A third property of X-bar theory is that structures are endocentric.
The LCA derives this eVect as well. Consider the trees in (29):
()
(a)
*
K (b)
*
K
JL JL
j
MP
j
MP
QR Q
RS
qr q
r T
t
Assume that L, M, and P are all maximal categories. L is unheaded in
both cases. Regardless of whether P (or M for that matter) is complex
(29b) or not (29a), M asymmetrically c-commands R, and P asymmet-
rically c-command Q, so both hq, ri and hr, qi are in d(A). Unheaded
structures will necessarily result in cases where a conXicting ordering
results. This rules out traditional categories like the unheaded S node,
and the kind of unheaded structures found commonly in LFG with
verb displacement. It also rules out ternary branching structures.
8.3.3 Adjunction
The discussion in the last section shows that several basic properties of
X-bar theory appear to follow from the LCA, although they are at least
inconsistent with the Speas–Fukui derived notions. But the LCA also
has a surprising property that appears to be undesirable. A careful look

is the two segments taken together. This can be seen in the abstract tree
in (30). Each of the XPs is taken as a segment of the larger XP category.
Individually the segments do not count as categories for the purposes
of calculating c-command in binding and scope interactions (May
1985).
()XP segment
XP category
12
YP
i
XP segment
WP …t
i
…
With this structure in place we can explain how speciWers and adjuncts
are allowed in Kayne’s system. First we require an extra stipulation on
c-command as given in (31) and (32). (These deWnitions are in the
spirit of May’s 1985 proposal):
(31) A c-commands B iV
(a) A and B are categories;
(b) A excludes B;
(c) every category that dominates A dominates B.
12 Notice again that this kind of structure is impossible in a Speas-style analysis, as there
is no primitive XP to be split into two segments. Only the topmost element would count as
an XP. For a critical look at Chomsky Adjunction, see Chametzky (1994).
set-theoretic constituency 151
(32) X excludes Y iV no segment of X dominates Y.
The idea here is that segments do not c-command elements which are
dominated by a distinct segment of the category they belong to. So
consider the tree in (33), where M (a phrasal level category is in an

c-commandsW. Thismeans that thepairs hw, ri, hw, ti and hr, wi, ht, wi are
152 controversies
in d(A).13 So a phrase adjoined to a head is unlinearizable. By contast,
consider the tree in (35), where a head is adjoined to a head:
()L
MP
UMRS
umrT
t
In this tree, U (surprisingly) c-commands P and Pc-commandsU,sothe
relation is symmetric. This means that the Antisymmetry relations are:
(36) A ¼ {hU, Mi, hU, Ri, hU, Si, hU, Ti, hM, Ri, hM, Ti, hR, Si,hR, Ti}
d(A) ¼ {hu, mi, hu, ri, hu, ti, hm, ri, hm, ti, hr, ti}
Neither hP, U i nor hU, Pi is in A, so it is not ruled out the same way as
(34); there is no contradictory ordering between u and r or t.
Kayne’s Antisymmetric approach also predicts that neither multiple
adjunctions nor multiple speciWers will exist (cf. Ura 1994). In the
following tree M and L should be taken either as multiple speciWers
or multiple adjunctions:
()U
P
LP
KM P
k QR S
qr T
t
Because the node not excluding all of L, M, R is U, it follows that
M asymmetrically c-commands K, and L asymmetrically c-commands Q.
13 A ¼ {hU, Mi, hU, Ri, hU, Si, hU, Ti, hM, Ri, hM, Si, hM, Ti, hR, Ti, hP, Wi},
d(A) ¼fhw, mi, hw, ri, hw, ti, hm, ri, hm, ti, hr, ti, hr, wi, ht, wig

suspect theory)
If we take scope to be an eVect of c-command, then we accept that the right-most post-
head modiWer must c-command elements to its left in violation of the LCA. One can
construct a derivation that gets around this by doing massive movements, but this does
seem very suspect.
154 controversies