SYNTACTIC- I\]~EAD- DRIVEN (zlENERA'I'ION 
Esther K6nig* 
Institute for Computational Linguistics, Azenbergstr.12, 70174 Stuttgart,Germany, esther@ims.uni-stuttgart.de 
Abstract 
The previously proposed semanlic-head-driw'.n Ken - 
eration methods run into problems if none of the 
daughter eonstituents in the syntact.o-semantic rule 
schemata of a grammar fits the definition of a semantic 
head given in \[Shieber et al., 1990\]. This is the case 
for the semantic analysis rnles of certain constraint- 
based semantic representations, e.g. Underspecified 
Discourse R,epresentation Structures (UI)RSs) \[l!'rank 
and R.eyle, 1992\]. 
Since head-driven generation in general has its me> 
its, we simply return to a syntactic definition of 
qmad' and demonstrate the feasibility of synlaclic- 
head-clriveu generation. In addition to its generality, 
a syntactic-head-driven algorithm provides a basis for 
a logically well-defined treatment of the nmvement of 
(syntactic) heads, for which only ad-hoc solutions ex- 
isted, so far. 
1 Introduction 
IIead-driven generation methods combine both, top- 
clown search and bottom-np combination, in an ideal 
way. \[Shieber el al., 1990\] proposed to define the 
'head' constituent It of phrase with category a~ on se- 
mantic grounds: the semantic representations of h 
and z are identical. This puts a strong restriction 
on the shape of semantic analysis rules: one of the 
leaves must share its semantic form with the. root 
node. IIowever, there are composition rules for seman- 
tic representations which violate this restriction, e.g. 
tim schemata for the construction of Underspecified 
Discourse It,epresentatim, Structures (UI)ILSs) \[l"rank 
and Reyle, 1992\] where, in general, the root of a tree 
is associated with a strictly larger semantic structure 
(,hal, a,ly of I, he leaves. Ill order to make at generation 
method available for grammars wl,ich do not follow 
the striet notion of a semantic head, a syntactic-head- 
driven generation algorithm is presented, which can 
be specialized to generate from UDRSs. In a second 
step, the method will be extended in order to han- 
dle the movement of (syntactic) heads in a logically 
well-defined manner. 
The (tactical) generation proble.m is tim task to 
generate a string from a semantic representation ac- 
cording to the syntax-semantics-relation defined in a 
given grammar. Let's assume that the latter relation 
*The research reported here has been funded by the Sonder- 
forsclmngsbereidt 340 "Sprachtheorctische GrmMlagen ffir die 
Computerllngulstik", a project of the German National Science 
Foundation I)I,'G. 
is stated by pairs of trees. The left tree stages a lo- 
cal syntactic dependeacy, i.e. the dominance relation 
between a root node and a set of leaf nodes and the 
linear precedence relation among the leaves. The right 
tree defines the relation among the semantic represen- 
tation of the root and the semantic representations of 
the leaves. We assume that there is a one-to-one map 
from the nonterminal leaf nodes of the (local) syntax 
tree on the le.af nodes of the. (locM) semantic deriw~tion 
tree. Example: 
np vp NP VP 
i i t I ,_ _ _ 5_-55, .... 
If one assumes a pairwise linking from M't to right 
then the links between the two trees can be on,itted. 
Although such pairs of trees are reminiscent of syn- 
chronons trees in TAG's \[Shieber and Schabes, 1991\], 
they are simpler in wtrious ways, in particular be- 
cause we will nol make use of the adjunction operM.ion 
later on. In essence, pairs of trees are just a graph- 
ical notation for what has been put forward as the 
'rule-to-rule'-hypothesis, el'. \[Gazdar el al., 1985\], the 
fact that in the grammar each syntax rule is related 
with a semantic analysis rule. However, on the long 
run, the tree notation suggests a more general relation, 
e.g. more internal structure or additional, terminal leaf 
nodes in the local syntax tree. 
An obvkms way to implement a generation proce- 
dure (see Fig.l) is to relate the inlmt semantics with 
the start symbol of the gramnuu" and then to try to ex- 
l}and this node in a top-down manner accordiug to the 
rules specitied in tl,e grammar. This node expansion 
corresponds to an application of the (predicl)-rule in 
the following abstract specification of a Lop-down gen- 
erator. Generation terminates successfully if all the 
leaf nodes are labeled with terminals (s.ucccss). The 
question is which method is used to nmke two, possibly 
complex symbols equal, l'~or the sake of simplicity, we 
assume that the open leaves at0 resp. X0 are matched 
by (feature) term unification with the corresponding 
mother nodes in the grammar rule. llowever, for the 
semantic form Xo, a decidable variant of higher order 
unification might be used instead, in order Lo inch, de 
the reduction of .\-expressions. Of course, the. neces- 
sary precautions have to be taken in order to avoid the 
confusion between object- and meta-level wtriables, cf. 
\[Shieber el al., 1990\]. 
A clepth-first realization of this abstract top-down 
algorithm would work line as long ms tl,e semantic rep- 
4Z5 
all leaves of the syntax tree are labeled with terminals (success) 
Xo Xo 
Figure 1: Top-Down Generation (G grammar description; xl syntactic category; Xi semantic representation) 
resentations of the leaves are always strictly smaller in 
size as the semantic form of the root node. But, if the 
actual semantic decomposition takes place in the lexi- 
con, the semantic representations of some subgoals will 
be variables, which stand for semantic representations 
of any size: 
X 
np vp 
, lambda • \[Y\] 
sere walk(Y) walks 
(2) 
A strict left-to-right, depth-first expansion of subgoals 
might run into problems with the grammar fragment 
in (2) if a left..reeursive up-rule exists, because the se- 
mantics of the np is only instantiated once the 'scman- 
tic head' of the vp has been looked up in the lexicon. 
2 Previous work 
A top-down, semantic-structure-driven generation al- 
gorithm has been defined by \[Wedekind, 1988\] which 
gives a basis for dynamic subgoal-reordering guided by 
the semantic input. Some proposals have been made 
for subgoal reordering at compile-time, e.g. \[Minnen 
et al., 1993\] elaborating on the work by \[Strzalkowski, 
1990\]. But there will be no helpful st, bgoal reordering 
for rules with semantic head recnrsion: 
f l ambda : A "~ 
Obviously, a bottom-up component is required. One 
solution is to keep to a top-down strategy hut to do 
a breadth-first search, ef. \[Kohl, 1992\], which will be 
fair and not delay the access to the lexicon forever, 
as a pure depth-first strategy does. Alternatively, one 
could adopt a pure bottom-up strategy like the one 
which has been proposed in \[Shieber, 1988\] and which 
is presented in Fig.2 in a lfighly schematic manner. A 
lexical entry qualifies as a potential leaf node if its se- 
mantic form is a non-trivial substructure of the input 
semantics (rule (lex)). The derivation trees are built 
up by the (complete}-rule. Generation finally succeeds 
if the root node of I, he current syntax tree is labeled 
with the start symbol of the grammar and the root of 
the semantic analysis trec with the input semantics. 
Due to tile exclusion of phr~es with 'empty' seman- 
tics (which would be trivial substructures of the input 
semantics), tile method always terminates, lIowever, 
tile lack of top-down guidance will lead, in general, 
to a lot of non-determinism. The strong substructure 
condition means that the algorithm will be incomplete 
for grammars which cover semantically void phrmses 
like expletive expressions, particles, and sul)phrascs of 
idioms. 
The head-corner generator in \[van Noord, 1993\] is 
an illustrative instance of a sophisticated combina- 
tion of top-down prediction and bottom-up structure 
building, see Fig.3. The rule (lez) restricts the selec- 
tion of lexical entries to those which can be 'linked' 
to the local goal category (visualized by a dotted 
line). According to van Noord, two syntax-semantics 
pairs are liukable if their semantic forms are identical, 
i.e. llnk((x, X), (z;, X)). The rule (hc-co,aptete) per- 
forms a 'head-corner' completion step for a (linked) 
phrase zh, which leads to the prediction of the head's 
sisters. A link marking can be removed if the linked 
categories resp. the linked semantic forms are identical 
(rule (local-success)). Generation succeeds if all the 
leaves of the syntax tree are labeled with terminals 
and if no link markings exist (rule (global-success)). 
In order to obtain completeness in the general c~e, 
the inference schemata of the head-corner generator 
must be executed by a breadth-first interpreter, since 
a depth-first interpreter will loop if the semantic anal- 
ysis rules admit that subtrees are associated with se- 
mantic forms which are not proper substructures of 
the input semantics, and if these subtrees can be com- 
posed recursively. Such an extreme case would be a re- 
cursive rule for semantically empty particles: ('empty' 
semantics is represented by the empty list symbol El): 
/~ /~ _ \[\] (~) 
part part X1 X2 x 
Ilowcver, if we a.ssume that structures of that kind do 
not occur, a depth-first interpreter will be sufficient, 
e.g. the inference rules of the algorithm can be encoded 
and interpreted directly in Prolog. Note that van No~ 
ord's method is restricted to grammars where phrases 
have always a lexical semantic head. The algorithm in 
\[Shleber et al., 1990\] relaxes this condition. 
476 
(±Z~/ 
Wl, • • • ~ tt)r (~) if V i, 1 <<_ i <_ r, Xi ~. G and Xi substructure of X 
xo Xo 
xo Xo \ 
G 
Figure 2: Bottom-Up Generation (G grammar description; s start symbol; X input semantics; xl syntactic 
category; X," semantic representatiou) 
all leaves are labeled with terminals and the tree does not contain any dotted lines 
(+; +)~, ~' (+ +1 
@tol,.l-success) 
( /z /z ) ~ ( z~, /z ) ,, ( ,!,, x,) 
~i ! " 
E G ~,.1 ti,,k((~, x), (~;, x;)) 
Xh xo Xo 
if E G 
Figure 3: IIead-Corner Generator (G grammar description; xi syntactic category; Xi semantic representation) 
477 
every 
dref : X 
ros : ~F~C8 
scope : Scope 
dre~ : X 
ros : J~es 
scope : Scope 
SeN. : 
womaxt sere woman(X) loves sere : love(X,Y) 
Figure 4: A grammar with UDRS-eonstruction rules - lexicon 
3 Underspecified Discourse 
Representation Structure 
In the following, we will present shortly a semanLic 
representation formalism and a corresponding set, of 
analysis rules wlfich resist to the definition of 'se- 
mantic head' as it is required in van Noord's bead- 
corner algorithm. \[Reyle, 1993\] developed an infer- 
ence system for Underspecified Discourse Represen- 
tation Structures (UDRS's), i.e. Discourse Represen- 
tation Structures \[Kamp and Reyle, 1993\] which are 
underspecified with respect to scope. The following 
UDll.S represents simultaneously the two readings of 
the sentence 'every woman loves a man' by leav- 
ing the exact structural embedding of the quantified 
phrases underspecified. 
\[ lovo(~, v) \] 
(~) 
An arrow pointing from X2 to XI is called a subor- 
dination constraint and means that the formula X2 
must not have wider scope than Xa. \[Frank and 1Zeyle, 
1992\] proposed rules for the construction of UDRS's 
in an ItPSG-style syntax, of. \[Pollard and Sag, 1993\], 
which are shown in Fig.4 and 5 in a somewhat adapted 
manner. Semantic composition is performed by the 
coindexing of the features dre:f, res, subj, etc. which 
serve as an interface to the value of the sore feature, 
the actual semantic representation. For the phrase- 
structure tree rooted with s, there is no leaf which 
would fulfill the definition of a semantic head given 
in \[Shieber et al., 1990\] or \[van Noord, 1993\]. IIence, 
the head-corner generator of Fig.3 with a link relation 
based on semantic beads will not be applicable. 
4 Syntactic-head-driven gener- 
ation 
4.1 A new link relation 
One could define a weak notion of o semantic head 
which requires that tile semantic form of the semantic 
head is a (possibly empty) substructure of the root 
semantics. But this is rather meaningless, sincc now 
every leaf will qualify ms a semantic head. As a way 
out, there is still tile notion of a syntactic bead, which 
can serve as the pivot of the generation process. 
Assmne that Lhe syntactic head leaf for each local 
syntax trec has been defined by the grammar writer. 
We get the following preliminary version of a syntax- 
based link relation: 
N,~k( (~,, X), (x,, Xd ) (6) 
1. if either x = xi 
2. 0r x d is a possible syntactic head of x 
and link( ('~j, Xj), 0", X,) ) 
This is the kind of link relation which is used for pars- 
ing. In general, it works line there, because with each 
lexlcal lookup a part of the input structure, i.e. of the 
inl)ut string, is consumed. In order to reduce the num- 
ber of non-termhiating cases for generation, a similar 
precantlon tl~ to be added, i.e. tile hipu~ structure 
h~ to be taken into account. The final version of a 
syntax-based link relation incorporates a test for the 
weak notion of a semantic bead: 
li,,k((~,,X), (x;,Xd) g (7) 
1. either x = x; and 
X; is a (possibly empty) substructure of X 
2. or zj is a possible syntactic head of x 
and link((xj, X), (x;, Xd) 
The substructure check makes only sense if the seman- 
tics X of the current goal is instautiated. This might 
478 
<Z, 
dro:\[ : X ) 
scope : Scope 
sem : Quant 
res : J ( . ); X 
scope : S pe sere . Rcs 
sere : Quant / 
8 
v2 np 
s elll : 
scope : SA'c subj : X dref : 
sere : Subj obj : Y scope : 
sere : Verb sere : 
Y) 
OSc 
Obj 
Figure 5: A grammar with UDl(S-construction rules - syntax rules 
> 
not be the case, when the proper semantic head and 
the syntactic head differ, and a sister goal of the se- 
mantic head is to be expanded before the head itself. 
IIence, in general, the sister goals must be reordered 
according to the degree of instantiation of their se- 
mantic representations. In addition to the improved 
termination properties, the condition on the seman- 
tic representation helps to filter out useless candidates 
from the lexicon, i.e. lexical entries which will never 
become part of the final derivation because their se- 
mantic representations do not tit. 
4.2 Grammars with head movement 
In order to simplify the representation in the following, 
we assume that each syntax tree in a grammar is iso- 
morphic to the corresponding semantic analysis tree. 
This means that both trees can merged into one tree 
by labeling the nodes with syntax-semantics-pairs: 
(xo, Xo) 
(~,x,) (~, x2) (s) 
In \[Shieber el al., 1990\] an ad-hoc solutiori was pro- 
posed to enforce termination when the semantic head 
has been moved. By adopting a syntactic-head-driven 
strategy, head-movement does not canse a problem if 
the landing site of the head is the 'syntactic bead' (or 
rather: the main fiinctor category of the chmse, in 
categorial grammar terminology) of a superordinate 
clause. This is postulated by syntactic descriptions 
like 
(cPS , X0) cp~ 
e~ spcc~~ 
I (vp, Xo)lr(v~,X,)\] I ~Ps/E.~ps\] 
(~, X1) vp s (9) 
where vp/r,.1 means that the deriwttion of the vp- * uvlJ 
node ll~s to include all empty v-leaf. Ill the example 
ill Fig.6, the syntactic head (the c-position) of the cpf 
will be visited before the vp is to be derived, hence the 
exact information of the verb trace will be available 
in time. Similarly for the movement to the 'vorfehl'. 
l\[owever, if verb second coufign,'ations are described 
by a single structure 
(cp,, Xo) 
(cp I , Xo) 
spe e c_..----------'--- ~~ ( 10 ) 
I (xs'~,x~) I ~v/D s , (xI-~,x~)\] 
vj 
the algorithm runs into a de.i~dlock: the vp-node can- 
not be processed completely, because the semantics of 
the XP-trace is unknown, and the expansion of the 
XP-filler position wile be delayed for tile same reason. 
If this syntactic description had to be preferred over 
the one in (9), the link relation should be further mod- 
ified. The substructure test wrt. the semantics of the 
current goal should be replaced by a substructure test 
479 
spec I 
vpl 
v dp 
I I Bananen gegessen 
eaten 
cps 
cp\] 
vp 
c 
I vp ~2 
I ,lp I vpl v2 
hat Peter I I 
has 
Figure 6: Movement of a complex non-head 
wrt. the global input semantics, which leads to a loss 
of tlexibility, as it has been discussed in connection 
with the pure bottom-up approach. 
4.3 Implementation 
Since the algorithm has been implemented in the CUF 
language t, which includes a wa±t-mechanism, the re- 
odcring of subgoMs can be delegated to CUF. 
Instead of a full-blown substructure test which 
might be quite complicated on graphs like UDI~S's, 
only the predicate names (and other essential 'seman- 
tic' keywords) of the lexical entry are mapped on the 
current goal semantics. If such a map is not feasible, 
this lexical entry is dropped. 
We restrict the grammars to lexicalized ones. A 
grammar is lexiealized if for every local syntax tree 
there is at least one preterminal leaf, cf. \[Sehabes and 
Waters, 1993\]. Note that lexicalization does not affect 
the expressibility of the grammar \[Bar-llillcl el al., 
1960\], \[Schabes and Waters, 1993\]. Ilowever, the gen- 
eration algorithm turns much simpler and hence more 
efficient. There is no need for a transitive link relation, 
since a goal can match immediately the mother node 
of a preterminal. The lexicon access and the head- 
corner completion step can be merged into one rule 
schema 2. 
A version of the Non-Local-Feature principle of 
IIPSG has been integrated into the algorithm. Every 
non-head nontcrminM leaf of a local tree must come 
with a (possibly empty) multiset of syntax-semantics 
pairs as the value of its to_bind:slash-feature (fea- 
ture abbreviated as /), cf. example (9). From these 
static values, the dynamic inherited:slash-values 
IThe CUF-system is an implementation of a theorem prover 
for a Horn clause logic with typed feature terms \[Dt;rre and 
Dorna, 1993\]. 
2An instance of our head-corner generator (without an inte- 
grated treatment of movement) is the UCG-generator by Calder 
et al. \[Calder et al., 1989\] (modulo the use of unary category 
transformation rules) which relies, in addition, on the symme- 
try of syntactic and semantic head. A syntactic-head-drlven 
generator for a kind of lexlcallzed grammars has been proposed 
independently by \[Kay, 1993\]. Another variant of a lexlcMized 
grammar by \[Dymetman ctal., 1990\] does not make use of the 
head-corner idea but rather corresponds to the top-down gen- 
eration schema presented in Fig.1. 
(feature abbreviated ms //) can be calculated during 
generation, see rule (lex) in Fig.7. 
(la) Choose a lexical entry as the head Xh of the 
current goal x0. Then the substructure condition must 
hold for the corresponding semantic forms Xh and Xo. 
The//-value Th mnst be empty. 
(lb) Or choose an element of the //-value 7b of 
the current head z0. Then the //-value Th becomes 
\[(xh, Xh)l. The associated string wh is empty. 
(2) There must be a lexicalized tree which connects 
the goal z0 and the chosen head xh. The//-value To is 
split into disjoint sets 7'1, ..., 7',, The//-values of the 
new subgoals xl, ..., :Co are the disjoint set unions 
T~ ~ 7~ where 7~ ~ is the /-value of zi in the local tree 
given in the grammar. 
Note that this version of the Non-LocM-Feature 
principle corresponds to the hypothetical reasoning 
mechanism which is provided by the Lambek eatego- 
rim grammars \[Lambek, 1958\], \[KSnig, 1994\]. This is 
illustrated by the fact that e.g. the left tree in example 
(9) can be rendered in categorial grammar notation as 
cpl/(vp/v ). IIeuce, the algorithm in Fig.7 has a clear 
logical basis. 
5 Conclusion 
This paper gives a syntactic-bead-driven generation 
algorithm which includes a well-defined treatment of 
moved constituents. Since it relies on tile notion of 
a syntactic head instead of a semantic head it works 
also for grammars where semantic heads are not avail- 
able in general, like for a grammar which includes se- 
mantic decomposition rules of (scopally) Underspec- 
itied Discourse Representation Structures. By using 
the same notion of head both for parsing and for gen- 
eration, both techniques become even closer. In ef- 
fect, the abstract specifications of the generation algo- 
rithms which we gave above, could be read as parsing 
algorithms, modulo a few changes (of the success con- 
dition and the link relation). 
Generation from Underspecified DI/,S's means that 
sentences can be generated from meaning represen- 
tations which have not been disambiguated with re- 
gard to quantifier scope. This is of particular impor- 
tance for applications in machine translatiou, where 
480 
all leaves are labeled with terminals 
(zh, Xh) 1. if I 
Wh 
(Sll ccegs) 
~el,x~)//7'~ w'q ('~h, Xh)//7;, (~,.,X.)//Tt;, ...... uJT",, 
I 
Wh 
C= G and Xh substructure of Xo and 7), := I\] 
or q (~,,, X,,) e 7; .,,a 7;, := \[(~,,, Xh)\] ,,,,d .),, := c 
(~o, Xo) 
2. and ~__~ G G and "I}~ := 7'I U...U'\[~ 
Figure 7: IIead-Corner Generator for lexicalized grammars (G grammar description; xl syntactic category sym- 
bol; Xi semantic representation; 7} zlash-values) 
one wants to avoid the resolution of scope relations as 
long as the underspeeified meaning can be rendered in 
the source and in the target language. Future work 
should consider more the strategic part of the genera- 
tion problem, e.g. try to find heuristics and strategies 
which handle situations of 'scope mismatch' where one 
language has to be more precise with regard to scope 
than the other. 
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