6.1 Elementary node relations

Since syntax graphs are two-dimensional objects, we need two operators to express the spatial relations. We simply take the nomenclature from linguistics, and call the vertical dimension the dominance relation and the horizontal dimension the precedence relation.

Labelled direct dominance

The symbol > means direct dominance. It is further specified by an edge label, for example HD. This means that labelled direct dominance is expressed by e.g. >HD. The constraint that an edge which is labelled HD leads from node #n1 to node #n3 (or that #n3 is a direct HD-successor of #n1) is written as follows:

#n1 >HD #n3

As a more comprehensive example, the following labelled dominance constraints encode the vertical dimension of the tree in the graph presented below. Note that labelled dominance is a relation among nodes, not a function like it is the case for feature structures. This means that there may be more than one edge with the same label leading out of one mother node, cf. the NK-edges in the presented graph.

#n1 >SB #n2
#n1 >HD #n3
#n2 >NK #n4
#n2 >NK #n5

Figure: A simple syntax graph

On the basis of the directed edges, which are defined by the dominance relation, the nodes of a syntax graph in the corpus annotation are classified in the following manner:

Inner nodes (nonterminal nodes)

Nodes with outgoing edges, i.e. nodes with children, are called inner nodes or nonterminal nodes. In the presented figure only the nodes #n1 and #n2 are inner nodes.

Leaf nodes (terminal nodes)

Nodes without successors are named leaf nodes or terminal nodes. For example, the nodes #n4, #n5, and #n3 are the leaves of the tree in the presented figure.

Direct precedence of leaf nodes

A syntax graph is not only defined by constraining the vertical arrangement of its nodes, but also by the horizontal order of its leaf nodes, i.e. by the precedence relation among the leaves. We use the . symbol to represent direct precedence, since it serves as the concatenation operator in some programming languages. Now, the horizontal dimension of the tree in the presented figure is determined by the two precedence constraints:

#n4 . #n5
#n5 . #n3