In (1), no node has more than one branch emanating from it. The
nodes in such a simple tree are related to one another by a single
relation, the dominance relation. Dominance is a theoretical
primitive; in other words, it is an irreducibly basic notion, comparable
to a mathematical concept like point. Dominance is represented
graphically in terms of top-to-bottom order. That is, if a node A
dominates a node B, A appears above B in the tree. In (1), for
instance, NP dominates N and Zelda, and
N dominates Zelda. The node that dominates all other
nodes in a tree, and is itself dominated by none, is called the root
node.
Dominance is a transitive relation (in the logical sense of
the term, not the grammatical one). In other words, if A dominates B,
and if B dominates C, then it is necessarily the case that A dominates
C.
Does a node A dominate itself? If the answer to this question is
defined to be yes, then the dominance relation is reflexive
(again, in the logical sense of the term, not the grammatical one); if not,
then it is irreflexive. In principle, it is possible to build a
coherent formal system based on either answer. From the point of view of
syntactic theory, it is preferable to define dominance as reflexive because
it simplifies the definitions of linguistically relevant, derived relations
such as c-command and binding.
An important subcase of dominance is immediate dominance.
This is the case where the two nodes in question are connected by a single
branch without any intervening nodes. More formally, immediate dominance
is defined as in (2).
Unlike dominance, immediate dominance is not a transitive relation.
This is apparent from even a simple structure like (1), where
NP immediately dominates N, and N immediately
dominates Zelda, but NP does not immediately dominate
Zelda.
In general, trees are more complex than the very simple case in (1),
and they contain nodes that have more than one branch emanating from
them, as in (3).
In such trees, two nodes are related either by dominance or by a
second primitive relation, precedence. Precedence is
represented graphically in terms of left-to-right order. Dominance and
precedence are mutually exclusive. That is, if A dominates B, A cannot
precede B, and conversely, if A precedes B, A cannot dominate B. Like
dominance, precedence is a transitive relation, and just as with
dominance, there is a nontransitive subcase called immediate
precedence. The definition of immediate precedence is analogous to
that of immediate dominance; the term dominates in (2) is simply
replaced by precedes. The difference between precedence, which is
transitive, and immediate precedence, which isn't, can be illustrated in
connection with (3). The first instance of Noun (the one that
immediately dominates secretary) both precedes and immediately
precedes TrVerb, and TrVerb in turn both precedes and
immediately precedes the second instance of NounPhr (the one
that dominates the letter). The first instance of
Noun precedes the second instance of NounPhr, but not
immediately.
Certain relations among nodes are often expressed by using kinship
terms. If A dominates B, then A is the ancestor of B, and B is
the descendant of A. If A immediately dominates B, then A is
the parent of B, and B is the child of A. If A
immediately dominates B and C, then B and C are siblings.
Often, the female kinship terms mother, daughter, and
sister are used for the corresponding sex-neutral ones. In
(3), Sentence is the ancestor of every other node in the tree.
Secretary is the child of the first Noun. The first
NounPhr and VerbPhr are sisters, and so are
TrVerb and the second NounPhr, but drafted
and the second instance of the are not (they don't have the
same mother). Notice, incidentally, that syntactic trees are
single-parent families. Most theories of syntax do not allow nodes
with more than one parent.
Depending on the number of daughters, nodes are classified as either
nonbranching (one daughter) or branching (more than
one daughter). A more detailed system of terminology distinguishes
nodes that are unary-branching (one daughter),
binary-branching (two daughters), and
ternary-branching (three daughters). Nodes with more than
three daughters are hardly ever posited in syntactic theory. Indeed,
according to an influential hypothesis (Kayne 1984),
Universal Grammar allows at most binary-branching nodes. According to
this hypothesis, it is a formal
universal of human language that the number of branches associated
with any node cannot exceed 2.
Some node A exhaustively dominates two or more nodes B,
C, ... iff (= if and only if) A dominates all and only
B, C, ... For instance, A dominates the string B C in (4a-c),
but exhaustively dominates it only in (4a). A doesn't exhaustively
dominate B C in (4b,c), because it runs afoul of the only condition
(it dominates too much material). A also fails to exhaustively dominate B
C in (4d), because it runs afoul of the all condition (it dominates
too little material).
As is evident from (4b,c), dominance is a necessary but not a
sufficient condition for exhaustive dominance.
Notice that the notion of c-command is defined in terms of dominance
and makes no mention of precedence. It is tempting to assume that
c-command logically implies precedence, or vice versa, but it is a
temptation to be firmly
resisted.2 < Notice further that c-command is not necessarily a symmetric
relation. In other words, a node A can c-command a node B without B
c-commanding A. For instance, in (3), VerbPhr c-commands
secretary (because the first branching node dominating
VerbPhr, namely Sentence, dominates secretary),
but not vice versa (because the first branching node that dominates
secretary, namely the first instance of NounPhr, doesn't
dominate VerbPhr).
Although c-command isn't necessarily a symmetric relation, it is
possible for two nodes to c-command each other. This is the case when
the two nodes are sisters. Syntactic sisterhood is also known as
mutual c-command or symmetric c-command.
The coindexing referred to in (6b) can arise either through coreference or through
movement. These two cases are illustrated in (7).
If A binds B, B is bound by A (not bounded !). If A
does not bind B, B is said to be free. B is free in C if
there is no A that binds B, with both A and B dominated by C.
Precedence
Derived terms and relations
Kinship terminology
Branching
Exhaustive dominance
C-command
A derived relation that is central to syntactic theory is
c-command,1
which is defined as follows.
Binding
An important derived relation that is defined in terms of c-command is the
notion of binding.
Notes
1. The odd name c-command is
short for 'constituent-command' and reflects the fact that the c-command
relation is a generalization of a relation (now obsolete) called
command, defined as in (i) (Langacker 1969:167).