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<?xml version="1.0" standalone="yes"?> <Paper uid="C94-2154"> <Title>TIIE CORRECT AND EFFICIENT IMI)LI~',MI,N.\[A&quot; '~ TION OF' APPI\[()PRIATENESS SPECIFI(:ATIONS FOR TYPF;D FlgATURI&quot; STRUCTUR\]~,S</Title> <Section position="4" start_page="0" end_page="957" type="metho"> <SectionTitle> 2 APPROPRIATENESS FOR, MALISMS </SectionTitle> <Paragraph position="0"> As discussed iu Gerdemann ,~ King \[8\], one ca.n view a.pl}rol)ria.teness CO\[lditions as (lelining GPSG style fea,1;tl re cooccurence restrict:ions (FCRs). In \[8\], we divided FCRs into co,j,,ctive and di.q,,~ctive ct~sses. A conjunctive FCI/. is a constra.int of the following fornl : i\[' a.n object is of ;~ cert;fin kind then ill deserves certa.in fea.tures with wdues of cert~till kinds An FCI~ stat:ing tha,2: a. verb must h~we v and N t'eatures with values A- and - respectively is a.ll example of a. conjunctive FCI{. A disjunctive I&quot;CI{. is of the form: l rl'he &quot;\]'roll ,qysl.em was implemented in Quintus Prolog by Dale (lerdemann and '\['hilo (\]Stz.</Paragraph> <Paragraph position="1"> if an object is of a. cel'taiu kiud then it deserves cerl;a.in \[ca,1;tll'C~s with vMues of certa.hi kinds, or it deserves cerl.ahi (pei'ha.liS other) fea.1;u res \vil, h viiiues of terra.in (perlla.ps other) kinds, or ...</Paragraph> <Paragraph position="2"> (31: it i:leserw.;s i:erl;a.in (lmrhal)S other) fea,1;llres wil.h Vi, l.\[ll(~S o\[ certain (perha.ps other) khi,<ls I lo:: exa~\]nple, the following F(',|/. sl.a.t.iug tha,t inverCed verbs lilt|S1, lie a.uxili;tries is disjunctive: a verb Ilitisl; ha.re the \['(~il.l.tll'(~s INV and AUX with va.l/ies d a.Iid I, - a.iitl</Paragraph> <Paragraph position="4"> Both o |these |el'illS or l,'(',lls iiHly I)(! expressed in a. foi'llla.iiSlli euiployhi<~ fiiiil.e lia,rtia.\[ order (Type, E) o |types tllldel' sub8illnptioli> a, finite sel. Feat of ro;./.t;tll.(~s, and an a.pprol)ria.teness parl, ial rliilcl.ion</Paragraph> <Paragraph position="6"> the l, ypes fornla.lize I;lie notion ol&quot; kinds +,j&quot; objecl, t g: t,' ill' ca.oh oil|eel, of tyl>e t' i~<i Mso of l;Ylle L, il, ll(\] Approp(l, f) = l I ill' (!;i('\[I object oF type t deserves \[eaA.urt~ f wil.\]i :i.</Paragraph> <Paragraph position="7"> Vi./.\]lle or type ft. ~@'e call S/IC\]I it. \[Ol'tll;liiSlll i-i, ii ;I,\])l)l&quot;Opl'\]al, olio,~/ fOl'lllil\]i~;lll. (',iLl'peliLel&quot;,s AI,F, and (,erdeliia. i ;ill( |(i(~t,z's Troll are ex:-t.niples o |illilllenienl.a.Lions o| a,pF, ro\]) ria, Loliess |or illa.\[iSlil,s.</Paragraph> <Paragraph position="8"> l low an a.i)ln'oprhi.teness \[orniaJisnl enco<les a conjunctive I:(',R is ob\.'i<>us~ bll(.</Paragraph> <Paragraph position="9"> llOW it encodes a disjuiictive I&quot;(',1{ is less so. Ali exa.niple i|\]usl;ral;es best how it. is done. ~Ul)pOS0 that F( ',1{ \[i sl.al.es l.hal, ob.iecls (if type t deserw! \[(!a.\[./ll'(!S f 'and .q, I)oth with boolea.I/ wdues a.ll(I \['lll'l,\[lel'lllOF(~ that the va.hies of f aild g iil/lSl al~r(!e, \[> is the disjunct\]w! I&quot;(111.</Paragraph> <Paragraph position="10"> if a,u object is o\[ type l then it deserw:s f with va.lue -Iand q with wdue +, or it deserw.~s f with va.lue a.nd 9 with value To 0ncode \[3> first iul,rodLiCe sul/l.yltes , t ~ ## ;+l.ll(\[ l&quot; of I (1 E I/, 1. ), O11(! SUl)tyl)e \['()l' ea,ch disjuuct iu the cousequenl, of'p. Then encode the \]'ea.tli\['e/wthl~.~ <'on(!il.illliS in l, he \[irst disjunct ILy putthlg Approp(t', ./) :: ~-</Paragraph> <Paragraph position="12"> This a pproa,ch Ina, kes two inll)ort;a, lll, closed-world type assumptious a, bouL (.he types tli~d; Slll)SlllIle 11o ogher types (hellCeforth species), l:irst, the p;i.rtition conditiOII states tha.t for each type t, if a.n object is (31' type t theu the object is of exax-I.ly o11(2 species subsulned by t. Second, the all-or-nothing cclndition sta, tes that 1'(31' each species ,q a.itd fea.ture f, either every el&quot; IIO ol>,iecl, or species s deserves feature .#c.3 All a.l)ltroltriM,eliess \[orli+ia.lisill sllc\]l a.s ALl:, (\[2\], \[3\])ti,;t.l. does not uieet both c.ouditions llla.y llOt; \]lroper\[y el|cOde a, disjull('five l&quot;(:l/. For exalnple, consider disjunctive I&quot;CI{. p. An a.I)prl;)pria.l, elleSS \[ornia.l-iSlli I/lily l/O( properly encode 1,hi~t t / a.lld t&quot; i'el)rt,selil, MI a.lid oilly the disjuncl, s ill the COll.qeqll(Hlt or \[i wiLhout the i)a.rl,ition COlld\]tion. <till a.llln'ol)riill.eness \[orlila.liSlll llia,y IIOl. llrOl)erly encode the \[t~ii.l.llle/vii.hle (:(lll<liiriOii: deinanded liy em'h disjuncl, hi the COli.~t!qllelil. o |p wilhoul, the a.i\[-Ol'-liot;hilig c(m(til.ion.</Paragraph> <Paragraph position="13"> As indicat.ed a.bove, AI, I.; is iLIi exa.tlli)le o |it. f(n'liialiSlU I.ha.l, does it(it ineel; llol;h o| 1.hese closed world aS,glllnlil,iOli.g. In AI+E :-/.</Paragraph> <Paragraph position="14"> \['eli.l.tlr(~ st.i'llCtlile i.<4 won typed ifl' for ea.ch arc iit the te:+d.ure sI.l'tlCl;tlr0, if' 1,he SOtll'('(~ node is labelled wil.h type /., the targel; node is lallelled with 1;ype l / a.lld the il.i'c is IMlelled with \[ea.tlll'(~ f 1,lien Approp(/.> .f) \[ l/. Furl.her|note> a \['eal, urt~ strut(tire is >l'lds exanll)h: I:(JR is, for eXlmsil.ory l)nrl)oses, quilt simph'. &quot;l'hc prolileni o\[ c.xpr('.sshig F(Jl/'s, however, is a l'Cal Iiuguisl.ic i)rol)lcin. As noted I)y Copcstakc. ct al. \[4\], it. was inipossihlc I.o c.xpress CV('II Ihc .~ilii\[)\]oM. forilis o\[ l&quot;(JRs in l.hc.ii7 cxtciidcd VCISiOII (it' AI.E.</Paragraph> <Paragraph position="15"> '\['hc basic principle of expressing l&quot;Clls also ex lends Io I&quot;(',\[(s iuvolviug longer palhs. For example, to (:llSllt't: thai. for the type l, I.he path (fg) lakes a vahie subsuuied I)y .% one nlust tirst hll, ro ducc the chaiu Approp(/, f) = .,, Approp('a, g) = .~.</Paragraph> <Paragraph position="16"> well-typable iff the feature structure subsumes a well-typed feature structure, in ALl.:, type infereneing is employed to ensure that all feature structures are welltypable--in fact, all feature structures are well typed. Unfortunately, well-typability is not sufficient to ensure that disjunctive FCRs are satisfied. Consider, For exampie, our encoding of the disjunctive FCR p and suppose that 99 is the fe, ature structure t\[f : +,9 : -\]. 90 is well-typed, and hence trivially well-typable. Unfortunately, 99 vb elates the encoded disjunctive FCR p. The only way one could interpret ~ as well-formed null By contrast, the Troll system described in this paper has an etfeetive algorithm f<>r deciding well-formedness, which is based on the idea of efficiently representing disjunctive possibilities within the feature struetu.re. Call a well-typed feature structure in which all nodes are labelled with species a resolved feature structure and call a set of resolved feature structures that have the same underlying graph (that is, they differ only in their node labellings) a disjunctive resolved feature structure.</Paragraph> <Paragraph position="17"> We write fS, ~vf8 and 'D~.)c$ for the collections of feature structures, resolved feature structures and disjunctive resolved feature structures respectively. Say that F' 6 &quot;l~f$ is a resolvaat of F C f,&quot;? ill' F and .F' have the same underlying graph and F subsumes 1 ''l. Let taype resolution be the total flmction ~: f5&quot; --+ DgfS such that 7~(1,') is the set of all resolvants of l i'.</Paragraph> <Paragraph position="18"> Guided by the llartition and all-or-nothing coMitions, King \[13\] has fOl'intilated a semantics of feature structures and developed a notion of a satisfiable feature structure such that l'7 C .T$ is satisfial~le if\[' 7~(F) 7 ~ (7). C, erdemann ,% King \[8\] have also shown that a feature strtlcture l\]leets all encoded FCRs ifl&quot; the feature structure is satisfiable. The Troll system, which is based on this idea, effectively inqflements type resolution.</Paragraph> <Paragraph position="19"> Why does type resohttion succeed where.</Paragraph> <Paragraph position="20"> type inferencing fails? Consider again the encoding of p and the feature structure 9~. Loosely speaking, the appropriateness sl)eeifieations for type t encode the part of p that sta, tes that an object of tyl)e t deserves features f and g, both with boolean vahles. However, the appropriateness specifications for the speciate sul)types t' and t&quot; of type t encode the part of p that states that these vallies lnust agree. Well-typability only considers species if forced to. In the case of ~, well-typability can be estahlished by consklering type t alone, without the l)artition condition forcing one to find a well-typed species subsumed hy t. Consequently, well-tyl)ahility overlooks the part offl exehisively encoded by the ai)propriateness specifications for t' and t&quot;. Type resolution, on the other hand, always considers species. Thus, type resolving 9o cannot overlook the part of p exclusively encoded by tile appropriateness specifications for t' and t'.</Paragraph> </Section> <Section position="5" start_page="957" end_page="958" type="metho"> <SectionTitle> 3 MAINTAINING APPROPRIATENES S CONDITIONS </SectionTitle> <Paragraph position="0"> l\[ow may these D~.TS be used ill an inlplenmntation? A very important prop-erty of the class of &quot;DT~fS is that they are closed under unification, i.e., if/&quot; and F' 6 D~f8 then F U F' 6 D'PvfS. 4 Given this prol)erty , it would in principle lie possible to list the disjunctive resolved feature sl;ructures h/ an iinplemental;ion withonl; any additional type infer01\]C/hig proc0dnre to ma.hltahi satisfialfility. It would, of course~ tier be very of\[icieut 1.o work with such large disjunctions of featiil'e strtlctilres. These disjunetiorls of fea.ture structnres, however, have a singular l)rol)erty: all of the disjuncts have the same shape. The disjuncts differ only in the types labeling i;he nodes. This prop- null fS then &quot;R ( F) tJ 1&quot;(1&quot;') = &quot;R ( F tO F'). Uni/ication of sets of fca.ture structures is defined here ill the standard way: S t2 ,S&quot; = {1&quot;\[ I&quot;' 6 S and l&quot;&quot; G S&quot; and 1&quot; = 1&quot;' H 1&quot;&quot;}.</Paragraph> <Paragraph position="1"> (!rty a.llows a. disjultctivo fesolv(,d featur(, structti re to I)e r(;l)rosetd,(~d more et\[icieutly a,s ~t sitlgle untyl)(~d l'eatur(' st.l'll(:l.llfe plus a, sel; of d(;pondlmt node la.h(~liugs, which ca.n be further (;oml)a,(:t(~d using mi, Nie(l dis.</Paragraph> <Paragraph position="2"> junction a.s in (',(~rdemann \[(i\], I)i'~\['re t(: Fo\]' exanH)le , SUl)l)OS(~ \v(~ I,,yl)(~ r(~solvc the \[ea, l, urc st, ructure t\[,f ; bool,fl; bool\] using our encoding of p. ()he can (rosily see tha.t this fea.tur(~ strut:fur(, has only two I'e solwl, nts, which ca, n I)e colla.ps(~d iuto one fea,1;ure strlll:ttlro with llallV2d d\]sjunci.ion a,s shown below: II'll;1} \[&quot;'&quot;' \] f:k , : :> f: (I t -) 0:t- LU: J ,u: (I t ) We now ha,vo a, \[;(mSolml)ly COml)a(:l l'q)resentaJ;ion hi which t.ho l&quot;(il{, ha.s lie(Hi tl';tllsl;I,t(~(\[ iul,o a. Ila, ill(!(I (\[iS.\]llll(:l.ioli. Ih,w O,V(H'> (Hie should note tha, t fills dis.iun(: l;ion is only l)l'eSeUl; b(~(:aats(~ the \['oaJ, tli'O~i .f a,\]l(l g ha>l)l)en 1:o I)o Fir(~s(HIt. Tilt!S(! I(,a tures would .eed l;o Im l)res(mt il w(~ wtwe enforchl<ej (Jaxpcnl,(H&quot;s \[:7\] lcil, al w(ql i.yl)iug r(xluiroti\]oilt ~ whhth ,qa,y's 1.1ial \[(!al:ilr('s I. lial a,l:e a.llowed ilillSt 1)o pres,.ml., lllil. Iol.a\[ well I.yping is, hi fax:t> incoinl)a.lib\]e ;villi lype resolul, ioli~ since I;hore lilil$' w(ql I)o all inli llit;(~ seL of tota, lly w(,ll iyl)od I'esolvalil.s of ;1 l'(;a, Lllr(J st\]'llcttir('~, For (~xa.llipi(~, a.ll illi(lei'.-Sl)ocifiod list stl'u('tlir(' couhl be iT(~S()/v0(I 1.o ;~ list of length (L a. list of h:ngl.h 1, el.c, ,qhlce I, ota.I well I,yliin g is liOt i'(!quir(!(\[, we lm~y i~s well a.ctiwqy un\[il\[ r0(lulid;lnt \['0a, tlires, 5 ill this (!Xalli\[)l(!> i\[ t, li(' f ail(l (7 fo.a, tllrOS ;~l'e reliiovod, we a,lO lell wil, h lh(, simple, disjunction {if,/'~}: which is (!quiva,lent, to l;\]le or(lillaJ'y l,Yl)(' l.(; Thus, iu lliis ca, so> \]lO (lisjtulcl, ion a.t all ix rc!(llliro(l 10 (!11&quot; force the I&quot;CIL All th',tt is requirc(I is tim ~qntuil, ively, \[eat, ui'cs arc rodundaui it Ilwir val llCS art'. eul,h'cl 5 predictaldc fl'oui ihc approluiaic .ross Sl>eCificatim,..%'c GStz \[1)\], (',cr,lemam, \[7\] k,r ;I. IIlOl;('. \[HXX:iHC forUllllalioii.</Paragraph> <Paragraph position="3"> deg\[n this casc, il. would also have b(:ml l)~>,~iblc to unlill Lhc oi'i<eiuai teal, life Sll'tl<ltllc I,.I.ie I*' solviug. /Snforl, unai,e, ly, llmvcvcr, this i~; l.>i ;ihvay~. the (:asc, as C;lll |)(! S(!t'II in the \[ollowiug (!Xalll\])lC: t{j: +\] :> {C/: +\]} ~ ~'.</Paragraph> <Paragraph position="4"> asSUml)tion tha.t t will only be ext(mded I)y unil'ying il with a.lmther (t;Oml)a.ct(~d) m(mll)(!r o\[' &quot;l)'\]?.Jr,_c,.</Paragraph> <Paragraph position="5"> This, h.w(wer, wa.s a. simple ca.se iu which a.I1 of the named dis.jun(:tion could ho removed. It would not lmve I)('en i)os sihle to relnov(' tim fea.tur('s f ~tll(I g if thest~ 17,atu\['es had I)oen involved iu re(mtranci(+s of i\[' tlt(,se lim.tures ha.d ha.d t:omi)h+x va.lu('s, lu gt+tlera.I, howover, our eXl)eri(!ll(:(~ ha,s I)(~(ql that, eV(;l! wil, li very (:()tit pl('x type hi(~ra, rchi(~s a.nd |'(m, tur(; SLI'UCl, lll'eS \[()1&quot; liPS(i, very i'ow named (lisjunclions a, re introdu('e(l. 7 q'hus~ uuilica.1;ion is e;(merally uo more (~xp(msive tha.n unifica.li,:)H with unlylmd l(mt.ur(~ sl.fu(:l.ur('s.</Paragraph> </Section> class="xml-element"></Paper>