagrammatic representation of PVP given last semester was rather complex. For convenience it is repeated below.

Phrasal Verb Phrase (PVP) Construction
Figure 13 (from Chapter 5 of Construction Grammar, 1995)

Once having stated the properties common to all headed constructions, we will find that little needs to be said about this construction beyond the fact that its head is verbal and that it is of the head-before-complement(s) subclass (as against the specifier-before-head subclass). The following three principles apply to all headed constructions.

I. HEAD FEATURE PRINCIPLE: The head values of the mother and head daughter unify.

II. SUBSET PRINCIPLE: Set values of the head daughter are subsets of corresponding values of the mother. (We assume, without justification here, that sem values are sets. Hence, by the Subset Principle, not only the valence value but also the sem value of the head daughter is a subset of the corresponding value of the mother.)

III. VALENCE PRINCIPLE: Each comp daughter unifies with a valence element of the mother.

Head-Complement Constructions

The family of head-complement constructions is displayed as an inheritance hierarchy with the abstract H-Comp construction at the top. Inheritance is indicated by downward lines connecting constructions. Left parts of reconstructible paths are not shown.

The H-Comp construction provides for a multi-daughtered constitutent structure of which the left daughter bears 'role head' and is stipulated to be lexical and non-maximal. The Kleene plus on the right daughter box indicates one or more non-head daughters, each bearing 'max +' and 'role comp'.

We consider the three principles in turn, noting in particular their effect in the simplification of V-Comp (formerly PVP).

The Head Feature Principle insures that the values for cat, lexh, and other head features (verbal morphology, etc.) are shared by mother and head daughter. In the case of V-Comp, this spares us the necessity of including the head feature in the construction.

The Subset Principle provides for inclusion in the semantics and valence values of the mother the respective values of the head daughter. For V-Comp, this allows us to dispense with the single and double-shafted arrows and associated numerical variables; in fact it allows us to dispense with all explicit mention of the semantics and valence features - except as stipulated in the Non-Local Subject construction, which V-Comp also inherits.

The Valence Principle insures that all complement daughters are licensed by valence elements of the mother, hence that the Kleene expansion on the right daughter box doesn't permit illicit constituents. (The need to specify (parts of) the unspecified sem and phon values that come with minimal lexical predicators will assure that we have all the constitutents we need in the licensed phrase.) For V-Comp in particular, the Valence Principle also permits us to eliminate the '#i' notation of PVP. Along with the Non-Local Subject construction, the Valence Principle lets us dispense with mention of any of the internal structure of the mother's valence. We eliminate the need for the 'loc +/loc -' distinction in eliminating the '#i' mechanism: valence elements not realized as daughters of VP receive role values distinct from 'comp' in the constructions which license their instantiation.

The Maximality construction bequeaths to INV, V-Comp and A-Comp the feature 'max +' in the external syntax. N-Comp structures (beginning of the story, construction of unstable buildings by unscrupulous contractors) must be able to accept 'max -' for the familiar reason that recursion of Spec-N ('Determination') must be blocked (*the the girl, *the Timothy). Recognizing now a Spec-P construction (which wasn't considered last semester), we block recursion of it in the same way, by making the right daughter of a Spec-P construct 'max -'. We'll come back to this below. For now it suffices to note that P-Comp doesn't inherit Maximality for the same reason N-Comp doesn't: both license structures that may occur as right daughters of a Spec-XP construct whose right daughter is specified 'max -' to block recursion.

The Non-Local Subject construction bequeaths to its heirs (V-Comp, A-Comp, P-Comp, and N-comp) the property that no comp daughter in a licensed construct realizes a subject gf. It is perhaps arguable whether all nouns have subjects, but in the predicative ones, which certainly do ([Kim is] a skilled practitioner of minimalism.), the subject requirement is never realized as a right sister to the predicating noun. Of the five ground-level constructions of the H- Comp family, only INV (Inverted Clause) allows the subject to be realized as a comp daughter.

Taking up the ground-level H-Comp constructions one by one, consider first our old friend V-Comp. Looking at the inheritance hierarchy we see that V-Comp itself need only stipulate 'cat v' and 'srs -', the remainder of its properties deriving either from inheritance of H-Comp, Maximality, and Non-Local Subject or from Principles I-III. Accepting the redundancy of restating properties inherited from H-Comp, Maximality and Non-Local Subject, a relatively long-winded version of V-Comp can be given (which does not, however, restate the properties deducible from Principles I-III):

Long-Winded V-Comp

Taking into account the fact that Maximality and Non-Local Subject inherit H-Comp (and assuming the head principles), we can give a succinct version of V-Comp:


Examples of A-Comp are ordinary adjective phrases containing complements: adept at minimalism, fond of HPSG, overflowing with sea water, easy for you to say. Such adjective phrases never (or maybe almost never) appear pre-nominally in English: *an adept at minimalism student, *the overflowing with sea water barrel, *three fond of HPSG speakers, ??an easy to understand argument. The marked infinitive complements of adjectives like hard and easy have numerous properties that differentiate them from the P-Comp complements of adjectives like adept, fond, and overflowing.

As noted briefly above, we want the P-comp construction to allow its mother to be unspecified for maximality. So, unlike V-Comp and A-Comp, P-Comp doesn't inherit Maximality. The reason for this is that P-Comp structures are often specified, as in [[spec 3 miles] [head outside of town]]. We must block recursion in Spec-P structures, such as *[[[spec far] [head [spec 3 miles] [head outside of town]]]. This will be done by marking the right daughter of Spec-P 'max -' and the mother of Spec-P 'max +'. While the P-Comp construction has to allow its constructs to unify with the 'max -' right daughter of Spec-P, it must also let them unify with a 'max +' slot, such as a comp constituent of a P-Comp construct (put the toy in the cupboard). So a P-Comp construct has to be unmarked for maximality. (Ordinary lexical prepositions will similarly be unspecified for maximality: put it [outside], put it [pretty far outside], put it [outside of the corral], put it [way outside of the corral].)

The N-Comp construction is like the P-Comp construction except for having category N.

It appears that N-Comp constructs can have more than one complement: [[head invasion] [of the earth] [by martians]], as can V-Comps: [[head threw] [me] [the ball]] and A-Comps: [[head easy] [for boys] [to sing]], while P-comp constructs can apparently have only a single complement: [[head between] [Sproul Plaza and Telegraph Avenue], [[head between] [two campus landmarks], *[[head between] [Sproul Plaza] [Telegraph Avenue]]. It is probably not necessary, however, to reflect these differences in stating of the various H-Comp constructions, since these properties of the corresponding constructs are more likely to be attributable either to limitations on the minimal valences of prepositions or to special features of the linking constructions applicable to prepositional valences. Notice that (2) is as bad as (1), presumably for the same reason. That reason can't be that the P-Comp construction only allows one comp sister to the head P, since (2) doesn't violate that stricture.

(1) *Sather gate used to be between Sproul Plaza Telegraph Avenue.

(2) *What used to be between Telegraph Avenue?

The Inverted Clause (INV) construction is the only living heir of H-Comp that does not inherit Non-Local Subject. As the diagram for INV shows, the subject is realized directly after the head, which is a finite auxiliary. Constructs licensed by INV always contain the finite auxiliary head and the subject, and often but not always a VP complement of the auxiliary. See the examples at the end of this outline.

Specifier-Head Constructions

In the ancestral Spec-XP construction there is no specification for maximality in the head (right) daughter. We could have written 'max [ ]' to draw attention to that matter, but left it out for the sake of visual simplicity.

Individual Spec-XP Constructions

In the Spec-VP (old S-P) construction the right daughter is marked 'max +', reflecting the maximal character of VPs. Recall that phrasal and non-phrasal VPs can be conjoined: cooked the food, sat down and ate. Phrasal VPs can be fronted: She said "Jump" and jump three feet straight in the air he did, pronominalized by do so,(I wouldn't leave but she did so), and ellipted: I wouldn't help the victims but she did [help the victims]. Non-recursion of this construction must be blocked, as with any Spec-XP construction. This is accomplished, not via opposed maximality markings on right daughter and mother, but by opposed srs markings on right daughter and mother. The unification of the subject with a valence element of the mother must be stipulated in Spec-VP, unlike V-Comp for example, because this unification does not follow from Principle III in the case of Spec-VP; Principle III only covers comp daughters. This difference in formal representation between Spec-VP and the H-Comp constructions is desirable: the Valence Principle functions to prevent overgeneration by unrestricted Kleene expansions in H-Comp constructs; in Spec-VP there is no Kleene expansion to restrict.

The Spec-NP construction replaces the old Determination construction. The head (right) daughter can accept both a simple noun and an N-Comp construct. Each of these is inherently unspecified for maximality and so can unify with the 'max -' specification on the head daughter of Spec-NP (or alterntively serve as an argument on its own, e.g., as a comp in V-Comp or as spec in Spec-VP (= subj). We assume that there is a construction, called Determiner (Det), which constructs determiner phrases, capable of serving as the spec (left) daughter of Spec NP. We do not know how to formulate this construction. It's proper formulation is undoubtedly heavily dependent on semantics, and formulating it should be an interesting topic of research - say for one of your term projects. Constructs of this construction will include such expressions as the following:

Doubtless, some classes of determiner expressions have been left out of this quickly constructed list. This is an area of English grammar shrouded in mystery.

The Spec-P construction is one that we did not consider last semester. It deserves more extensive discussion than can be given here. Briefly, many spatial and temporal expressions that are commonly considered to be ordinary PPs (that is, P-Comps), such as


can be specified by measure phrases, yielding espressions like


The Spec-P construction accepts P-Comp expressions such as those in (3) as right daughters and precedes them with a specifying measure expression. It appears, perhaps even more clearly than in the case of the specifier of N-Comps, that semantic considerations largely determine what can serve as an acceptable measure expression for the spec (left) daughter of Spec-P.

Some Examples Licensed by These Constructions

H-Comp Examples:

V-Comp (Old PVP): bought a fish, elapsed suprisingly fast, may have been eaten by a bear, have been eaten by a bear, been eaten by a bear, eaten by a bear

P-Comp (Old PP): on Friday, under the rug, over Chicago

A-Comp (Old AP): eager to serve, aware of their presence, interesting to everyone, good at chess

INV: Are you there?, Where did you put the frying pan?, Am I?, Who is he?, Had you been there ... , Never will I leave you.

N-Comp: pile of books, invasion of the island before dawn by pirates

Spec-XP Examples:

Spec-VP (old S-P): Jill shrugged, Lettuce loves to be eaten by rabbits

Spec-NP (old Determination): The boys, three girls, all three of those children, my hat, the King of England's hat, the King of England's old hat, several boys from Boston, the man I saw yesterday

Spec-PP : three miles from Boston, a long time after the end of the race, fifteen minutes ago, far away