Grammars and Constituency Structure › Phrase Structure and Tree Geometry

A parse tree is an ordered tree, which means the left-to-right order of children matters. That order is what connects the tree to the original token sequence: the yield of a parent is the concatenation of its children's yields in order. Reversing two children can therefore change the token sequence even when their labels and dominance relations remain the same. Order is part of the representation, not an afterthought.

Several structural relations are useful when discussing trees:

• Dominance: A node $A$ dominates a node $B$ if $B$ is a descendant of $A$, including $A$ itself in the reflexive case. The root dominates every node.
• Immediate dominance: $A$ immediately dominates $B$ if $B$ is a child of $A$.
• Precedence: A node $A$ precedes a node $B$ if every leaf dominated by $A$ comes before every leaf dominated by $B$ in the yield.
• Yield: The yield of a node is the sequence of terminal leaves it dominates. In a constituency tree, the yield of every node is a contiguous span of the sentence.
• Head: Under a head-selection convention, many phrase types have a distinguished head child. The parent's lexical head is inherited from that child: usually a noun in an NP and a verb in a VP. In $NP \to NP\ PP$, for example, the head child can be the inner NP while the headword lies deeper in the tree. For ordinary compositional phrases, heads contribute category and lexical meaning.

Under the reflexive definition above, dominance is a partial order. For nodes with nonempty yields, precedence is a strict partial order: it is transitive and irreflexive, so a node does not precede itself. They let us talk about structure without constantly referring to the original token positions. Immediate dominance is the local relation that grammar rules license. If a node labeled VP immediately dominates a V and an NP, then the rule $VP \to V\ NP$ must be in the grammar. Precedence tells us how sister constituents are ordered. The yield connects the abstract tree back to the concrete sentence.

The head relation is not built into the bare definition of a CFG. A CFG rule such as $NP \to Det\ N$ does not formally say that N is the head. Linguists often annotate headedness separately. But headedness is why constituency and dependency grammar are not as far apart as they first appear. A dependency tree makes the head-dependent relations explicit. A bare constituency tree does not identify head-dependent links by itself. Given additional head-selection conventions, you can derive a dependency representation from many constituency analyses.

An ordinary ordered CFG tree gives each node a contiguous substring as its yield. It therefore does not directly represent a constituent whose words are separated by material outside that constituent. Some linguistic analyses use discontinuous constituents; treebanks may instead introduce empty categories and links to represent displaced material. This continuity property should not be confused with dependency projectivity, which concerns head-dependent links over token positions and will be defined in the next chapter. Head conventions and treatment of empty categories matter when converting between the representations.

A parse tree has a yield, a root, nonterminal nodes, and production rules that license each local configuration. Parsing searches for a tree whose root is the start symbol, whose terminal leaves are the input tokens in order, and whose local configurations are licensed by the grammar.