Translating reentrancies

The discussion of reentrancies in relation with the definition of the p-parsing problem in the foregoing chapter (section 2.4) is not without ramifications for the organization of a transfer grammar and the definition of semantic structures. Some constructions such as control verbs and relative clauses may be represented using such reentrancies (essentially as in LFG's f-structure); for example

may be represented by an argument structure where the first argument of `try' is reentrant with the first argument of `shoot', cf. :

$$\avm{\mbox{\it sort}: \mbox{\rm binary} \\ \mbox{\it pred}... ...x{\rm whisky\_priest} \\ \mbox{\it num}: \mbox{\rm sg} } } }$$

The translation of such argument structures to Dutch equivalents can be defined as in the following rule in matrix notation:

In this rule the equality representing the control relation is explicitly mentioned for two reasons. The first reason simply is that, given the definition of the p-parsing problem, transfer will not produce anything without explicitly mentioning the reentrancy! The second reason is, that we do not want to translate the two noun phrases in isolation, but rather we want to obtain the same translation for both arguments. These two problems are now explained as follows.

Suppose we did not explicitly mention the reentrancy in the transfer rule. In that case, one of the signs defined by the transfer grammar has the leftmost feature structure in the following figure as the value of its gb label (leaving the sort attribute out for reasons of space):

On the other hand, the gb value of the input for transfer would be the rightmost feature structure. The definition of the p-parsing problem (12) requires that the constraints on the gb path should be equivalent. However, the second constraint has more solutions than the first constraint (and hence is not equivalent) because the first constraint requires that the paths X₀ arg1 and X₀ arg2 arg1 be mapped to the same feature graph, whereas solutions of the second constraint may map these paths to different feature graphs. Hence transfer does not produce a solution if the reentrancy is not `reproduced' in the transfer grammar.

Even if we were to allow the p-parsing problem to produce translations in the case discussed above this would result in some (practical) problems. Suppose indeed that the p-parsing problem were relaxed in order to ignore reentrancies. In this case the transfer grammar might be written without mentioning the reentrancy. However, this is also not what we want: the translation of the arg1 and the embedded arg1 should clearly be the same. Note that the translation of `soldier' into Dutch can be both `soldaat' or `militair'. If the reentrancy is not mentioned the transfer grammar might also produce the corresponding Dutch semantic representation:

$$\avm{ \mbox{\it sort}: \mbox{\rm binary}\\ \mbox{\it pred}... ...\rm whisky\_priester} \\ \mbox{\it num}: \mbox{\rm sg} } } }$$
In most cases the monolingual grammar fails to relate such representations to an utterance, and the system may eventually come up with the appropriate translation as well. However, it is not clear that the monolingual grammar can always be used as a filter for such ill-formed structures. Furthermore such a generate-and-test approach is grossly inefficient.

Note though that unbounded reentrancies can be translated directly in case the reentrancy is between variables. Suppose that the representation for control verbs is not the one shown above, but rather the following (cf. chapter 1):

$$\avm{\mbox{\it sort}: \mbox{\rm binary} \\ \mbox{\it pred}... ...x{\rm whisky\_priest} \\ \mbox{\it num}: \mbox{\rm sg} } } }$$
where I introduce the sort `refer' as a special sort of argument structure. In this case, the reentrancy is only between `variables' and not between `structure'. Hence, it suffices to simply state that the value of the attribute `index' translates as itself, eg. in bilingual lexical entries which translate nullary argument structures:

$$\mbox{\it sign}(\avm{ \mbox{\it gb}: \avm{ \mbox{\it sort}... ...\it num}:\mbox{\rm Num}\\ \mbox{\it index}: \mbox{\rm I}}}).$$
What remains to be done is to define the following rule for argument structures of type `refer':

$$\mbox{\it sign}(\avm{ \mbox{\it gb}: \avm{ \mbox{\it sort}: ... ...ort}: \mbox{\rm refer}\\ \mbox{\it index}: \mbox{\rm I}}}) .$$
Hence if we can limit the need for reentrancies in semantic structures to reentrancies between variables, then the problem disappears.