If rule ( 
) is chosen, then the selected element will be the verb
phrase, because it shares its semantics with the mother node. Using this
rule, the predictor will introduce instantiations of the rules (r 
),
(r 
) and ( 
). The latter one, however, has no body, so that it
can directly be used for completion. Completion with the former
introduced rule, will further introduce the same set of rules (modulo
restriction), which clearly brings a termination problem.
The basic problem for generation is that the empty head will receive most important information from the filler element, which however, cannot be determined as long as the base case is not found. In order to solve this problem, we have to take into account filler information at the time the empty head rule is predicted.
A first obvious solution
would be to redefine the rule that introduces the verb to be
argument to the slash value, i.e., to change rule ( ) such
that the verb and the verb phrase share the semantics. Now, our
selection function would choose the verb first, whose completion would
instantiate the verb phrase proper, so that
the above semantic expression can be handled by the algorithm to produce
the string ``heute erzaehlt peter luegen''.
The changed definition expresses that the semantics of the verb second is identical with the whole verbal phrase. In general however, the verb will not be the semantic head of the sentence, at least in the case of adverbial modifiers. Thus using the modification above, it would not be possible to process a sentence like ``heute erzaehlt peter gerne luegen'.
But then, we have to live with the original verb second rule. We now
present a solution which is similar to the one presented in
[Shieber et al.1990]. Our approach works as follows.
When the predictor is applied on a
selected element, that could predict the empty head rule, then after
unification with the (restricted) selected element but before the
new item is added to the agenda, we check whether we can
scan with the information of the filler (in our grammar, the value of
the V2 feature) a lexical entry. Since, the filler has been
instantiated with information from the selected element, this will only
be possible, if the generator has traversed the semantic expression
to the point of finding a verb. For a semantic expression like,
``heute(gerne(erzaehlen(peter,luegen)))'' this will be the case for the
partial expression ``erzaehlen(peter,luegen)'' but not for
``heute( 
)'' or ``gerne( )''. Only, if a matching filler can be
found, the thereby ``completed'' empty head rule will be added to the
agenda. This means, that the empty head rule will only be instantiated
(including subcategorization information) by genuine potential fillers.
The empty head can now serve as the base case for the recursive process
in the same way as it would for the lexical filler.
If we assume that the interface between the grammar and the uniform algorithm provides us with a predicate EMPTY-HEAD-P (which returns true if the current grammar rule is the empty-head rule) and function FILLER (which extracts the information from the filler), then the modified prediction rule is as follows:
One could criticise this approach because this solution raises the issue of tuning programs to treat specific problems as they are encountered. Clearly, if an analysis would be available, that is specified in the grammar rules (in the same sense, as we used the V2 feature to cope with empty heads in parsing), the specific modifications are no longer necessary.
In fact, [VanNoord1993] proposes a completely different analysis of the verb second phenomenon. In this analysis grammar rules may combine their daughters by more complex string operations, e.g., wrapping operations. However, the problem with van Noord's approach is that parsing cannot be performed on-line, because at least for the head-corner parser Van Noord's approach requires that the whole input string is known in advance. Thus his approach seems problematic for incremental processing. In this case a left-to-right scheduling combines more naturally with an incremental (and on-line) approach.