In this section, we discuss some possible extensions of the TIGER language and the reasons why we have not adopted them (yet).
There are already implicit ('don't care') variables for edge labels, i.e. the unlabelled dominance operator > and the dominance wildcard >* etc. If explicit variables for edge labels were available, the user could require co-reference of edge labels. To us it is unclear what kind of computational complexity will be introduced by this additional expressivity. And furthermore, there is a work-around: Since the number of edge labels (grammatical functions) tends to be rather small, it does not seem too inconvenient to define appropriate templates which enumerate pairs of edges with the same labels.
Negation on the level of graph descriptions seems somewhat difficult to be grasped conceptually. Since it would have to be pushed down to the level of node relations and feature values anyway, and there is negation available on these lower levels, this might give enough expressivity.
You might be tempted to state the following expression to find trees which are rooted in a VP, but which do not contain any NP:
[cat="VP"] >* [cat=(!"NP")]
But in the TIGER language, this query has the interpretation: 'Find a (sub-)graph rooted in a VP with at least one inner node #n which is not labelled NP':
exists #child: ([cat="VP"] >* #child:[cat=(!"NP")])
The desired constraint of finding a graph which does not contain any NP requires universal quantification and the implication operator (i.e. negation of graph descriptions):
exists #node: forall #child: ( (#node:[cat="VP"] >* #child) =>
(#child:[cat=(!"NP")])
)
The use of the universal quantifier causes computational overhead since universal quantification usually means that a possibly large number of copies of logical expressions have to be produced. For the sake of computational simplicity and tractability, the universal quantifier is (currently) not part of the TIGER language.