Abstract
| Josef van Genabith | Anette Frank | Michael Dorna |
|---|---|---|
| Dublin City University | Xerox Research Centre Europe | IMS, Universität Stuttgart |
| Computer Applications | 6, chemin de Maupertuis | Azenbergstr. 12 |
| Dublin 9, Ireland | F-38240 Meylan | D-70174 Stuttgart |
| +353+(0)1 704 5074 | +33+(0)4 76 61 50 37 | +49+(0)711 121 1367 |
| josef@compapp.dcu.ie | Anette.Frank@xrce.xerox.com | michl@ims.uni-stuttgart.de |
Proceedings of the LFG98 Conference
The University of Queensland, Brisbane
Miriam Butt and Tracy Holloway King (Editors)
1998
CSLI Publications
http://www-csli.stanford.edu/publications/
Abstract
We present a modular, lexicalized, reversible and ambiguity preserving approach to semantic-based transfer on sets of linear logic meaning and transfer constructors. In many cases, transfer on sets of meaning constructors (rather than on derived disambiguated meaning assignments) obviates the need for spurious multiple transfer on disambiguations. We concentrate on adjuncts and embedded head switching phenomena.
A set of meaning constructors induced by a 
-projection of an
f-structure [1] can be seen as an underspecified
semantic representation [12]. Different scopes
of quantifiers, modifiers, etc. are obtained via different deductions
from such a set of meaning constructors. Transfer on sets of meaning
constructors rather than on derived disambiguated meaning assignments
holds the potential to avoid the complexity of multiple (often
spurious) transfer on disambiguations.
To our knowledge the idea to formalize transfer rules in linear logic was first presented by Fujinami [5,6] in a somewhat different setting (Verbmobil). In his case there is no distinction between meaning language and glue language. Here we apply linear logic based transfer in a LFG framework. Sections 2 and 3 introduce the approach, Section 4 considers problematic cases of head switching. Section 5 concludes.
Consider the following f-structure associated with the German sentence Hans schwimmt :
![\begin{displaymath}
\left[\begin{array}
{@{}l@{\;}l@{\;}}\mbox{\scriptsize\sc SU...
...\\ \end{array}\hspace*{-2pt}\right]
\fbox {\footnotesize 1}
\, \end{displaymath}](img2.gif)
In the linear logic based semantics of [1] the following meaning constructors are used:
![\begin{displaymath}
\begin{array}
{ll}
hans: & \uparrow_{\sigma} \leadsto hans \...
...x}\circ$}\;\uparrow_{\sigma} \leadsto schwimmen(X) ]\end{array}\end{displaymath}](img3.gif){kind=small}
Instantiated to the semantic projections of the f-structure nodes above we get a set of meaning constructors Source :
![\begin{displaymath}
\mbox{\emph{Source}} = \left\{ \begin{array}
{c}
(f_{2})_{\s...
...$}\;(f_1)_{\sigma}
\leadsto schwimmen(X)]\end{array} \right\} \end{displaymath}](img4.gif)
Since (
, 
.
Let the set of instantiated meaning constructors for the English
sentence be referred to as Target . The task of transfer is to
relate the two sets Source and Target . This can be
achieved in terms of a set of linear logic ``transfer constructors''
Trans . In the forward direction, i.e. from Source to
Target, each transfer constructor in Trans relates a source
meaning constructor to a corresponding target meaning
constructor 
: 
. For the backward direction
the 
arrow is reversed (equivalently, its two arguments are
swapped): 
. For our simple example Source
and Target are related by:
![\begin{displaymath}
\mbox{\emph{Trans}} = \left\{ \begin{array}
{c}
\forall F ~[...
....4ex}\circ$}\;F_{\sigma}\leadsto
swim(X))]\end{array} \right\} \end{displaymath}](img12.gif)
Informally, below we will sometimes refer to particular transfer
constructors as in 
. Note that in each case the transfer constructors have wide scope
quantification over f-structure nodes. The f-structure nodes provide
the scaffolding for how meaning constructors can be put together in
derivations. Hence, we need to carry this information
over in transfer (otherwise constructors would not be connected in the
target meaning constructor set).
The general idea is that a transfer constructor set Trans is
used to rewrite a source meaning constructor set Source into a
target meaning constructor set Target . Strictly speaking, we do
not have separate source and target constructor sets (related by the
rewriting) but continuously rewrite 
by means of linear logic
deductions. Of course, the derived set
Target should be the set of meaning constructors associated with
the semantic projection of the target f-structure as obtained by
independent analysis (parsing) of the target string. In the simple
example discussed above this is indeed the case:
where 
is just like 
except that arrows relating source and target meaning
constructors are reversed.
generation retrieves
a matching lexical entry 
in the target grammar.
Matching spreads instantiated f-structure nodes in to
co-indexed f-structure nodes in the f-description parts 
in
lexical entires . The conjunction 
over such yields an f-description 
.Alternative matches may produce alternative . is then
passed on to standard f-structure generation
[9,13] which produces the target string.
![\begin{displaymath}
\begin{array}
{cc} \left[\begin{array}
{@{}l@{\;}l@{\;}}\mbo...
...ay}\hspace*{-2pt}\right]
\fbox {\footnotesize 1}
\, \end{array}\end{displaymath}](img23.gif)
The meaning constructor for adjuncts (cf. [2])
involves inside-out functional uncertainty 
to access semantic material induced by the adjunct
embedding f-structure:
![\begin{displaymath}
\begin{array}
{ll}
usually: & \forall P~ [ (\mbox{\scriptsiz...
...sc ADJN} \in\uparrow)_{\sigma} \leadsto usually(P)]\end{array} \end{displaymath}](img25.gif){kind=small}
From the meaning constructors associated with the English example sentence
![\begin{displaymath}
\mbox{\emph{Source}} = \left\{ \begin{array}
{ll}
1_e : & (f...
...$}\;
(f_{1})_{\sigma} \leadsto usually(P)]\end{array} \right\}\end{displaymath}](img26.gif)
we deduce the two readings
as required. The German target meaning constructors and deductions are completely analogous:
![\begin{displaymath}
\mbox{\emph{Target}} = \left\{ \begin{array}
{ll}
1_g : & (f...
...f_{1})_{\sigma} \leadsto normalerweise(P)]\end{array} \right\} \end{displaymath}](img28.gif)
It can be seen that the set Trans of transfer constructors
![\begin{displaymath}
\mbox{\emph{Trans}} = \left\{ \begin{array}
{cc}
1_t : & \fo...
...\;
F_{\sigma} \leadsto normalerweise(P))]\end{array} \right\} \end{displaymath}](img29.gif)
relates Source and Target : 
. Transfer on the set of
source meaning constructors carries over the ambiguity intact and
avoids multiple transfer on disambiguations.
Sections 3.1 and 3.3 have illustrated the basic idea. The reader may have noticed that as stated above, first, transfer constructors are massively redundant and second, there is nothing to guarantee that our deductions terminate in a set of target meaning constructors rather then in disambiguated target meaning assignments. These issues are addressed below.
The resource sensitivity of linear logic provides a natural setting to define transfer. In addition to providing a homogeneous framework for both the construction of and transfer on semantic representations in current LFG architectures we can exploit the resource sensitivity of linear logic to ensure that transfer exhaustively covers all source meaning contributions.
In order to be able to define transfer on underspecified
representations we need to relate corresponding sets of source
and target meaning constructors. If transfer is defined in terms of
linear logic transfer constructors (and linear logic deductions) we
need to ensure that transfer operating on a set of source meaning
constructors and a set of transfer constructors terminates in a
set of target meaning constructors. In other words, we need to
prevent transfer deductions from delivering disambiguated target
meaning assignments. As stated in the introductory sections above,
there is nothing to prevent transfer deductions to terminate in
completely disambiguated target meaning assignments. While this would
not deliver incorrect results it would defeat the very idea of
ambiguity preserving transfer on underspecified
representations. Termination in sets of target meaning constructors
can be ensured in a number of ways. Here we define a special
transfer connective 
and restrict application of
to linear implication elimination (linear modus ponens -
here in a natural deduction style format [11]) as its
only inference rule:
This together with the stipulations that (i) transfer deductions
may only be applications of elimination
(together with the required universal eliminations/introductions and
and 
equivalences), (ii) transfer constructors have
exactly one occurrence of as its main connective and (iii)
meaning constructors are not allowed to contain the connective, ensures that transfer terminates in sets of target meaning
constructors. In this scenario, transfer is a very simple and
restricted operation.
There is a further issue to be dealt with here: so far we have simply
assumed that in each of the transfer deductions we have at our
disposal exactly the set of transfer constructors relevant to
whatever is the current task at hand. This assumption was needed to
insure that transfer deductions consume both the source meaning
constructor set and the relevant transfer constructor set. Transfer is
complete once the two ``input'' sets are consumed. This begs the
question: how do we manage to obtain the set of transfer constructors
relevant to the task at hand in the first place? For a realistic
transfer scenario we will have to assume one large set Trans of
transfer constructors associated with a given pair of source and
target grammars. Furthermore, since, in all likelihood, transfer
constructors may be used more than once, we'll have to assume that all
transfer constructores are prefixed by the ``of course'' operator,
! , also known as bang . There are two possibilities to ensure
termination in sets of target meaning constructors in this more global
scenario. Given a local set of source meaning constructors
Source, obtained from analysing a source sentence, and the global
set of banged transfer constructors Trans , associated with a
pair of source and target grammars, we retrieve, at each stage of the
transfer deductions, one source meaning constructor , perform
Trans 
and collect the result, a
target meaning constructor in a new set Target . Transfer
into sets of target meaning constructors is completed once
Source is empty.
INPUT Source , Trans
OUTPUT Target
Target := 
REPEAT UNTIL Source =
BEGIN
Source := Source -
Trans
Target := Target 
END
An alternative is to simply tag transfer constructors to terminal
strings (i.e. the words - and thereby the lexical entries - in the
lexcion). In this way, relevant sets of transfer constructors tailored
to the task at hand can be constructed automatically during analysis
of the source input string. Given the constraints on and
the derivation will terminate in a set Target consisting
only of target meaning constructors.
The transfer constructors we have presented so far are massively redundant. We identify two types of redundancy:
First, transfer constructors of the form 
which relate identical source and target meaning constructors can be
dropped. In fact, 
is a simple tautology
in linear logic.
The second type of redundancy occurs when the source and the target
meaning constructors related by the transfer constructor have
left-common prefixes 
:
This transfer constructor matches a source meaning constructor 
to produce a target meaning constructor 
under linear modus ponens. We can achieve exactly the same
effect by reducing the transfer constructor to the more perspicuous
and combining this with the source meaning constructors under transitivity of linear implication (recall that
is restricted to linear modus ponens and
confined to single occurrences as main connective in transfer
constructors):
In fact, 
is a tautology in linear logic.
Assuming that we restrict to applications of transitivity
of linear implication, we can now collapse the set of transfer
constructors given in Section 3.3 above
relating the source and target meaning constructor sets corresponding
to Usually Hans suggests a restaurant and Normalerweise
schlägt Hans ein Restaurant vor to the much more readable:
As before, this set of transfer constructors relates underspecified
representations (sets of source and target meaning constructors) thus
obviating the need for multiple (and in this case spurious) transfer
on disambiguated representations. Unless explicitly indicated, in the
rest of the paper we will always give transfer constructors in the
compact, non-redundant form. Note that the compact transfer
constructors are still fully reversible: simply changing the direction
of in the set above provides ambiguity preserving transfer
from German into English.
Before concentrating on problems of structural mismatches with head switching, we briefly illustrate how this transfer approach deals with more unproblematic types of lexical transfer. One of the basic exercises in transfer is argument switching. A typical case is the translation of German mißlingen into French râter , as in Das Photo ist Hans mißlungen - Hans a râté la photo (Hans messed up/ruined the photo ), with the two f-structures
![\begin{displaymath}
\begin{array}
{cc} \left[\begin{array}
{@{}l@{\;}l@{\;}}\mbo...
...ay}\hspace*{-2pt}\right]
\fbox {\footnotesize 1}
\, \end{array}\end{displaymath}](img49.gif)
In the more redundant formalization of Section
3.3 the transfer constructor miß
lingen râter would have to rewrite the SUBJ
of mißlingen into the OBJ of râter , and its
secondary object OBJ2 into the SUBJ of râter . In
our more sparse formalization the transfer constructor miß
lingen râter reduces to:
From the set of instantiated meaning constructors and transfer constructors we derive the appropriate set of target meaning constructors:
![\begin{displaymath}
\left\{ \begin{array}
{c}
(f_{2})_{\sigma} \leadsto photo \\...
...gma}
\leadsto \emph{mi{\ss}lingen}(X,Y)] \end{array} \right\} \end{displaymath}](img51.gif)
The instantiated target meaning constructor (3.) correctly binds the meanings X and Y, which can be seen by comparison with the non-instantiated source and target versions, to be used in analysis and generation:
![\begin{displaymath}
\begin{array}
{ll}
$\emph{mi\ss lingen}$: & \forall X\forall...
...}\;\uparrow_{\sigma} \leadsto
$\emph{r\^ater}$(X,Y)]\end{array}\end{displaymath}](img53.gif){kind=small}
In the compact formalization of transfer constructors the transfer of simple argument mismatches - where an argument is syntactically realized by distinct grammatical relations in source and target languages - goes in fact unnoticed. Since transfer constructors operate on instantiated meaning constructors, the argument bindings carried through in transfer are sufficient to allow for instantiation of the appropriate grammatical functions in the target structure for generation.
The resource sensitivity of linear logic also fares well with another type of lexical transfer, exemplified by the pair commit suicide and its French translation se suicider . Here the meaning of a transitive support verb construction must be rewritten into the meaning of an intransitive verb. This is captured by consuming the second argument of commit in the following transfer constructor:
Just as in the fully structure preserving examples of Sections 3.1 and 3.3 the transfer constructors for lexical argument mismatches considered here are fully reversible.
The English translation of Hans schwimmt gerne is Hans likes swimming . These sentences are associated with the following f-structures:
![\begin{displaymath}
\begin{array}
{cc}\left[\begin{array}
{@{}l@{\;}l@{\;}}\mbox...
...ay}\hspace*{-2pt}\right]
\fbox {\footnotesize 3}
\, \end{array}\end{displaymath}](img55.gif)
Note that the German adverb gerne translates into a control verb
construction like in English. The f-structures associated with
the German and English sentences show structural misalignment (head
switching): in the German case the adjunct f3 is embedded inside
the main f-structure f1 with
as its governing
while in the English case the corresponding f-structure
f1 governed by 
is
located inside the top f-structure f3 governed by
,the translation of the adjunct gerne . Embedded head switching
cases are problematic for the LFG correspondence based transfer
approach [7,10]. Essentially
the problem is that what used to be an embedding f-structure in the
source (in our example f1) turns out to be an embedded f-structure
in the target representation. If, in addition, the embedding
f-structure f1 in the source was itself embedded inside another
f-structure (say f0) in the source then head switching in
translation may destroy the link between its (i.e. f1's) translation
and the translation of its embedding f-structure (f0). From the
f-structure associated with the German sentence we derive the set
Source:
The meaning constructor for like , to be used for independent
analysis of the English sentence, is
![\begin{displaymath}
\begin{array}
{lc}
like: & \forall X, P~ [ ((\uparrow\mbox{\...
...c$}\;\\ & \uparrow_{\sigma} \leadsto like(X,P(X))]\end{array} \end{displaymath}](img61.gif){kind=small}
and analysis of the English sentence yields the set Target :
![\begin{displaymath}
\left\{ \begin{array}
{c}
(f_{2})_{\sigma} \leadsto hans \\ ...
...c$}\;(f_1)_{\sigma}
\leadsto swim(X)] \\ \end{array} \right\} \end{displaymath}](img62.gif)
Note that in our transfer constructors we refer to f-structures that
project -structures (in fact we have wide scope universal
quantification over such nodes). Hence if we are not careful we would
expect to get problems with embedded head switching cases here as
well. ``Pure'' semantic representations tend to avoid such problems
since structural differences such as head switching would be expected
to be ironed out on the level of semantic representation
[8,4]. Meaning constructors,
however, relate syntactic and semantic representations. It is in this
sense that they are not ``pure''. On the
other hand, they naturally provide underspecified semantic
representations and the possibility of ambiguity preserving transfer
on such representations, an issue not addressed by earlier approaches
such as [8].
Since there are no left-common prefixes in the meaning constructors
for gerne and like , the transfer constructor
gerne like consumes the entire meaning constructor
for gerne and produces a full meaning constructor for like :
![\begin{displaymath}
\begin{array}
{c}
\forall F ~[ \forall P (F_{\sigma} \leads...
...e*{-.4ex}\circ$}\;F_{\sigma} \leadsto like(X,P(X)))]\end{array}\end{displaymath}](img64.gif)
Note crucially that the meaning constructor on the right-hand side of
rewrites a node F rather than accessing a node
to match P(Y). From the instantiated source meaning
constructors together with the transfer constructors (and since
) we deduce
![\begin{displaymath}
\left\{ \begin{array}
{ll}
1. & (f_{2})_{\sigma} \leadsto ha...
...1 )_{\sigma} \leadsto like(X,P(X))]\end{array} \right\} \vdash \end{displaymath}](img68.gif)
as required. Observe, however, that (3.) above is not exactly like the
original meaning constructor for like employed in independent
analysis of the target string Hans likes swimming
(cf. p. 
above). The difference is that the constructor
obtained through the transfer operation ``rewrites'' a single node
rather than accessing a complement node 
to match against P(Y).
Next, we consider a complex instance of embedded head switching:
The corresponding f-structures are:
![\begin{displaymath}
\begin{array}
{cc}\left[\begin{array}
{@{}l@{\;}l@{\;}}\mbox...
...y}\hspace*{-2pt}\right]
\fbox {\footnotesize 1}
\, \end{array} \end{displaymath}](img73.gif)
The following meaning constructors are associated with vermuten and suspect :
![\begin{displaymath}
\begin{array}
{ll}
vermuten: & \forall X, P ~ [ ((\uparrow\m...
...x}\circ$}\;\uparrow_{\sigma} \leadsto suspect(X,P) ]\end{array}\end{displaymath}](img74.gif){kind=small}
The corresponding transfer constructor is simply:
![\begin{displaymath}
\forall F, X, P ~
[F_{\sigma} \leadsto vermuten(X,P) \;\mbox{$-\hspace*{-.4ex}\circ_t$}\;
F_{\sigma} \leadsto suspect(X,P)]\end{displaymath}](img75.gif){kind=small}
The semantic projection of the f-structure associated with the German sentence induces the following set of instantiated meaning constructors:
![\begin{displaymath}
\mbox{\emph{Source}} = \left\{ \begin{array}
{ll}
1. & (f_{2...
...\circ$}\;(f_3)_{\sigma} \leadsto gerne(P)]\end{array} \right\} \end{displaymath}](img76.gif)
Furthermore, transfer yields
![\begin{displaymath}
\left\{ \begin{array}
{ll}
1. & (f_{2})_{\sigma} \leadsto ed...
...3 )_{\sigma} \leadsto like(X,P(X))]\end{array} \right\} \vdash \end{displaymath}](img79.gif)
as required. This set of target meaning constructors obtained
via transfer is close to the set of meaning constructors obtained via
independent analysis of the taget string. They differ, however, with
respect to the constructor for like . The constructor obtained
through transfer (5. above) rewrites node 
rather than
accessing a separate 
projection to match
P(Y).
Let us briefly take stock: the linear logic based transfer approach provides ambiguity preserving transfer on underspecified representations and an elegant solution for embedded head switching cases. As it stands, however, for head switching cases it will not deliver exactly the set of target constructors obtained by independent analysis of the target string. This may cause problems for target language generation from underspecified representations (sets of target meaning constructors). Recall that the linear logic based transfer solution to embedded head switching relies on node rewriting in a resource sensitive formalism. In order to enable generation as outlined in Section 3.2, transfer should deliver exactly the set of meaning constructors as would be obtained by independent analysis of the target string. Alternatively, generation would have to proceed from fully disambiguated target meaning assignments. At the moment, generation from disambiguated target meaning assignments is not available to us yet and even if it were, it would defeat the idea of ambiguity preserving transfer.
However, it is possible to adapt a variant of a solution to embedded head switching in correspondence-based syntactic transfer approaches [10] to our present ambiguity preserving transfer scenario.
The basic idea is that in order to define transfer from a flat
f-structure into an f-structure configuration involving an additional
XCOMP layer, the transfer rule that maps the f-structure node
f3 under the COMP arc of vermuten in the German
f-structure (cf. p. ) into the target structure
has to foresee that - in case of head switching - the arcs of this
node have to map to a lower position in the target, namely the node
under the path COMP XCOMP. One way to ``foresee'' such a
possible deeper embedding is to ``push down'' the predicate-argument
nucleus of verbs (here schwimmen ) one or more levels down, via
functional uncertainty over XCOMP. This is defined below, where
we redefine the transfer constructor schwimmen swim :
We also redefine the transfer constructor gerne
like: we now rely on the fact that the predicate argument structure and
the corresponding semantic projector associated with the translation
of the proposition in the scope of the adjunct in the source will be
``pushed down'', in the target representation in terms of functional
uncertainty (see schwimmen swim above). The
new constructor gerne like is:
![\begin{displaymath}
\begin{array}
{c}
\forall F ~[ \forall P (F_{\sigma} \leadst...
...ce*{-.4ex}\circ$}\;F_{\sigma} \leadsto like(X,P(X))]\end{array}\end{displaymath}](img84.gif)
This transfer constructor consumes the entire source meaning
constructor for gerne and produces the proper target meaning
constructor for likes (as used in independent target
analysis). From the set of source meaning constructors Source
together with the set of transfer constructors Trans - this
time with the updated schwimmen swim and
gerne like - we derive
![\begin{displaymath}
\left\{ \begin{array}
{ll}
1. & (f_{2})_{\sigma} \leadsto ed...
...3 )_{\sigma} \leadsto like(X,P(X))]\end{array} \right\} \vdash \end{displaymath}](img85.gif)
where XCOMP* is resolved to XCOMP. Now the set of
target meaning constructors derived via transfer does indeed
correspond to the set of target meaning constructors obtained by
independent analysis of the target string. In particular, the
f-structure node instantiations of the target meaning constructor
ensure that (i) the subject of like is the same as the subject
of swim (sharing is also required by the control equation
in the
lexical entry for like ) and (ii) the meaning assignment
produced by swim is available and retrieved at the XCOMP
node required by like .
It may be presumed that the resulting set of target meaning constructors may not always correspond exactly to the set obtained from independent analysis of the target string: if the embedded target predicate requires complements other than the shared SUBJ would it not be the case that those complements be located and found at the ``wrong'' level of the target f-structure? Fortunately, this is not the case. Consider Ede vermutet daß Hans gerne Chomsky liest and its translation Ede suspects that Hans likes reading Chomsky . The corresponding f-structures are
The source and target meaning constructors for simple transitive verbs are the standard
![\begin{displaymath}
\begin{array}
{lc}
\mbox{\emph{lesen}}: & \forall X, Y ~ [...
...ex}\circ$}\;\uparrow_{\sigma}
\leadsto read(X,Y) ] \end{array} \end{displaymath}](img87.gif){kind=small}
With these the set of instantiated source meaning constructors is
The transfer constructor lesen read is
![\begin{displaymath}
\forall F, X, Y ~ [ F_{\sigma}
\leadsto lesen(X,Y) \;\mbox{$...
...(F~\mbox{\scriptsize\sc XCOMP*})_{\sigma} \leadsto read(X,Y) ] \end{displaymath}](img90.gif){kind=small}
We derive
The set of target constructors obtained via transfer again corresponds to the set obtained by independent analysis of the target string.
Take 2 is made reversible as follows: first, swap the left- and
right-hand sides of
![\begin{displaymath}
\begin{array}
{c}
\mbox{\emph{like}} \;\mbox{$-\hspace*{-.4e...
...e*{-.4ex}\circ$}\;F_{\sigma} \leadsto gerne(P)) ]\\ \end{array}\end{displaymath}](img93.gif)
second, redefine transfer constructors for main verbs, such that
they admit functional uncertainty over XCOMP to both sides of
:
![\begin{displaymath}
\forall F, X, Y ~ [ (F~\mbox{\scriptsize\sc XCOMP*})_{\sigma...
...F~\mbox{\scriptsize\sc XCOMP*})_{\sigma} \leadsto
lesen(X,Y) ] \end{displaymath}](img94.gif){kind=small}
Taking the second f-structure of p.12 as input for transfer, we obtain the set of meaning constructors:
![\begin{displaymath}
\mbox{\emph{Source}} = \left\{ \begin{array}
{ll}
1. & (f_{2...
...]\\ 6. & (f_{6})_{\sigma} \leadsto chomsky\end{array} \right\} \end{displaymath}](img95.gif)
When applied to this set, the inverted transfer constructors derive
the set of target meaning constructors required to generate the German
f-structure. In this case the functional uncertainty over XCOMP
will be resolved to 
to satisfy completeness and coherence
conditions.
In the present paper we have outlined an approach to semantic transfer based on linear logic transfer constructors operating on sets of linear logic meaning constructors. Transfer on sets of meaning constructors offers the advantage of ambiguity preserving transfer and in many cases obviates the need for multiple transfer on disambiguations. Linear logic transfer constructors blend well with the linear logic based semantic components of current LFG architectures [1]. Furthermore, the resource consciousness of transfer constructors allows a close modelling and provides a formalization of semantic transfer as developed and implemented in [3], a fact first noticed in [5].
Transfer as outlined in the present paper is reversible, modular and lexicalized. Lexical entries have corresponding and independently stated transfer constructors retrieved during transfer. A set of source meaning constructors and their corresponding transfer constructors together define transfer.
Transfer as outlined in the present paper comes with a well-formedness
check on the resulting Target set representation. Target is
well-formed iff it admits of target meaning assignments established
via linear logic deductions consuming all target meaning constructors:
.
Meaning constructors crucially refer to semantic projections induced by f-structure nodes to constrain composition possibilites during linear logic meaning assignment derivations. Ideally, transfer on sets of meaning constructors instantiated to f-structure nodes produces a target set of meaning constructors with f-structure node instantiations directly useful for target string generation. Since transfer constructors operate on instantiated meaning constructors, differences in syntactic function do not have to be transferred explicitly in many cases. Here, instantiation of the appropriate syntactic functions can be left to generation as long as the target meaning constructors match the meaning constructors used in analysis.
For instances of structural mismatches, in particular the notoriously difficult case of head switching, we have presented a way (Take 2) to define transfer constructors which produce a set of target meaning constructors with f-structure designators structurally corresponding to those obtained by independent analysis of the target sentence.
Meaning constructors effectively encode a syntax-semantics interface. Transfer as outlined in the present paper transfers syntax-semantics interfaces. Further research is directed at ambiguity preserving linear logic based transfer on ``pure'' semantic representations.