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<Paper uid="P85-1006">
  <Title>MEINONGIAN SEMANTICS FOR PROPOSITIONAL SEMANTIC NETWORKS</Title>
  <Section position="1" start_page="0" end_page="0" type="metho">
    <SectionTitle>
MEINONGIAN SEMANTICS FOR PROPOSITIONAL SEMANTIC NETWORKS
</SectionTitle>
    <Paragraph position="0"> rapapor t%buffalo~csnet-re la y.</Paragraph>
  </Section>
  <Section position="2" start_page="0" end_page="0" type="metho">
    <SectionTitle>
ABSTRACT
</SectionTitle>
    <Paragraph position="0"> Tilts paper surveys several approaches to semanttc-netw,~rk semantics that have not previously been treated ~n the AI or computattonal lingutsttcs hterature, though there ~s a large ptulu.</Paragraph>
    <Paragraph position="1"> ~)ph~cal hterature invest)gating them m ~mledetad. In parttcular, proF~n~onal semanttc networks (exemphhed hv ~,NeP%)are dis cus.~d, it ts argued that ~mlv a Iull'; mtenstonal (&amp;quot;Mem(mgtan&amp;quot;) semantics is apprt)prtate I(~r them. and se'~eral \|eln(~nglan svstenls are presented.</Paragraph>
  </Section>
  <Section position="3" start_page="0" end_page="48" type="metho">
    <SectionTitle>
1. SEMANTICS OF SEMANTIC NETWORKS.
</SectionTitle>
    <Paragraph position="0"> ~emantlc netwC/~rks have pr(~ed rt~ I~ a uselul dahl ,,true.lure for representing mlormatttm. =.e., a &amp;quot;knt~wledt, e'&amp;quot; repre~ntatmn svs tenn. (A I'~tter termmtdogv ix &amp;quot;'belief&amp;quot; teptexentatiott system; t.f.</Paragraph>
    <Paragraph position="1"> Rapa~)rt and Shaptn~ 1984. Rapap(trt 198.1hL The ~tlt'.= =,, an ,lid one: Inheritance networks (Iqg. I), hke tht,se ~1 ()ulllti|II 1968.</Paragraph>
    <Paragraph position="2">  (1979,), bear strong tamttv re~mblanues t() &amp;quot;l'.wphvrv',, I'ree'&amp;quot; (I ~t,. 2)---a mediaeval device u.~d t~&gt; dlustrate the .\r:st,.~ehan 'het,rv ,~I definn~(m by ~pe~:e~ and d~fferent~a ((-I. Kret~'mann I~'hh. ('It 2; Kneale and Kneale It~hh: 232). It has been r~,nted (~ut that titere ~s nothing essentmlly &amp;quot;~emanttc&amp;quot; about semantic networks (llendnx 1979; hut cf. Woods 1975. Brachman 1979). Indeed. v~ewed ,as a data structure, it is arguable that a semantic network m a language (r,,~.,~lhlV w~th an a~st~lated Ingle (~r ~nference mechanmm) f(~r representing inlornlatl(}n ah~)ut ,aline d(,mam, and, as such, IS a purely syntactic entity. They have (-(~me to he (-ailed &amp;quot;semanttc'&amp;quot; primarily hecau.~ ~d their uses as wart, ~ll representing tile meanings (~f hngutstic !temsC/.</Paragraph>
    <Paragraph position="3"> As a notatt(mal device, a semanuc net'a.'tlrk ~an ~tseil be g~','en a semantic,s. That is, the art, s. nc,Jes, and rules (~l :. semantic net~,'(irk representational system (.an 1~' given interpretations, in terms (if the entities they are u~d tit represent. Witilout ~;uch a semantics, a semantic network is an arhltrar'C/ not-':tt(mal dev;ce Imble tt~ mtsmterpretat=on tel. Wtx.ds 1975; I!,rathman i977. 1983; Mclgerm~ltt 1981 ). The task (~! prov:ding a semantt~s For semantic networks is more ak=n tt~ the task t)f providing a ,~mant~cs For a language than I'()r a logic. ,crate in the latter ca.;e, hut not m the  (.jenlls ..................... &gt; Differentia ..... &gt; C()R~)~ / NON-CORPOREAL Species .............. &gt; ~ L  A mediaeval inheritance network.</Paragraph>
    <Paragraph position="4"> l~rmer, nt,tltms like al gunte;~t validity mu,d Fn: c,,Iahllshed and ctmneLthHl'~ rl~u~.l |~' made with JXl(~nl?., ,nd rules ~1 Hllerent,C/. ~uinltrl,ltlng ideall',' Ill ',,~undne~', and Ltmtpletene,,,, thet~rem',. }lut unllerlvinu the h~glc&amp;quot;~ ~.enlantlL:~, there must P~ ,k ~;erllafltlcs I(ir the Itlglc',C/ underlvin~ I.lngthl~.e. alltl thl,~ ~.~.L~uh.I h~ ~lkell in terms ~l '~uLh .i rltlfll~n ,1~ llldJflnitt,~. Ilere. tvpltallv, .in inlerpret.dlL~n lunc tl(in IS e~tahllshed P~t~.~.een K&amp;quot;*'tttdLtlCa\[ iter11~ Irtlnl the language l, and ~lntt~l~lc;Jl items Inml rile &amp;quot;~(~rtd'&amp;quot; W lhat the langua~de is t() de~t, rlt)e. J'hts, m turn. ~ u~,uall~, at.conlphsiled b',' dexcrdlm~ the 'Aorld in .in{ither language. 1, . and '~htl~.lng that /'. and /'4 are nld.ll'l(in;ll V,lrt;infs hv ,~ho',X.'lng that tile'*' ,ire l~m{)rphl(-. Recentlv. hngu~sts and phdosopilers have at'cued for the ~ml'*~lrranke (~1 intenaional ,~..muntlt:S For natural languages (t;l'. ~lontat;tie 1(~7.1. I~ar,~ms 1981). Rapar~lr? 1981L .-\t the same t~me, computat~tmal Ilnt~ulS(~; and ~ther .-\1 researche~ have n~PSun \[o re~:{)gnt/~ tile ii~lr~rtanke (~1 representing intensIonal entitles (cl. \,V(x)ds 1975. IIrachman 1979. Mc('arthv 1979. \lards and ~,hap~ro 1982).</Paragraph>
    <Paragraph position="5"> It ~ems rea,~)nahle t|laI .~ ~mantlcs For such a repre'.~entatl()nal system should ~tself he an mtensmnal ~mant~cs. In tht~ paper. 1 ()utline ~,.'eral fully tntensttmal semantlc.S for ~nten,cltmal semantic net,x(~rk~, hv discu~sHag tile relatmns between a semantic-network &amp;quot;!anguage'&amp;quot; /, :~nd ~','eral ~anthdates For L w . For /,. I Focus on ~,haptro's propositional ,Semantic Network Processing System (SNell.': Shaptn) 1979). For which Israel (1983) has offered a I'w~sible-w~lrlds semantics. But p~stble-worlds semantic,s, while countenancing mtenmonal entities, are not fu/,/y intensional, since they treat mtens,mal entities extensionally. The L w s 1 di~uss all  have t'ullv intenslonal components.</Paragraph>
    <Paragraph position="6"> 2. SNePS.</Paragraph>
    <Paragraph position="7">  'A l~rson named &amp;quot;John&amp;quot; ha~ the proper~F of being rich.' tional network (see below), it can. however, als,) he used to represent the mherttabthtv of properties, e~ther hv explicit rules or by path-based inference (Shapiro lq781. It ctins~stx of labeled nodes and labeled, directed arcs satl~fwng (inter alia) the folh)wmg condition (of. Malda and Shapiro lq82): iS) There is a I-I ~orrespondence betv, een nodes and represented concepts.</Paragraph>
    <Paragraph position="8"> A concept is &amp;quot;anything about whtch mlormat~on can he stored and/or transmitted&amp;quot; (Shapiro 197q: 179). Widen a semantic network such as SNePS ~s u~d to model &amp;quot;the behel structure ol a thinking, rea.~onlnt.,, language using be,ng&amp;quot; (Matda and Shaptru 1982: 296: of. ~';haplro 1971h: 51.),;. the ct)nt.epts are the oh)ectx of mental (i.e.. mtentu)nal) acts ..u~.h as thinking, behev:ng, wishing, etc. Such oblect,~ are mren~mal i~.t. Rapaport l()7g).</Paragraph>
    <Paragraph position="9"> It t'ollov,'s I rc,m (%) that the arcs do not represent concepr-s.</Paragraph>
    <Paragraph position="10"> Rather. they repre',ent binary, structural relations between concept.s. If ~t )s des)red to talk about certain relations between concepts, then tho~e relations must be represented by nodes, smce they have r.neJt become objects o= thought, =.~, concepts. In terms of Oume's dictum that &amp;quot;t~ be is to be the value of a \[hound\] variable&amp;quot; (Qume 1980: 15; cf. Shapiro 1971a: 7q-80). nodes represent such values, ar~s do not. That Is. given a domain of dlscours~--mcludlng ~tems, .'~ arv relations among them, and prolX)S~tions--SNeP% nodes ~,ouid be used to represent all members t)l the domain. The arcs are used to structure the items, relations, and p)(,I')()'~tJons ,)l the domain into ((:chef.) prl)p(~sltmns. As ~n analogy, SNel)% arcs are to %Nel). ~, nodes as the svmn()ls '~&amp;quot; and &amp;quot;+' are to the symbols %', '5.P'. ond &amp;quot;VI )' in the rewrite rule: S -, &amp;quot;;I ) + VI ). It ~s because m) prorxts~ t~ons :are represented hv arcs that SNel)% ts a &amp;quot;pr()rx)sltlonal&amp;quot; semantic network (c:. Maida and Shapiro 1982: 292).</Paragraph>
    <Paragraph position="11"> When a ~manttc network such as SNePS is u~d to model a mind, the nodes represent only intensional ~tems (Maida and Shapiro 1982; of. Rapaport 1978). Simil-',rly, if such a network were to be used ~s a notation for a fully lntensional natural-language semantics (such as the semantics presented in Rapaport 198-1 ), the n(~es would represent only mtensional items. Thus, a semantics for such a network ought )tsetf to be fully mtensional.</Paragraph>
    <Paragraph position="12"> There are two pairs of t3tpes of nodes in S.Nel)S: constant and variable nixies, and atomic (or individual) and molecular (or propositumal) nodes. (Molecular md~wdual nodes are currently being implemented: see Sect. 7. 8. For a dt~usstt)n ol tile semantics of varmble nodes, see ShaDro 1985.) Except for a few pre-de)ined arcs for u~ by an inference package, all arc labels are ~hosen by the user: such labels ,re completely arbitrary (albeit often mnemonic) and depend ,m the domain being represented. The &amp;quot;meanings&amp;quot; of the labels are provided (hv the u~rt only by means of explicit rule re)des. ',~.hlch allo~' the retrieval ,)r constructam (by referencing) of pr(~l'xtsltlonal ntvJes.</Paragraph>
  </Section>
  <Section position="4" start_page="48" end_page="48" type="metho">
    <SectionTitle>
3. ISRAEL'S POSSIBLE-WORLDS SEMANTICS FOR SNePS.
</SectionTitle>
    <Paragraph position="0"> David Israel's semantics f~r SS, ePS a~sumes &amp;quot;~he general framework of Knpke-\lontague style model theoretic a~counts&amp;quot; (Israel 1983: 3), presumahlv because tie takes tt as &amp;quot;quite ~lear that \[Malda and Shapiro\] ... vnew their formahsm ,isa '~,lontague type type theoretic, inten,~uonal system&amp;quot; (Israel 1983: 2). lie mtrc~luces &amp;quot;a domam I) ,,I i')()~.sible entitles, a non empty ,~t / ( . ,)l ~)~.Slble ~.or\[ds), ,lnd .... l distinguished element w (~) I h) represent the real world&amp;quot;(IsraC/l Iq83: 3). ..\n individu,d,',)ncept )s a lunc rlon ic : I ~ I). linch constant mdiv)dual %Nel)% node =~ m,N.leted hv an ic; variable mdl~)dual m~ies are handled hv &amp;quot;.~.~)gnments relative to such a model&amp;quot;, l\[()~.c,.er, predicates--which, the reader should re,.all, are al.~) represented m %\el)% hv t.~mr, tant mdlvlduat n(xJes~are modelled as lunctl,,)ns &amp;quot;I r()m / tn!i~ the p()~.er set ol the set ol redly)dual Loncept~&amp;quot; J)ror~),,)tlonal nt~Je,~ are mL,.ielled bv &amp;quot;'functtons from / mto{Y . I'}.&amp;quot;alth~)ugh Israel Icets th,~t. &amp;quot;hvr~rmtens.mal'&amp;quot; h,glc ~,,uld Ix~ needed m ,,rder t,, h.ndle proD,.~Uonal attitudes.</Paragraph>
    <Paragraph position="1"> Israet has dlthL.ultv mterpretln~ \II!MIII'.R. ('I.AS%. ,,nd \[SA arcs in this Irame~x'~)rk. &amp;quot;l'hl~ is to be eM&amp;quot;~.tcd for tx~,,, reasons. Ihr~r. i) is arguahtv a mistake to i~.terpret them (rather ~han g~,, mg rule~ lot them}, since they are arcs, hence arhttrarv and rainconceptual. Second, a pos.slhle-worlds semantics is not the best approach (nor ~s tt &amp;quot;clear&amp;quot; that this m what Ma=da and Shapiro had in mmd--indeed, they explicitly reject it: cf. Malda and Shapiro 1982: 2c)7}. Israel himself hints at the mapproprlatene.~ ol this approach: H&amp;quot; one )s l'(~u.~ing on prop(~monal attitude{s} ... =t can seem hke a waste ol time to mtroduce m(Mel-the~ret)~, accounts()l'intens.)nahrv at all. Thus the air of de~F)erat)on alx~ut the loregomg attempt .... (Israel !O83: 5.) More~wer--and sigmficantlv--a possible-worlds approach ms misguided it' ,,ne wants to be able tn represent intpossible oh)errs..~r, ,,ne should want to it&amp;quot; one ts doing natural-language semanttcs (Rapa-I~)rt 1&amp;quot;)78. 1981: Routlev 1979). A fully mtensmnal semantic network demands a :ullv mtenstonal semantics. The mare rival to klontague-stvle, p(,~,,~hle worlds semantics (as well as tt) ~ts close kin. '~ltUatlon sem~nllL% !lklr~.~.l'.:.e and Perry lq8311 ~.~ Meinot~iatt ~emonlics.</Paragraph>
  </Section>
  <Section position="5" start_page="48" end_page="48" type="metho">
    <SectionTitle>
4. MEINONG'S TIIEORY OF OKJEC'TS.
</SectionTitle>
    <Paragraph position="0"> A!cxlus Metnong's (19(M) theory of the oh)e~ts of psvchologl~i acts ~s a more appropriate foundation for a semantics of propositional semantic networks as well a.s for a natural-language semantics. in brier, 5,1emong's the()rv camsists of the f~)llo~ing theses (c|'.</Paragraph>
    <Paragraph position="1"> Rapap)rt 1976, 1978): (MI) Thes/s oj&amp;quot; Intentionality: livery mental act (e.g., thmkmg, believing, judging, etc.) is &amp;quot;directed&amp;quot; towards an &amp;quot;ob.)ect&amp;quot;. l'here are two kmds of Memongian objects: (I) objecta, the individual-like oh}ectx of such a mental act as thmking-of, and (2)  objectives, the proposttlon-hke objects tat such mental acts as believlng(-that) or knowing(-that). E.g.. the object of my act of thinking of a unicorn is: a unicorn; the object or mv act of believing that the I~rth is flat is: the Earth is flat.</Paragraph>
    <Paragraph position="2"> (M2) Not every object of thought exists (technically, &amp;quot;has being&amp;quot;). (M3) It is not self-contradictory to deny. nor tautologous to al'firm. existence of an object of thought.</Paragraph>
    <Paragraph position="3"> (M4) Thesis of Au~sersein: All objects of thought are ausserse/~nd (&amp;quot;beyond being and non-being&amp;quot;).</Paragraph>
    <Paragraph position="4"> For present pur~ Aussersein ts most easily explicated as a domain of quantification for non-existentially-loaded quanttfiers. required by (M2) and (M3).</Paragraph>
    <Paragraph position="5"> (MS) I!verv oblect of thought has properties (technically. &amp;quot;Sosein&amp;quot;). (M6) Principle of Independence: (M2) and (MS) are not inconsistent. ( For more d,~'ux, c,on. if. Rapal~rt I984c.) ('atoll'dry: liven oblectx of thought that do not exist have properties.</Paragraph>
    <Paragraph position="6"> (M7) Principle of l&amp;quot;teedom of Assumption : (a) I!verv set ol properties (S, asein) ci~rres(~mds ti~ ,in ~hlect ~fl&amp;quot; thought.</Paragraph>
    <Paragraph position="7"> (b) livery oblet:t t~l thought can be thought ol (retatl'.e to certain &amp;quot;perfornlance'&amp;quot; IlnlltiltlonsL (x,18) ~me objects of Ihought are ,ncomplete (i.e.. undeternllned with respect t(a ,~lme prtIpertleSL (Mg) The meaning tal every ~ntence ;anti noun phrase Is an -hi~ct ~I thought.</Paragraph>
    <Paragraph position="8">  It should be obvious that there is a close relationship between Memong's theory and a rullv mtensnonat ~mantlc network hke %NePS. SNel)S it.'.,elf ts much hke .4usse~ein; %haplro (personal communication) has said that all nixies are :mpIncntlv m the network ,ill the ume. In particular, a SNePS base (i.e.. attempt constant) n(xJe represents an ohlectum, and a %NePS pr(q'x~ltn(mal nixie represents :in ,~hlt~tnve. Thus. when %NeP% ,s used as a mtx.lel ~,1 ,~ mind. pr(q'xxstttonal taxies represent the able, tires ol behels (d. Matda and ~hapnro 1982. Rapal'~rt and ~,hapiro 1984. Raparxwt !984b;; and When S\-l )':, t,C/ used xn a natural language pr(x:e~.,~ing system tcf. Shaptn) 1982. Rapal~)rt and %hapirn 1984). Lndivtdual nixies represent the meanmgs ill' noun phra~s and verb phrases, and pr(arx~slttonal taxies represent the meannng'~ (af sentences.</Paragraph>
    <Paragraph position="9"> Memong's theory wa.s attacked by llertrand Ru~setl tan gr, aunds of inconsistency: (1) According t(a Meinong, :he round square is boil: round and square (mdeed. this ,s a tautology); vet. according to Rus~ll. ~i&amp;quot; ~t is r(aund, then ~t ~s not square. (2) %lm~larlv, the extsung .~{)lden mounuHn must ha;e .ill three of its definmg prtaperttes: benng a m(,untam, h~mv ~,,lden. and existing; but. as Russell re)ted. I: doest(t exu'~t. I('l. Rapapt~rt 1976. 1978 It)r rel erences.) There have bee.n several I.rmahzatnons ,fl Melnonglan theories in recent philosophical literature, each of which overcomes these problems. In ~ul~,,quent ce~tnon.~ I briefly de.~rxbe three of these and show their relatmnshir~ to SNePS. (Others, not described }'.ere. include Routlev 1979----cf. Raparx~rt lqg4a--and Zalta 1983.)</Paragraph>
  </Section>
  <Section position="6" start_page="48" end_page="48" type="metho">
    <SectionTitle>
5. RAPAPOIIT'S THEORY.
</SectionTitle>
    <Paragraph position="0"> On my own reconstruction of Meinong's theory (Rapaport 1976, 1978--which bears a coincidental r~mblance to McCarthy 1979). there are two types of objecLs: M-objecta (i.e~ the objects of thought, which are intensional) and actual objects (which are extensional). There are two modes of predication of properties to these: M-objects are constituted by properties, and both M- and actual objects can exemplify properties. For instance, the pen with which l wrote the manumnpt of this paper is an actual object that exemplifies the property of being while. Right now. when I think about that pen. the object of my thought is an M-oblect that is constitLaed (in part) by that property. The M-object Jan's pen can be represented as: &lt;belonging to Jan. being a pen&gt; (or. for short, as: *J. P&gt;). Ileing a pen is also a constituent of this M-object: P c &lt;J. P &gt;; and 'Jan% pen is a pen' is true in virtue of this objective.</Paragraph>
    <Paragraph position="1"> \[n addition. &lt;J. P &gt; exemplifies (ex) the property of being constituzed by two properties. There might be an actual (abject, .say. ~. corresrxmding to &lt;J. P &gt;, that exemplifies the property of being a pen (iv ex /&amp;quot; ) as well as (say) the property of being 6 inches &amp;rag. But being 6 inches long C/ ('J. l&amp;quot; &amp;quot;,.</Paragraph>
    <Paragraph position="2"> &amp;quot;\['he M-object the round square. * R. A' &amp;quot;,. IS c,nstntuted bv precn~ly two properties: being round ( R ) and being ~uare (S): &amp;quot;The round square is round' is true m virtue of this. and 'The round ~uare ts not .~luare&amp;quot; ts fal~ ,n virtue of it. But (R, S &gt; exemplifies neither of thine pn)pertles, and 'The round ~quare ts not ~uare&amp;quot; ts true In virtue of lhtll, i.e., 'I'~&amp;quot; Is .imhl~UOUS.</Paragraph>
    <Paragraph position="3"> An ~' |tlhleCt o eXl..ls ill there is .n .ctu. I ,~hleCt tl th.t Is &amp;quot;'&amp;quot;kin-correlated'&amp;quot; wnh It: ,, extsrs lfl' 3(,\[ t, %( &amp;quot;o\] Iff&amp;quot; \]c~l&amp;quot;\[l'&amp;quot; c o * ,tex 1'&amp;quot; 1. X, ole th.t tnct~nlplete oble~.ts, such am .Y. I'',. can ex,st. Ih~wever. the \t-.hleC/.-t the existing golden mountain. &lt; E. (i. M &gt;, has the property t,l exnstnng ( hecause 1:&amp;quot; C , 1:'. (;, M &gt;) hut does not exnst (because 3t~{t* S(7 * I:'. (;. M &gt;\]. as an empirical fat.t I.</Paragraph>
    <Paragraph position="4"> The mtensmnal fragment ol this theory can he used to provnde it semantics I.r %NeP% m mut.h the ,~lme way that It can been u.,~d ttl provide a ,,emanttt.s lt)r natural languaEe (Rapap(irt 1981).</Paragraph>
    <Paragraph position="5"> %Nel)9; hase nodes can t~ taken to represent \1 t~b~ecta and prl)pertles;  &amp;quot;The round square is round', 'The round square is square', and &amp;quot;The round square is impossible' on Rapaport's theory.</Paragraph>
    <Paragraph position="6"> paradox&amp;quot;; ',.ca. Rapalx,r! 1978. It~82.) ,-\Ltual (i.e.. extensnonal) oh~cts, however, sht~uld nl~t be represented (~1, \lalda and %hHplrl) 1982: 2t~h t,~). I'. the extent to which %uch ot)le~ts ;ire essential to this %|etnon~lan Iheorv. the present thei~rv Is r~r|lap~; an mapproprtate tree. (A similar remark holds, of course, l'or Mc('arthy 1979.)</Paragraph>
  </Section>
class="xml-element"></Paper>