In many linguistic theories, a `head' of a construction plays an important role. For example, heads of a construction determine what other parts the construction may have. Furthermore, heads carry the features associated with the construction as a whole (such as case, agreement). The notion `head' plays an important role in grammatical theories as diverse as Government and Binding, (Xbar theory); Generalized Phrase Structure Grammar (the head-feature convention); and Head-driven Phrase Structure Grammar.
A headed TAG is a TAG in which each elementary tree is a headed tree. As an example of a headed TAG, consider figure 2. For each non-terminal node in a headed tree it is specified which daughter is the head of that tree. In the examples I use arrows to indicate the head-daughter of a local tree. The notion `head-corner' is defined as the reflexive and transitive closure of the head relation. For example, in the terminal symbol `saw' is a head-corner of the root node. Similarly, in , the foot node is a head-corner of the root node. In talking about `the' head-corner of a tree , I refer to the unique terminal t in such that t is a head-corner of .
I define a parser for headed and lexicalized TAGs for which the following two constraints hold:
The constraints reflect how I want to use headed TAGs in a head-corner parser. In this parser processing will proceed essentially in an anchor-driven way for initial trees, and in a foot-driven way for auxiliary trees. The notion `head' generalizes the two cases, and is also meaningful in order to define an order of proceesing for sub-trees of elementary trees that do not contain an anchor or a foot node.
The parser proceeds anchor-driven because we want to make use of the fact that elementary trees are lexicalized. The parser proceeds foot-driven in order to avoid a problem that otherwise occurs in bidirectional parsers (cf. discussion below).