The Semantics of Resource Sharing in 
Lexical-Functional Grammar 
Andrew Kehler" 
Aiken Computation Lab 
33 Oxford Street 
Harvard University 
Cambridge, MA 02138 
Mary Dalrymple t 
John Lamping t 
Vijay Saraswat t 
Xerox PARC 
3333 Coyote Hill Road 
Palo Alto, CA 94304 
Abstract 
We argue that the resource shar- 
ing that is commonly manifest in 
semantic accounts of coordination 
is instead appropriately handled in 
terms of structure-sharing in LFG 
f-structures. We provide an extension 
to the previous account of LFG seman- 
tics (Dalrymple et al., 1993a) accord- 
ing to which dependencies between 
f-structures are viewed as resources; 
as a result a one-to-one correspon- 
dence between uses of f-structures and 
meanings is maintained. The result- 
ing system is sufficiently restricted in 
cases where other approaches overgen- 
erate; the very property of resource- 
sensitivity for which resource sharing 
appears to be problematic actually 
provides explanatory advantages over 
systems that more freely replicate re- 
sources during derivation. 
1 Introduction 
The resource-based approach to semantic compo- 
sition in Lexical-Functional Grammar (LFG) ob- 
tains the interpretation for a phrase via a logical 
deduction, beginning with the interpretations of 
its parts as premises (Dalrymple et al., 1993a). 
The resource-sensitive system of linear logic is 
used to compute meanings in accordance with 
relationships manifest in LFG f-structures. The 
properties of the system ensure that meanings are 
used exactly once, allowing coherence and com- 
pleteness conditions on f-structures (Kaplan and 
Bresnan, 1982, pages 211-212) to be maintained. 
However. there are cases where a single con- 
stituent appears to yield more than one contribu- 
tion to the meaning of an utterance. This is most 
*kehl er@das, harvard, edu 
t{dalrymple, i amping, saraswat }@parc. xerox, tom 
obvious in, but is not limited to, sentences involv- 
ing coordination. In example (1), for instant,'. 
NAFTA is the object of two different verbs: 
(1) Bill supported, and Hillary opposed, 
NAFTA. 
Since the hallmark of the linear logic approach is 
to ensure that f-structure contributions are uli- 
lized exactly once in a derivation, such construc- 
tions would at first glance appear to be problem- 
atic for the approach. 
We argue that the resource sharing that is 
commonly manifest in the treatment of coordi- 
nation in other approaches is appropriately han- 
dled by exploiting the structure-sharing in LF(', 
f-structures. We refine our previous analysis to 
account for cases where an f-structure is reached 
by multiple paths from an enclosing f-structure. 
Dalrymple et al. (199aa) provides an account 
of LFG semantics that represents the meaning of 
lexical items with linear logic formulas. These 
formulas manipulate basic assertions of the form 
f~,r'.~M, for f-structures f and meaning logzc 
terms M. Here (r is a mapping, the semantic pro- 
jectign, that relates f-structures to semantic struc- 
tures. To distinguish between multiple paths en- 
tering an f-structure, we now take cr to map from 
sets of paths in f-structures to semantic structures. 
Further, the paths between f-structures are made 
available in the semantic space as resources. This 
makes it possible for the semantic formulas to ex- 
ploit information about the multiple paths into 
an f-structure in order to account for the multi- 
ple uses of the f-structure's semantic contribution. 
The resulting system is sufficiently restricted in 
cases where other approaches overgenerate; the 
very property of resource-sensitivity for which re- 
source sharing appears to be problematic actu- 
ally provides explanatory advantages over systems 
that more freely replicate resources during deriva- 
tion. 
In Section 2, we review previous approaches to 
the semantics of coordination and argument shar- 
31 
ing. and make note of some of their drawbacks. 
We describe the revised sere.antic framework in 
Section 3. and work through several examples of 
non-constituent coordination (specifically, right- 
node raising) in Section 4. We discnss examples 
involving intensioual verbs in Section 5, 
2 Previous Work 
2.1 Combinatory Categorial Grammar 
Steedman (198.5; 1989; 1990), working in the 
framework of Combinatory Categorial Grammar 
(CCG), presents what is probably the most ade- 
quate analysis of non-constituent coordination to 
date. As noted by Steedman and discussed by 
Oehrle (1990), the addition of the rule of function 
composition to the inventory of syntactic rules in 
Categorial Grammar enables the formation of con- 
stituents with right-peripheral gaps, providing a 
basis for a clean treatment of cases of right node 
raising as exemplified by sentence (1). Such exam- 
ples are handled by a coordination schema which 
allows like categories to be conjoined, shown in 
(2). 
(2) Coordination: X CONJ X ~-.- X 
This schema gives rise to various actual rules 
whose semantics depends on the number of ar- 
guments that the shared material takes. For the 
cases of RNR considered here, the rule has the 
form shown in (3). 
(3) (coordination) 
X/Y:F CON J:& X/Y:G =~ X/Y:Ax.(Fx&Gx) 
The contraction from )~x.Fx and Ax.Gx to 
)~x.(Fx&Gx) in this rule allows for the single ar- 
gument to be utilized twice. 
As noted by Hudson (1976), however, not all 
examples of RNR involve coordinate structures: 
(4) Citizens who support, paraded against 
politicians who oppose, two trade bills. 
Obviously, such cases fall outside of the purview 
of the coordination schema. An analysis for this 
sentence is avi~ilable in the CCG framework by the 
addition of the xsubstitute combinator (Steedman, 
p.c.), as defined in Steedman (1987). 
(5) (<xsubstitute) 
Y/Z:G (X\Y)/Z:F =~ X/Z: )~x.(Fx(Gx)) 
The use of this combinator assimilates cases of 
noncoordinate RNR to cases involving parasitic 
gaps. 
While this approach has some drawbacks, 1 we 
do not offer a competing analysis of the syntax of 
sentences like (4) here. Rather, we seek an anal- 
ysis of RNR (and of resource sharing in general) 
that is uniform in the semantics; such a treatment 
isn't available in CCG because of its tight integra- 
tion between syntax and semantics. 
2.2 Partee and Rooth 
Perhaps the most influential and widely-adopted 
semantic treatment of coordination is the ap- 
proach of Partee and Rooth (1983). They pro- 
pose a generalized conjunction scheme in which 
conjuncts of the same type can be combined...ks 
is the case with Steedman's operators, contraction 
inherent in the schema allows for a single shared 
argument to be distributed as an argument of each 
conjunct. Type-lifting is allowed to produce like 
types when necessary; the combination of the co- 
ordination scheme and type-lifting can have the ef- 
fect of 'copying' an argument of higher type, such 
as a quantifier in the case of coordinated inten- 
sional verbs. They propose a 'processing strat- 
egy' requiring that expressions are interpreted a! 
the lowest possible type, with type-raising taking 
place only where necessary. 
To illustrate. Partee and Rooth assume that ex- 
tensional verbs such as find are entered in the lex- 
icon with basic type (e, (e, t)}, whereas intensional 
verbs like want, which require a quantifier as an 
argument, have type (((e, t}, t), (e, t}) (ignoring in- 
tensionality). Two extensional verbs such as find 
and support are coordinated at their basic types: 
(6) find and support (type (e, (e, t}}): 
)W.)~x.\[f ind( x, y) A support(x, y)\] 
Two intensional verbs such as want and seek are 
also coordinated at their basic (higher) types: 
(7) want and seek (type (((e, t), t}, (e, t))): 
)~P.)~x.\[want(x, 79) A seek(z, 79)\] 
The argument to this expression is a quantified 
NP. When an intensional and an extensional verb 
are coordinated, the extensional verb must be 
1We find two problems with the approach as it 
stands. First, the intuition that one gap is 'parasitic' 
upon the other in cases like (4) is not strong, whereas 
the CCG analysis suggests an asymmetry between the 
two gaps. Second, the combinator appears to cause 
overgeneration. While it allows sentence (4), it also 
allows sentence (b), where two trade bills is analyzed 
as the object of both verbs: 
(b) *Politicians who oppose, paraded against, two 
trade bills. 
32 
type-raised to promote it to the type of the in- 
tensional verb: 
(8) want and find (type <<(e,t>,t),<e,t>>): 
,\7).Ax.\[want(x, 7 9) A 7)( Ay.find(x, y))\] 
Again, this leads to the desired result. How- 
ever, an unwelcome consequence of this approach, 
which appears to have gone unnoticed in the lit- 
erature, arises in cases in which more than two 
verbs are conjoined. If an intensional verb is co- 
ordinated with more than one extensional verb, a 
copy of the quantifier will be distributed to each 
verb in the coordinate structure. For instance, in 
(9), two extensional verbs and an intensional verb 
are coordinated. 
(9) want, find, and support: 
AP.Ax.\[ want(x, 7 0) 
A ~P(Ay.find(x, y)) 
A 7)(Ay.support(x, y)) \] 
Application of this expression to a quantifier re- 
sults in two quantifiers being scoped separately 
over the extensional verbs. This is the wrong re- 
sult; in a sentence such as Hillary wanted, found, 
and supported two candidates, the desired result is 
where one quantifier scopes over both extensional 
verbs (that is, Hillary found and supported the 
same two candidates), just as in the case where all 
the verbs are extensional. Further, there does not 
seem to be an obvious way to modify the Partee 
and Rooth proposal so as to produce the correct 
result, the problem being that the ability to copy 
quantifiers inherent in their schema is too unre- 
stricted. 
A second problem with the account is that, as 
with Steedman's coordination schema, Partee and 
Rooth's type-raising strategy only applies to coor- 
dinate structures. However, the need to type-raise 
extends to cases not involving coordination, as in 
sentence (10). 
(10) Citizens who seek, paraded against politi- 
cians who have, a decent health insurance 
policy. 
We will present an analysis that preserves the 
intuition underlying Partee and Rooth's process- 
ing strategy, but that predicts and generates the 
correct reading for cases such as (9). Furthermore, 
the account applies equally to examples not in- 
volving coordination, as is the case in sentence 
(10). 
3 LFG and Linear Logic 
LFG assumes two syntactic levels of representa- 
tion: constituent structure (c-structure) 2 encodes 
phrasal dominance and precedence relations, and 
functional structure (f-structure) encodes syntac- 
tic predicate-argument structure. The f-structure 
for sentence (11) is given in (12): 
(11) Bill supported NAFTA. 
(12) 
f: 
"PILED 'SUPPORT' \] 
SUBJ g: \[ PRED 'BILL'\] 
OBJ h: \[ PILED 'NAFTA'\] 
Lexical entries specify syntactic constraints on 
f-structures as well as semantic information: 
(13) Bill NP (7 PRED) : 'BILL' 
\[c, ~ Bill 
supported V (\[ PRED)= 'SUPPORT' 
VX, Y. (T susJ)o---*X 
® (T osJL"~Y 
---o ~o ~ supported(X, Y) 
NAFTA NP (T PRED) = 'NAFTA' 
Ta ~ NAFTA 
Semantic information is expressed in (1) a mean- 
ing language and (2) a language for assembling 
meanings, or glue language. The meaning lan- 
guage could be that of any appropriate logic: 
for present purposes, higher-order logic will suf- 
rice. Expressions of the meaning language (such 
as Bill) appear on the right side of the meaning 
relation ---~. 
The glue language is the tensor fragment of lin- 
ear logic (Girard, 1987). The semantic contribu- 
tion of each lexical entry, which we will refer to 
as a meaning constructor, is a linear-logic formula 
consisting of instructions in the glue language for 
combining the meanings of the lexical entry's syn- 
tactic arguments to obtain the meaning of the 
f-structure headed by the entry. For instance, the 
meaning constructor for the verb supported is a 
glue language formula paraphrasable as: "If my 
SUBJ means X and (®) my OBJ means Y, then 
( ---o ) my sentence means supported(X, Y)". 
In the system described in Dalrymple et 
al. (1993a), the ~ relation associates expressions 
in the meaning language with f-structures. As a 
result, each f-structure contributed a single mean- 
ing constructor as a resource to be used in a 
derivation. Because linear logic does not have 
any form of logical contraction (as is inherent in 
2For discussion of c-structure and its relation to 
f-structure, see, for example, Kaplan and Bresnan 
(1982). 
33 
the approaches discussed earlier), cases where re- 
sources are shared appear to be problematic in 
this framework. Intuitively. however, the need 
for the multiple use of an f-structure meaning re- 
sults not from the appearance of a particular lex- 
ical item (e.g., a conjunction) or a particular syn- 
tactic construction (e.g., parasitic gap construc- 
tions), but instead results from multiple paths 
to it from within the f-structure that contains it, 
where structure sharing is motivated on syntactic 
grounds. We therefore revise the earlier frame- 
work to model what we will term occurrences of 
f-structures as resources explicitly in the logic. 
F-structures can mathematically be regarded 
as (finite) functions from a set of attributes to 
a set of atomic values, semantic forms and (re- 
cursively) f-structures. We will identify an oc- 
currence of an f-structure with a path (from the 
root) to that occurrence; sets of occurrences of an 
f-structure can therefore be identified with path 
sets in the f-structure. We take, then, the do- 
main of the a projection to be path sets in the 
root f-structure. Only those path sets S are con- 
sidered which satisfy the property that the exten- 
sions of each path in S are identical. Therefore 
the f-structure reached by each of these paths is 
identical. Hence from a path set S, we can read 
off an f-structure S I. In the examples discussed 
in Dalrymple et al. (1993a) there is a one-to-one 
correspondence between the set of path sets S and 
the set of f-structures S I picked out by such path 
sets, so the two methods yield the same predic- 
tions for those cases. 
Relations between path sets are represented ex- 
plicitly as resources in the logic by R-relations. 
R-relations are represented as three-place predi- 
cates of the form R(F, P, G) which indicate that 
(the path set) G appears at the end of a path P 
(of length 1) extending (the path set) F. That 
is, the f-structure Gf appears at the end of the 
singleton path P in the f-structure Fy. For ex- 
ample, the f-structure given in (12) results in two 
R-relations: 
(i) R(f, SUB J, 9) 
(ii) R(f, OBJ, h) 
Because f and g represent path sets entering an 
f-structure that they label, R-relation (i) indicates 
that the set of paths (f sun J) (which denotes the 
set of paths f concatenated with SUB J) is a subset 
of the set of paths denoted by g. An axiom for in- 
terpretation provides the links between meanings 
of path sets related by R-relations. 
Axiom I: !(VF, G,P,X. Go-'-*X 
--o !(R(F,P,G) --o (F P)o.-.~X)) 
According to this axiom, if a set of paths G has 
meaning X. then for each R-relation R(F, P,G) 
that has been introduced, a resource (F P)¢---*.\" 
can be produced. The linear logic operator '!' al- 
lows the conclusion (R(F, P,G) --o (F P)~,.-.~X) 
to be used as many times as necessary: once 
for each R-relation R(F, P, G) introduced by the 
f-structure. 
We show how a deduction can be performed to 
derive a meaning for example (11) using the mean- 
ing constructors in (13), R-relations (i) and (ii). 
and Axiom I. Instantiating the lexical entries for 
Bill, NAFTA, and supported according to the la- 
bels on the f-structure in (12), we obtain the fol- 
lowing premises: 
bill: go ~ Bill 
NAFTA: ha"-* NAFTA 
supported: VX, Y. (f SUBJ)a'x~X 
® (f OBJ>o"--*Y 
-o fa.-.~ supported( X, y) 
First, combining Axiom I with the contribution 
for Bill yields: 
(14) !VF, P. R(F, P, g) ---o (F P)o...., Bill 
This formula states that if a path set is R-related 
to the (path set corresponding to the) f-structure 
for Bill, then it receives Bill as its meaning. From 
R-relation (i) and formula (14), we derive (15). 
giving the meaning of the subject of f. 
(15) (f suBJ)a"~Bill 
The meaning constructor for supported com- 
bines with (15) to derive the formula for 
bill-supported shown in (16). 
(16) V\]". (fOBJ) "-~r 
-o f~ ~ supported(Bill, Y) 
Similarly, using the meaning of NAFTA, R- 
relation (ii), and Axiom I, we can derive the mean- 
ing shown in (17): 
(17) (f OBJ)o'..*NAFTA 
and combine it with (16) to derive (18): 
(18) fo'--* supported( Bill, NAFTA) 
At each step, universal instantiation and modus 
ponens are used. A second derivation is also pos- 
sible, in which supported and NAFTA are com- 
bined first and the result is then combined with 
Bill. 
The use of linear logic provides a flexible mech- 
anism for deducing meanings of sentences based 
on their f-structure representations. Accounts of 
34 
various linguistic phenomena have been developed 
within the framework on which our extension is 
based, including quantifiers and anaphora (Dal- 
rymple et al., 1994a), intensional verbs (Dalrym- 
pie et al., 1994b), and complex predicates (Dal- 
rymple et al., !993b). The logic fits well with the 
'resource-sensitivity' of natural language seman- 
tics: there is a one-to-one correspondence between 
f-structure relationships and meanings; the multi- 
ple use of resources arises from multiple paths to 
them in the f-structure. In the next section, we 
show how this system applies to several cases of 
right-node raising. 
4 Examples 
4.1 RNR with Coordination 
First we consider the derivation of the basic case 
of right-node raising (RN R) illustrated in sentence 
(i), repeated in (19). 
(19) Bill supported, and Hillary opposed, 
NAFTA. 
The f-structure for example (19) is shown in (20). 
(~o) 
f: 
"PRED 
fl : SUBJ 
OBJ 
'SUPPORT' \] 
g:\[ PRED 'BILL'\] 
h: \[ PRED 'NAFTA' \] ,-- 
PRED ~OPPOSE' H~ 
SUBJ i: \[ PRED ' A: 
OBJ 
The meaning constructors contributed by the lex- 
ical items are as follows: 
Bill: ga"-* Bill 
Hillary: io ~ Hillary 
supported: gX, Y. (fl soaa)o--~X 
® (k oaa)~-,* Y 
-o f,o..., supported(X, Y) 
opposed: VX, Y. (f2 SUBJ)~-~X 
® (f~ osJL~ v 
-o f2a-,-~opposed(X, y) 
and: VX, Y. (f CONJ)a"~X 
® (f coNa)~r 
---o f~ ~ and(X, Y) 
and2: !(VX, Y. (f CONJ)a"-,*X 
®f~--* Y 
--o f,-,~and(X, r)) 
NAFTA: ho-.~ NAFTA 
Here, we treat and as a binary relation. This 
suffices for this example, but in general we wiil 
have to allow for cases where more than two 
constituents are conjoined. Therefore, a second 
meaning constructor and2 is also contributed by 
the appearance of and, prefixed with the linear 
logic operator '!'. so that it may be used as many 
times as necessary (and possibly" not at all, as is 
the case in this example). 
The R-relations resulting from the feature-value 
relationships manifest in the f-structure in (20) 
are: 3 
(i) R(f, CONJ. ft) 
(ii) R(f, CONJ, f2) 
(iii) R(fl, SUB J, 9) 
(iv) R(fl, oaa, h) 
(v) R(f2, SUB J, i) 
(vi)  (A, oBJ, h) 
There are several equivalent derivation orders: 
here we step through one. 4 Using the meanings for 
Bill. supported, Hillary, and opposed, R-relations 
(iii) and (v), and Axiom I, we can derive mean- 
ings for Bill supported and Hillary opposed in the 
fashion described in Section 3: 
bill-supported: VY. (ft OBJ}e"'~Y 
---o fla "-" supported(Bill, Y ) 
hillary-opposed:gZ. (f20BJ} o"~ Z 
.--o f2~, ~ opposed( IIillary, Z) 
We combine the antecedents and consequents of 
the foregoing formulae to yield: 
bill-supported ® hillary-opposed: 
VY, Z. (fl ®B J) ----~Y ® (f2 oaJ)a"-"Z 
---o fla-,-+ supported(Bill, Y) 
® f2a ~ opposed( Hillary, Z) 
Consuming the meaning of and and R-relations (i) 
and (ii), and using Axiom I, we derive: 
bill-suppor ted-and-hillary-opposedl: 
vY, z. (k osaL ~ r ® (A oaaL-,-, z 
--o f~ ~ and(supported(Bill, Y), 
opposed( Hillary, Z) ) 
Using Axiom I and R-relations (iv) and (vi), the 
following implication can be derived: 
VX. hc~"~ X 
-o (fl oaJ)o"-+X ® (f20BJ)~,---*X 
Using these last two formulae, by transitivity we 
obtain: 
bill-supported-and-hillary-opposed2: 
VX. h~',~ X 
-o f o -,., and( supported( Bill, X), 
opposed( ttillary, X) ) 
aWe treat the CONJ features as unordered, as they 
are in the f-structure set. 
4In the interest of space, we will skip some inter- 
mediate steps in the derivation. 
35 
Finally, consuming the contribution of NAFT\4, 
by Ulfiversal instantiation and modus ponens we 
obtain a meaning for the whole sentence: 
fo'--*and( supported( Bill, N :tFTA ), 
opposed( Hillary, NAFTA) ) 
At this stage, all accountable resources have been 
consumed, and the deduction is complete. 
4.2 RNR with Coordination and 
Quantified NPs 
We now consider sentence (21), where a quantified 
NP is shared. 
(21) Bill supported, and Hillary opposed, two 
trade bills. 
Partee and Rooth (1983) observe, and we agree, 
that the quantifier in such cases only scopes once, 
resulting in the reading where Bill supported and 
Hillary opposed the same two bills. 5 Our analysis 
predicts this fact in the same way as Partee and 
Rooth's analysis does. 
The meanings contributed by the lexieal items 
and f-structure dependencies are the same as in 
the previous example, except for that of the ob- 
ject NP. Following Dalrymple et al. (1994a), the 
meaning derived using the contributions from an 
f-structure h for two trade bills is: 
two-trade-bills: 
VH, S. (Vz. h~-.~x --o H~S(~)) 
-o g..~two(z, tradebill(z), S(z)) 
The derivation is just as before, up until the 
final step, where we have derived the formula 
labeled bill-supported-and-hillary-opposed2. 
This formula matches the antecedent of the quan- 
tified NP meaning, so by universal instantiation 
and modus ponens we derive: 
f a "-* two( z, tradebill( z ), and(supported(Bill, z ), 
opposed( Hillary, z ) ) ) 
With this derivation, there is only one quantifier 
meaning which scopes over the meaning of the 
coordinated material. A result where the quan- 
tifier meaning appears twice, scoping over each 
conjunct separately, is not available with the rules 
we have given thus far; we return to this point in 
Section 5. 
The analysis readily extends to cases of nonco- 
ordinate RNR such as example (4), repeated as 
example (22). 
SWe therefore disagree with Hendricks (1993), who 
claims that such sentences readily allow a reading in- 
volving four trade bills. 
(22) Citizens who support, paraded against 
politicians who oppose, two trade bills. 
In our analysis, the f-structure for two trade bills 
is resource-shared as ttle object of the two verbs, 
just as it is in the coordinated case. 
Space limitations preclude our going through 
the derivation; however, it is straightforward given 
the semantic contributions of the lexical items and 
R-relations. The fact that there is no coordination 
involved has no bearing on the result, since the s,.- 
mantles of resource-sharing is distinct from that of 
coordination in our analysis. As previously noted. 
this separation is not possible in CCG because of 
the tight integration between syntax and seman- 
tics. In LFG, the syntax/semantics interface is 
more loosely coupled, affording the flexibility to 
handle coordinated and non-coordinated cases of 
RNR uniformly in the semantics. This also al- 
lows for our semantics of coordination not to r,'- 
quire schemas nor entities of polymorphic type: 
our meaning of and is type t x t --+ t. 
5 Intensional Verbs 
We now return to consider cases involving inten- 
sional verbs. The preferred reading for sentence 
(23), in which only one quantifier scopes over the 
two extensional predicates, is shown below: 
(23) Hi llary wanted, found, and supported two 
candidates. 
and(wanted( Hillary, 
~)~Q.two( x, candidate(z), \['Q\](x))), 
two(z, candidale( z ), 
and(found( Hillary, z), 
supported( Hillary, z ) ) ) ) 
The f-structure for example (23) is given in (24). 
/ g:\[P o 1 • \[PRED 'CANDmATE'\] I I ,\]\ fl: L TM 
I: I2/s~J 
L OBJ 
Ia: ~ sum 
OBJ 
The meaning constructors for the lexical items are 
given in Figure 1. Recall that a second meaning 
36 
Hillary: 
wanted: 
found: 
supported: 
and: 
and2: 
go "~ Hillary 
VX, Y. (fl SUBJ)~ ~'" X 
(Vs,p. (VX. (fl susJ)~'--*X -o s--~p(X)) --o s-,~ Y(p)) 
---o flz"'* wanted(X, "}") 
VX, Y. (f2 sUBJ)~-~.¥ '.9 (f20BJ)a""~ Y --,o f2~-.-~found(X, Y) 
VX, Y. (f3 SUBJ),,---+X ® (f30BJ)o"--~Y --<, f3o-.--supported(X, Y) 
VX, Y. (f CONJ)a",~X @ (f CONJ)o.",.-~ Y ---o fo.-.-+and(X, Y) 
!(VX, Y. (f CONJ)cy"c*X @ fa-.~ Y --o fo-.~and(X, Y)) 
two-,:andidates:VH, S. (Vz. h~X --o lf~S(z)) --o H-.-*two(z, candidate(z), S(z)) 
Figure 1: Meaning constructors for sentence (23) 
constructor and2 is introduced by and in order to 
handle cases where there are more than two con- 
juncts; this contribution will be used once in the 
derivation of the meaning for sentence (23). The 
following R-relations result from the f-structural 
relationships: 
(i) R(f, CONJ. fl) 
(ii) R(f, CON J, f2) 
(iii) R(f, CONJ, f3) 
(iV) ~(fl, SUBJ, g) 
(v) R(f2, SUB J, g) 
(vi) /~(f3, SUB J, g) 
(vii) R(I1, OBJ, h) 
(viii) R(f2, OBJ, h) 
(ix) R(f3, OBJ, h) 
Following the analysis given in Dalrymple et al. 
(1994b), the lexical entry for want takes a quan- 
tified NP as an argument. This requires that the 
quantified NP meaning be duplicated, since other- 
wise no readings result. We provide a special rule 
for duplicating quantified NPs when necessary: 
(25) QNP Duplication: 
!(VF, Q. 
\[VH, S. (Vx. Fa-.-.x --~ H..-~S(x)) 
--o H-,~Q(S)\] 
-o \[ \[VH, S. (Vx. G~x --0 H-.~S(x)) 
--o H.,-.Q(S)\] 
o \[vtL s. (vx. F~x --o H~S(x)) 
--o H-,~,Q(S)\] \]) 
In the interest of space, again we only show a few 
steps of the derivation. Combining the meanings 
for Hillary, found, supported, and and, Axiom I, 
and R-relations (ii), (iii), (v), (vi), (viii), and (ix), 
we can derive: 
ha..~ x ---o f¢,-,-*and(found( Hillary, x), 
supported( Hillary, x ) ) ) 
We duplicate the meaning of two candidates using 
QNP Duplication, and combine one copy with the 
foregoing formula to yield: 
f o ..... t wo( z, candidate(z), 
and(found( Hillary, z), 
supported( Hillary, z ) ) ) 
We then combine the other meaning of two can- 
didates with the meanings of Hillary and wanted. 
and using Axiom I and R-relations (i), (iv), and 
(vii) we obtain: 
(f CONJ ) o- "'+ 
wanted(Hillary, 
" AQ.two( z, candidate(z), \[-Q\](z))) 
Finally, using and2 with the two foregoing formu- 
lae, we deduce the desired result: 
f~ .-~ and(wanted( Hillary, 
"AQ.two( x, candidate(x), I-Q\] (x))). 
two(z, candidate(z), 
and(found( Hillary, z ), 
suppo~ted( HiUa~y, z)))) 
We can now specify a Partee and Rooth style pro- 
cessing strategy, which is to prefer readings which 
require the least use of QNP duplication. This 
strategy predicts the readings generated for the 
examples in Section 4. It also predicts the de- 
sired reading for sentence (23), since that reading 
requires two quantifiers. While the reading gener- 
ated by Partee and Rooth is derivable, it requires 
three quantifiers and thus uses QNP duplication 
twice, which is less preferred than the reading re- 
quiring two quantifiers which uses QNP duplica- 
tion once. Also, it allows some flexibility in cases 
where pragmatics strongly suggests that quanti- 
tiers are copied and distributed for multiple ex- 
tensional verbs; unlike the Partee and Rooth ac- 
count, this would apply equally to the case where 
there are also intensional verbs and the case where 
there are not. Finally, our account readily applies 
to cases of intensional verbs without coordination 
as in example (10), since it applies more generally 
to cases of resource sharing. 
37 
6 Conclusions and Future Work 
We have given an account of resource sharing in 
the syntax/semantics interface of LFG. The mul- 
tiple use of semantic contributions results from 
viewing dependencies in f-structures as resources; 
in this way the one-to-one correspondence be- 
tween f-structure relations and meanings is main- 
tained. The resulting account does not suffer from 
overgeneration inherent in other approaches, and 
applies equally to cases of resource sharing that do 
not involve coordination. Furthermore, it lends it- 
self readily to an extension for the intensional verb 
case that has advantages over the widely-assumed 
account of Partee and Rooth (1983). 
Here we have separated the issue of arriving at 
the appropriate f-structure in the syntax from the 
issue of deriving the correct semantics from the 
f-structure. We have argued that this is the cor- 
rect distinction to make, and have given a treat- 
ment of the second issue. A treatment of the first 
issue will be articulated in a future forum. 
Acknowledgements 
We would like to thank Sam Bayer, John Maxwell, 
Fernando Pereira, Dick Oehrle, Stuart Shieber, 
and especially Ron Kaplan for helpful discussion 
and comments. The first author was supported in 
part by National Science Foundation Grant IRI- 
9009018, National Science Foundation Grant IRI- 
9350192, and a grant from the Xerox Corporation. 
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