Computing Discourse Semantics

45 Pages·2012·0.34 MB·English

ComputingDiscourseSemantics: ThePredicate-Argument
Semantics of Discourse Connectives in D-LTAG
KatherineForbes-Riley BonnieWebber AravindJoshi
UniversityofPennsylvania UniversityofEdinburgh UniversityofPennsylvania
Abstract. D-LTAGis adiscourse-level extension of Lexicalized Tree-Adjoining Grammar
(LTAG),in which discourse syntax is projected by different types of discourse connectives
and discourse interpretation is a product of compositional rules, anaphora resolution, and
inference.Inthispaper,wepresentaD-LTAGextensionofongoingworkonanLTAGsyntax-
semanticinterface.First,weshowhowpredicate-argumentsemanticsarecomputedforstan-
dard, (cid:148)structural(cid:148) discourse connectives. These are connectives that retrieve their semantic
arguments from their D-LTAG syntactic tree. Then we focus on discourse connectives that
occursyntacticallyas(usually)frontedadverbials.Theseconnectivesdonotretrieveboththeir
semantic arguments from a single D-LTAG syntactic tree. Rather, their predicate-argument
structureandinterpretationdistinguishthemfromstructuralconnectivesaswellasfromother
adverbials that do not function as discourse connectives. The unique contribution of this
paperliesinshowinghowcompositionalrulesandanaphoraresolutioninteractwithintheD-
LTAGsyntax-semanticinterfacetoyieldtheirsemanticinterpretations,withmulti-component
syntactictreessometimesbeingrequired.
1. Introduction
Thenotionthatdiscourserelatestosyntaxandsemanticsinacompletelydif-
ferentwaythandoesthesentenceseemsstrangewhenweconsiderexamples
such as (1), where an entire discourse is contained within a relative clause,
exhibitingthesamecohesiveandargumentativeconnections characteristicof
multi-sentential discourses suchas(2).
(1) Any farmer who has beaten a donkey but gone home regretting it and
hasthenreturnedandapologized tothebeast,deserves forgiveness.
(2) Afarmerbeatadonkeybuthewenthomeregrettingit.Thenhereturned
andheapologized tothebeast.Asaresulthedeserves forgiveness.
Althoughseveraldiscoursemodelsprovideasyntaxandsemanticsfordis-
course(Schilder,1997;Gardent,1997;PolanyiandvandenBerg,1996;Scha
and Polanyi, 1988), their syntax and semantics differ from what one (cid:2)nds at
thesentencelevel.D-LTAGpresentsamodeloflow-leveldiscoursestructure
and interpretation that exploits the same mechanisms used at the sentence
levelandbuilds themdirectly ontopofclausestructure andinterpretation.
In this paper, we address the computation of discourse semantics in D-
LTAG.Westartbyintroducing D-LTAGinSection2.Section3thenpresents
a D-LTAG extension of ongoing work on an LTAG syntax-semantic inter-
face,and showshow itisused tocompute the predicate-argument semantics
2 Forbes-Riley,Webber,Joshi
for D-LTAGstructural connectives. In Section 4, we describe how adverbial
discourse connectives differ from structural connectives, and from other ad-
verbials, in terms oftheir predicate-argument structure and interpretation. In
Section 5, we show how their predicate-argument semantics is computed in
D-LTAG’ssyntax-semantic interface.InSection6,wecomparethecomputa-
tionofdiscourse semantics inD-LTAGwiththatinprevious discourse mod-
els. In Section 7, we highlight unresolved issues arising due to the on-going
natureofthiswork,bothatthediscourse levelandtheclauselevel.
2. D-LTAG:Anintermediatelevelofdiscourserepresentation
D-LTAG (Creswell et al., 2004; Webber et al., 2003; Forbes et al., 2003;
Creswelletal.,2003;Creswelletal.,2002;Forbesetal.,2001;Webberetal.,
1999b;Webberetal.,1999a;WebberandJoshi,1998)buildsanintermediate
level of discourse structure directly on top of the clause. D-LTAG’s syntax
is currently modeled using the structures and structure-building operations
of a lexicalized tree-adjoining grammar (LTAG) (Joshi and Vijay-Shanker,
1999;XTAG,2001),whichiswidelyusedtomodelthesyntaxofsentences.
2.1. AN INTRODUCTION TO LTAG
LTAGis an extension of a tree-adjoining grammar (TAG) (Joshi, 1987) that
includes lexicalization and uni(cid:2)cation-based feature structures, and repre-
sents the underlying structure of a surface string, as well as the string itself.
LTAG consists of 1) a (cid:2)nite set of elementary trees, each associated with at
leastonelexicalitem(theanchor),and2)operations forcombiningthem.
There are two types of elementary trees in LTAG:initial trees, which en-
code basic predicate-argument relations, and auxiliary trees, which encode
recursion and(cid:0) must contain a non-terminal node, called the foot node and
indicated by ,whose label matches thelabel ofthe root. Therightmost tree
inFigure1isanauxiliary tree,alltheothersareinitialtrees.
(cid:18) (cid:19) (cid:20)
(cid:4)(cid:6)(cid:2) (cid:5) (cid:2) (cid:2) S(cid:1) (cid:1) (cid:1) NP (cid:10)t(cid:18) (cid:12) NP (cid:10)t(cid:19) (cid:12) (cid:15)VP(cid:15) (cid:10)(cid:14)t(cid:20) (cid:14)(cid:12)
(cid:3) (cid:7)(cid:9)(cid:8) (cid:10) (cid:11) b b b
NP t (cid:15)VP(cid:15) (cid:14)tb(cid:11)(cid:13)(cid:14)(cid:12) (cid:4) (cid:5) N N ADV VP(cid:21) (cid:10)t(cid:20)(cid:20)(cid:19)(cid:19) (cid:12)
(cid:16) (cid:17)(cid:8) b
V NP t John Fido often
walks
Figure1. ElementaryLTAGTrees
Each elementary tree represents a domain of locality encoding the syn-
tactic/semantic arguments of its anchor. An anchor may be associated with
multipleelementarytrees;eachtreeinthisfamilyre(cid:3)ectsaminimalsyntactic
ComputingDiscourseSemantics 3
construction.Forexample,theverbwalkmaytakethetransitivetreeshownin
Figure1oranintransitivetree.Eachnodeinanelementary treeisassociated
with at least one feature structure (cid:150) a top feature structure in the case of
substitution nodes, and both a top and bottom feature structure in the case
of all other nodes. These for several nodes are shown in Figure 1. Feature
uni(cid:2)cation then implements the dynamic speci(cid:2)cation of local constraints
concerning hownodesinteractduringstructure-building, including linguistic
constraints onagreement,case,andtense(XTAG,2001).
There are twostructure-building operations in LTAGthat create complex
trees, called derived trees: sub(cid:22)stitution and adjunction. Substitution consists
of replacing the node marked , as in the leftmost tree in Figure 1, with the
treebeingsubstituted. Onlyinitialtreesortreesderivedfrominitialtreescan
besubstituted, andtherootnodeofthetreebeingsubstituted mustmatchthe
label ofthenode being replaced. Forexample,wecan substitute theNPtree
anchored by Fido in Figure 1 for the internal NP argument (annotated here
with i) in the tree anchored by walks, and the NP tree anchored by John for
theexternal NPargument (annotated herewithe).Ineachcase,theresulting
node takes the union of the features of the involved nodes. In this union,
the features common to both nodes must match. The remaining featur(cid:23)es are
simplyassigned. Forexample, ifthetopagreement features oftheNP node
are 3rd person, singular, they must either match the top agreement features
oftheNPnodeintheJohntreeorbeassigned. TheNPnodeintheFidotree
will not carry case(cid:24) features, so accusative case will be assigned by the top
features of the NP node. The derived tree resulting from these substitutions
isshowninFigure2(a).
(cid:2) (cid:2) (cid:2) (cid:2) S(cid:1) (cid:1) (cid:1) (cid:1) (cid:26) (cid:26) (cid:26) S(cid:25) (cid:25) (cid:25)
(cid:7) (cid:18) (cid:11) (cid:20)
NP (cid:10)t(cid:18) Ut (cid:12) (cid:26)(cid:26) (cid:26) V(cid:25)P (cid:25)(cid:25) (cid:17) (cid:19) NP (cid:26)V(cid:26) P(cid:26) (cid:10)t(cid:20)(cid:25) Ut(cid:25) (cid:25)(cid:12)
bN V NP (cid:10)tb(cid:19)Ut (cid:12) N ADV bVP(cid:28) (cid:28)(cid:10)t(cid:20)(cid:11)(cid:19)(cid:27) (cid:27) (cid:20) (cid:19) (cid:12)
walks Joe b Ub
Joe N often
V NP
Fido
walks N
Fido
(a) (b)
Figure2. LTAGDerivedTreesAfterSubstitutionandAdjunction
Adjunctionisrestrictedtonon-terminalnodesnotalre(cid:29) adymarkedforsub-
s(cid:30) titution, and bu(cid:29)ilds a n(cid:30) ew tree from an auxiliary tree a(cid:29) nd any other tree
. To combine (cid:31)and (cid:30) by adjunction, the root node of m(cid:29)ust match the
label(cid:31)of the node in to which it adjoins. The root nod(cid:29)e of is identi(cid:2)ed
with ,theirtopfeaturesunify,andthebottomfeaturesof areinherited;the
4 Forbes-Riley,Webber,Joshi
(cid:31) (cid:29)
sub(cid:31)treedominatedby isattachedtothefootnodeof ,thebottomfeatures
o(cid:31) f unifywiththoseofthefootno(cid:29) de,andtherestofthetreethatdominated
nowdominatestherootnodeof .Forexample,thetreeanchoredbyoften
inFigure1canadjointotheVPnodeinFigure2(a);theresult,withrelevant
featureuni(cid:2)cations,isshowninFigure2(b).
Because derived trees such asinFigure 2donot indicate whattreeswere
combined or what operations were used to combine them, this information
is recorded in an associated derivation tree. A node in a derivation tree is
labeled with the elementary tree involved at that point in the derivation; the
root of the derivation tree is labeled with the (unique) initial tree that is not
substituted into anyother treeinthisderivation. In(cid:29)general, initial treelabels
start with , and auxiliary tree labels start with . A tree address is also
associated with each node in the derivation tree except the root. This is the
address ofthenode inthe parent treeatwhich thesubstitution oradjunction
operation has occu!#rr"%e$ d. The address of the root node in the parent tree is 0,
t&h"%e$ address of the child of that root’is (k), and (p.q) is the address of the
child of the node whose address is . The derivation tree corresponding
to Figure 2(b) is shown in Figure 3. (Dashed lines indicate adjunctio )n(+,*-a,/n.10d
s 3o25li4d lines, substitution 7.)(+*-T,8h.10e initial tree that ro(cid:23)ots(cid:29)9t4(cid:13)h:is(cid:23) derivation is 7(;*<,/.10.
$16 " 6
substitutesinto >= (cid:24)@? 4ataddress(1)(NP 7(+),*-,8.10 adjoinsinto (cid:24)
ataddress(2)(VP),and substitutes into ataddress (2.2)(NP ).
A#BDC(cid:13)EGFIH
A#J<KMLON KMQ(cid:13)R N ATS K
P (cid:3) (cid:16)/U
(1) (2) (2.2)
Figure3. LTAGDerivationTree
2.2. AN INTRODUCTION TO D-LTAG
D-LTAG builds on the observation that discourse connectives function syn-
tactically andsemantically inthediscourse akintothewayverbsfunction in
the clause. In LTAG,verbs are viewed as predicates, which supply relations
between entity interpretations of noun phrases (NPs) and/or clauses (Ss),
producing asentence interpretation. InD-LTAG,thepredicates arediscourse
connectives, whose arguments are entity interpretations derived from either
simplediscourseunits(e.g.individualclauses)orcomplexunitsV composedof
clausesanddiscourseconnectives.Wewillusethenotation(cid:147)D (cid:148)forboth,to
indicatethattheseunitsarebeinganalyzed atthediscourse level.
AsinLTAG,each elementary tree inD-LTAGisanchored by atleast one
lexical item. Although the research is ongoing, our current view of the set
of lexical items that convey discourse-level predication is that it includes
subordinating and coordinating conjunctions, an empty connective at clause
boundaries that are not marked by an explicit discourse connective, certain
ComputingDiscourseSemantics 5
adverbsandprepositionalphrasescalleddiscourseadverbials,andevensome
verbformssuchas(cid:147)provided that(cid:148)andimperative(cid:147)suppose(cid:148).
D-LTAG has both initial trees and auxiliary trees. Initial trees localize
thepredicate-argument dependencies ofdiscourse connectives. Forexample,
the tree family associated with subordinating conjunctions contains the two
initialtreesshowninFigure4withtheanchoralthough, representing theba-
sic syntactic alternations shown in (3a)-(3b) that subordinating conjunctions
displayrelativetotheirarguments (Quirketal.,1985).1
(3) a.Johnisveryhardto(cid:2)nd,althoughheisverygenerous.
bAlthoughJohnisverygenerous, heisveryhardto(cid:2)nd.
(cid:26) (cid:26) (cid:26) (cid:26) D(cid:25)W (cid:25) (cid:25) (cid:25) (cid:15)(cid:15) (cid:15) (cid:15) D(cid:14)XXW (cid:14) (cid:14)(cid:14)
(cid:4) (cid:4) (cid:4) (cid:4)
W W W W
D although D although D D
Figure4. D-LTAGInitialTreesforSubordinatingConjunctions
InLTAG,subordinatedclausesaretreatedasadjunctsbecausetheyarenot
part of the extended projections (e.g. argument structure) of the verb of the
mainclause.InD-LTAG,however,itistheextendedprojections ofdiscourse
connectivesthatarebeingmodeled:forexample,subordinating conjunctions
relate two clausal interpretations toform alarger discourse unit and are thus
representedastakingtwostructuralarguments.(Assuch,wecallthemstruc-
tural connectives.) As is also true of local dependencies at the clause level
(e.g. Apples, Bill says John may like.), these dependencies can be stretched
long-distance viaadjunction ofadditional clauseunits,asshownin(4).
(4) a.AlthoughJohnisverygenerous -
b.ifyouneedsomemoney,
c.youonlyhavetoaskhimforit-
d.he’sveryhardto(cid:2)nd.
TwotypesofauxiliarytreesareusedinD-LTAG.The(cid:2)rstisforstructural
connectives that convey a continuation of the prior discourse, e.g. a modi(cid:2)-
cation that serves to further a description of a discourse situation or of one
or more entities withinY it (Webber et al., 2003). Auxiliary trees for and and
theemptyconnective areshowninFigure5.Whilebothargumentsinthese
treescomestructurally,onecomesviasubstitution,whiletheothercomesvia
adjunctiontoadiscourseunitinthepriordiscourse.Continuationisthusakin
tothenotionofelaboration inKnottetal.(2001),asexempli(cid:2)edin(5).
(5) Johnwenttothezoo[and/.]H/hetookhiscellphonewithhim.
1 IndisplayingD-LTAGtrees,wesuppressannotationoffeaturestructures,asconstraints
onhowdiscoursenodesinteractduringstructurebuildinghavenotyetbeexhaustivelystudied
(cf.Section5.4,7).EmpiricalevidenceforsuchconstraintsmaycomefromthePennDiscourse
Treebank(Miltsakakietal.,2004;Prasadetal.,2004)aswellasfromtheoreticalstudies.
6 Forbes-Riley,Webber,Joshi
(cid:26) (cid:26) (cid:26) (cid:25)W (cid:25) (cid:25) (cid:15)(cid:15) (cid:15) (cid:14)W (cid:14)(cid:14)
D (cid:4) D (cid:4)
W (cid:21) W W (cid:21) Z W
D and D D D
Z
Figure5. D-LTAGAuxiliaryTreeforandand
Y
More generally, the relations supplied by and or in these examples are
syntactically under-speci(cid:2)ed, analogous to the syntax of noun-noun com-
pounds,andtheycanberepresentedinthelexiconassemanticallyunderspec-
i(cid:2)ed.2 In many instances there may be additional inferred relations between
the incoming unit and the prior discourse over and above simple elaboration
(indicated here bycoordination), whichmayberepresented assemantic fea-
tures in the (cid:2)nal discoursY e structure. For example, in addition to the simple
elaboration relation that supplies between the interpretations of John came
home late and Mary berated him in (6), a temporal relation will be inferred
between these two clauses and a causal one as well. While these additional
inferencesarecriticaltoafullaccountofdiscoursemeaning,becausetheycan
becanceled,3 wedonotconsider suchinferences tobepartofcompositional
semanticsandhencedonotdiscussthemwithinthesyntax-semanticinterface
wepresent hereforD-LTAG.
(6) Yesterday,Johncamehomelate[and/.]Maryberated him.
Where conjunctions convey more than continuation, they are represented
withinitialtrees.Forexample,soconveysaresult relation,asin7:
(7) Youdidn’teatyourspinachsoyouwon’tgetdessert.
The second type of auxiliary D-LTAGtree, shown in Figure 6, is used to
represent discourse adverbials such as then, otherwise, (in the) meanwhile,
etc. Like structural connectives, discourse adverbials relate the interpreta-
tions of two simple or complex discourse units. However, unlike structural
connectives,theyretrieveonlyoneargumentstructurally(cid:150)fromthediscourse
unitthey modify. Againthere aretwotrees inthis treefamily too,due to the
factthatdiscourse adverbials canappearS-initialandS-(cid:2)nal.4
Exceptfortheirnodelabels,theD-LTAGtreesfordiscourseadverbialsare
identicaltoLTAGtreesforS-modifyingadverbials;adjunctionrepresentsthe
2 E.g.Knott(1996)treatsthelexicalsemanticsofconnectivesasfeatureinheritance.
3 Inferenceofacausalrelationcanbecanceledasin(i).Thewell-knownexamplein(ii)
showsthatevenaninferenceoftemporalordercanbecanceledaswell.
(i)JohncamehomelateandMaryberatedhim.Butitwasbecausehehadforgottentostop
atthegrocerystore,ashehadpromised.
(ii)Marygotmarried,andshegavebirthtoason,butnotinthatorder.
4 Whilebothdiscourseadverbialsandsubordinateclausescanappearclause-internally,D-
LTAGcurrently does not posit separate trees for them. Rather, our D-LTAGparser (Forbes
et al., 2003) extracts them from clause-internal position, leaving a trace for information-
structureanalysesandrepresentingthemwithanS-initialtree.
ComputingDiscourseSemantics 7
optionalcontinuationthatalladverbialsmake.Butsincediscourseadverbials
retrieve only one of their argumenV t(cid:0)s structurally (from the discourse unit at
the foot of the adjunction site D ), D-LTAG must account for where the
otherargumentcomesfrom.Elsewherewehaveargued(Webberetal.,2003)
thatitisprovided anaphorically.
\ \ [W[ \ \ [W[
D D
W](cid:21) W](cid:21)
D then then D
Figure6. D-LTAGAuxiliaryTreesforDiscourseAdverbials
Thisdistinction betweenstructuralandanaphoric connectivesinD-LTAG
is based on considerations of computational economy and behavioral evi-
dence from cases of multiple connectives (Webber et al., 1999b). In (8),
because encodes a causal relation between the event of Sally raising ire and
Sallyenjoyingcheeseburgers, whileneverthelessencodesaviolatedexpecta-
tion relation between Sally enjoying cheeseburgers and Sally subscribing to
theVegetarianTimes(Creswelletal.,2002).
(8) a.Sallysubscribes toVegetarianTimes.
b.Lately,she’sraisedtheireofherveganfriends
c.because shenevertheless enjoys theoccasional baconcheeseburger.
To model both because and nevertheless as structural connectives would
create a directed acyclic graph with crossing dependencies, which goes be-
yond the computational power of LTAG and creates a completely uncon-
strained model of discourse structure (Webber et al.,2003). However, inves-
tigations into the behavior of discourse connectives reveal that while sub-
ordinating and coordinating conjunctions are constrained to take adjacent
discoursesegmentsoflikesyntactictypeastheirarguments,discourseadver-
bials seem to share many properties with anaphora. For example, discourse
adverbialscan(likeNPanaphora)taketheirpriorargumentintra-sententially
asin(9),whereembeddedneverthelessrelatestheinterpretationofthematrix
clausetotheinterpretation oftherelativeclause(Webberetal.,2003).
(9) Many people who have developed network software have nevertheless
nevergottenveryrich.(i.e.despitehaving developed networksoftware)
AnotherfeaturethatdiscourseadverbialssharewithanaphoricNPsisthat
they can access inferred entities as well as ones introduced explicitly. For
example, in (10a) the discourse adverbial otherwise can access the inferred
condition of if the light is not red. This material is not available to struc-
tural connectives: that is, or in (10b) can only access what is to its left (cid:150) the
consequent clause(stop)ortheantecedent(cid:150)consequent pair.
8 Forbes-Riley,Webber,Joshi
(10) a.Ifthelightisred,stop.Otherwisegostraighton.
b.Ifthelightisred,stop,orgostraight on.
Furthermore,aproperty ofallEnglishstructural predicates isthattheydo
notallowcrossing ofpredicate-argument dependencies.5 Forexample,while
example (4) above is interpretable as an embedded if S1, S2 construction
within an although S1’, S2’ construction, crossing these dependencies as in
(11) is either uninterpretable or at least yields a different interpretation; the
dependencies intheoriginal constructions arelost.
(11) a.AlthoughJohnisverygenerous -
b.ifyouneedsomemoney-
d.he’sveryhardto(cid:2)nd-
c.youonlyhavetoaskhimforit.
However,discourse adverbials doallow crossing dependencies, asshown
in(12)(Webberetal.,2003).Forthenin(d)togetits(cid:2)rstargumentfrom(b),
itmustcrossthestructural connection betweentheclausesin(c)and(d)that
arerelatedbybecause.Ofcourse,asWebberetal.(200^ 3)note,it_isco^ mmon
foranaph_oratoshowcrossingdependencies(e.g.John toldMike he would
meethim later.).Whetheralldiscourseadverbials allowcrossingdependen-
cies is still an unanswered empirical question. Forbes et al. (2003) outline
an empirically-based approach to modeling discourse connectives, in which
predicate-argument dependencies are de(cid:2)ned structurally until contradicted
bycorpusexamples.
(12) a.JohnlovesBarolo.
b.Soheorderedthreecasesofthe’97.
c.Buthehadtocanceltheorder
d.because thenhediscoveredhewasbroke.
Thereisoneexceptiontodiscourseadverbialsbeingassociatedwithauxil-
iarytrees,andthatisforparallelconstructions, i.e.pairedconnectiveswhich
togetherassertdisjunction ((cid:147)either...or(cid:148)),addition(cid:147)notonly...butalso(cid:148)),con-
cession ((cid:147)admittedly...but(cid:148)), and contrast ((cid:147)on the one hand...on the other
hand(cid:148)). Because of the interpreted inter-dependency of the connectives in
theseconstructions, theyaremodeledwithinitialtrees,asinFigure7.
Parallel constructions have multiple anchors, but one or the other anchor
may not be realized: for example, (cid:147)or(cid:148) without (cid:147)either(cid:148), (cid:147)not only(cid:148) without
(cid:147)butalso(cid:148),or(cid:147)ontheotherhand(cid:148)without(cid:147)ontheonehand(cid:148).Onemightargue
inthelattercasethatanauxiliarytreeshouldbeusedinsteadofaninitialtree,
accessing the non-structural argument of (cid:147)on the other hand(cid:148) anaphorically.
But this is best viewed as an empirical question whose answer depends on
5 CrossingispossibleinDutchclauses,e.g.theDutchversionof(cid:147)Theratthecatthedog
chasedatedied.(cid:148)Butthereisnoevidence,eveninDutch,ofcrossingstructuralconnectives.
ComputingDiscourseSemantics 9
aa a a a a D‘W ‘ ‘ ‘ ‘‘
(cid:26) (cid:26) (cid:26) (cid:25)W (cid:25) (cid:25) (cid:26) (cid:26) (cid:26) (cid:25)W (cid:25) (cid:25)
D (cid:4) D (cid:4)
W W
Ontheonehand D Ontheotherhand D
Figure7. D-LTAGInitialTreeforParallelAdverbialConstructions
where the other argument is found. Data from the annotated corpus that will
comprise thePennDiscourse Treebank(Miltsakaki etal.,2004;Prasad etal.,
2004)willhelpanswerthisquestion.
We conclude this section by making clear our assumptions about dis-
coursestructure.Whileweassumethatdiscourseisprimarilytree-structured,
thereareafewsimpleexceptions thatrequire simpleDAGs(directed acyclic
graphs).First,aswenotein(Webberetal.,2003),wemustallowforexamples
suchas(13)fromBateman(1999):
(13) ...(vi)The(cid:2)rst to do that were the German jewelers, (vii) in particular
Klaus Burie. (viii) AndMorris followed very quickly after, (ix) using a
lacquetry technique tomakethebrooch, (x)andusing acrylics, (xi)and
exploring the use of colour, (xii) and colour is another thing that was
newatthattime...
Bateman analyzes this example as containing a transitional clause (here,
clause viii) that stands in one relationship (here succession, aka sequence)
to the clause preceding it (here, clause vi) and another relationship (here,
manner) to the clause following it (here, clause ix). The result illustrated in
Figure8(1)isasimpleDAGinwhichanodehasmorethanoneparent.
elaboration
succession manner elaboration
(vi) (viii) (ix) a b c
(1) (2)
Figure8. Simplemulti-parentstructurefor(1)(cid:147)transitional(cid:148)clause,(2)clausewithindepen-
dentpost-modi(cid:2)ers
Second, we may want to allow for a discourse structure that corresponds
in clause-level syntax to a head with independent post-modi(cid:2)ers, as in (14).
Inthiscase,bothpost-modi(cid:2)ers(b)and(c)relateasindependentelaborations
ofthemainclause(a),asillustrated inFigure8(2).
(14) a.JohnlovesBarolo.
b.He(cid:2)rsttasteditin1992.
c.According toHughJohnson,it’soneofItaly’ssupremereds.
10 Forbes-Riley,Webber,Joshi
This is again a simple DAG, in which a node has more than one parent.
BothcaseswouldrequirethatD-LTAGbeextendedtoallowthesameelement
tosubstituteintomorethanonetree(ortoallowanelementtobothsubstitute
intoonetreeandserveasanadjunction siteforanauxiliary tree).
But neither simple DAG (Figure 8 (1) or (2)) has crossing structural de-
pendencies: While the structure of Figure 8 (2) can be drawn in such a way
thatthearcfrom(a)to(b)crossesthearcfrom(a)to(c),simplydroppingthe
arc from (a) to (b) lower down in the (cid:2)gure removes it. So, contra (Danlos,
2004), this type of structure has no intrinsic crossing structural dependency,
and we continue to believe that the cost of moving to arbitrary DAGs for
discourse structure is too great to be taken lightly. In fact, the one discourse
structure given in (Danlos, 2004) of a DAG with real crossing dependencies
is one that she herself excludes as an analysis as violating what she calls a
left1-right2 principle.
While the syntax-semantic interface given in Section 3 does not cover
the structures given in Figures 8, it is because the adjoining and substitution
operatorsinTAGdonotletusproducethem.Thiswouldhavetobeaddressed
insubsequent work.
Wenowturntoourproposed syntax-semantic interface forD-LTAG.
3. ASyntax-SemanticInterface(SSI)forD-LTAG:Part1
3.1. STARTING POINT: SSIS FOR LTAG
Joshi and Vijay-Shanker (1999) were the (cid:2)rst to propose an SSI for LTAG.
Theysuggested thatifsubstitution andadjunction areviewedasattachments
ofonetreetoanothertree,thenasyntacticderivationconsistsofanunordered
set of attachments whose semantics can built monotonically and described
by a (cid:3)at semantic representation. For example, the (cid:3)at semantic representa-
tion corresponding to Figure 2(b) might be as in (15), where i1, i2 denote
individuals ande1denotesanevent.
b b b
(15) john(i1) Fido(i1) walks(e1,i1,i2) often(e1)
Theproblem that Joshi and Vijay-Shanker (1999) note, isthat adjunction
does not preserve monotonicity with respect to immediate dominance.6 Al-
though syntactic under-speci(cid:2)cation ofimmediatedominance wouldremove
this non-monotonicity, the tacit assumption in many LTAG formalisms is
that the nodes along the spine of a tree (the path from the root to the an-
chor) are not distinguished semantically. As an alternative to this syntactic
under-speci(cid:2)cation, Joshi and Vijay-Shanker (1999), Candito and Kahane
6 For example, in Figure 2(a), theA VKMQ(cid:13)PR(cid:3)tNhat is immediately dominated by S immediately
dominatesV,butinFigure2(b),after isadjoined,thisisnolongerthecase.