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.