Báo cáo khoa học: "MEINONGIAN SEMANTICS FOR PROPOSITIONAL SEMANTIC NETWORKS" doc

MEINONGIAN SEMANTICS FOR PROPOSITIONAL SEMANTIC NETWORKS William J. Rapaport Department of Computer Science University at Buffalo State University of New York Buffalo, NY 14260 rapapor t%buffalo~csnet-re la y. ABSTRACT Tilts paper surveys several approaches to semanttc-netw,~rk seman- tics that have not previously been treated ~n the AI or computattonal lingutsttcs hterature, though there ~s a large ptulu. ~)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 ("Mem(mgtan") semantics is apprt)prtate I(~r them. and se'~eral \|eln(~nglan svstenls are presented. 1. SEMANTICS OF SEMANTIC NETWORKS. ~emantlc netw¢~rks have pr(~ed rt~ I~ a uselul dahl ,,true.lure for representing mlormatttm. =.e., a "knt~wledt, e'" repre~ntatmn svs tenn. (A I'~tter termmtdogv ix "'belief" teptexentatiott system; t.f. 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. (,has feather~) Fig. 1. An inheritance network. I~>hrnw and Win(~grad's KRI. (1977), ,,r IIra~.hman',, KI.()',I. (1979,), bear strong tamttv re~mblanues t() "l'.wphvrv',, I'ree'" (I ~t,. 2) a mediaeval device u.~d t~> 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 "~emanttc" 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 "semanttc'" primarily hecau.~ ~d their uses as wart, ~ll representing tile mean- ings (~f hngutstic !tems¢. 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'¢ 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 > Differentia > C()R~)~ / NON-CORPOREAL Species > ~ L / "- RA~ /NON-RATIONAL "~. ~ < Principle of Individual)on (-'P~'~ M~., k-'~y "_ < Individuals Fig. 2. Porphyry's Tree: A mediaeval inheritance network. l~rmer, nt,tltms like al gunte;~t validity mu,d Fn: c,,Iahllshed and ctm- neLthHl'~ rl~u~.l |~' made with JXl(~nl?., ,nd rules ~1 Hllerent,¢. ~ui- nltrl,ltlng ideall',' Ill ',,~undne~', and Ltmtpletene,,,, thet~rem',. }lut unllerlvinu the h~glc"~ ~.enlantlL:~, there must P~ ,k ~;erllafltlcs I(ir the Itlglc',¢ 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"*'tttdLtlCa[ iter11~ Irtlnl the language l, and ~lntt~l~lc;Jl items Inml rile "~(~rtd'" 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'. ~lon- tat;tie 1(~7.1. I~ar,~ms 1981). Rapar~lr? 1981L \t the same t~me, com- putat~tmal Ilnt~ulS(~; and ~ther \1 researche~ have n~£un [o re~:{)g- nt/~ tile ii~lr~rtanke (~1 representing intensIonal entitles (cl. \,V(x)ds 1975. IIrachman 1979. Mc('arthv 1979. \lards and ~,hap~ro 1982). It ~ems rea,~)nahle t|laI .~ ~mantlcs For such a repre'.~entatl()nal sys- tem should ~tself he an mtensmnal ~mant~cs. In tht~ paper. 1 ()ut- line ~,.'eral fully tntensttmal semantlc.S for ~nten,cltmal semantic net,x(~rk~, hv discu~sHag tile relatmns between a semantic-network "!anguage'" /, :~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 48 have t'ullv intenslonal components. 2. SNePS. A SNePS semantic network (Fig. 3) is primarily a proposi- ) / Fig. 3. A SNePS representation for 'A l~rson named "John" 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. A concept is "anything about whtch mlormat~on can he stored and/or transmitted" (Shapiro 197q: 179). Widen a semantic net- work such as SNePS ~s u~d to model "the behel structure ol a thinking, rea.~onlnt.,, language using be,ng" (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). It t'ollov,'s I rc,m (%) that the arcs do not represent concepr-s. Rather. they repre',ent binary, structural relations between con- cept.s. If ~t )s des)red to talk about certain relations between con- cepts, 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 "t~ be is to be the value of a [hound] variable" (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 '~" and "+' are to the symbols %', '5.P'. ond "VI )' in the rewrite rule: S -, ";I ) + VI ). It ~s because m) prorxts~ t~ons :are represented hv arcs that SNel)% ts a "pr()rx)sltlonal" seman- tic network (c:. Maida and Shapiro 1982: 292). 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. There are two pairs of t3tpes of nodes in S.Nel)S: constant and variable nixies, and atomic (or individual) and molecular (or propo- situmal) 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 "meanings" 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. 3. ISRAEL'S POSSIBLE-WORLDS SEMANTICS FOR SNePS. David Israel's semantics f~r SS, ePS a~sumes "~he general framework of Knpke-\lontague style model theoretic a~counts" (Israel 1983: 3), presumahlv because tie takes tt as "quite ~lear that [Malda and Shapiro] vnew their formahsm ,isa '~,lontague type type theoretic, inten,~uonal system" (Israel 1983: 2). lie mtrc~luces "a domam I) ,,I i')()~.sible entitles, a non empty ,~t / ( . ,)l ~)~.Sl- ble ~.or[ds), ,lnd l distinguished element w (~) I h) represent the real world"(Isra¢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 ".~.~)gnments relative to such a model", 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 "I r()m / tn!i~ the p()~.er set ol the set ol redly)dual Loncept~" J)ror~),,)tlonal nt~Je,~ are mL,.ielled bv "'functtons from / mto{Y . I'}."alth~)ugh Israel Icets th,~t. "hvr~r- mtens.mal'" h,glc ~,,uld Ix~ needed m ,,rder t,, h.ndle proD,.~Uonal attitudes. Israet has dlthL.ultv mterpretln~ \II!MIII'.R. ('I.AS%. ,,nd [SA arcs in this Irame~x'~)rk. "l'hl~ is to be eM"~.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 rain- conceptual. Second, a pos.slhle-worlds semantics is not the best approach (nor ~s tt "clear" 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" one )s l'(~u.~ing on prop(~monal attitude{s} =t can seem hke a waste ol time to mtroduce m(Mel-the~ret)~, ac- counts()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 mis- guided it' ,,ne wants to be able tn represent intpossible oh)errs ~r, ,,ne should want to it" one ts doing natural-language semanttcs (Rapa- I~)rt 1")78. 1981: Routlev 1979). A fully mtensmnal semantic net- work 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. 4. MEINONG'S TIIEORY OF OKJEC'TS. 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 proposi- tional semantic networks as well a.s for a natural-language seman- tics. in brier, 5,1emong's the()rv camsists of the f~)llo~ing theses (c|'. Rapap)rt 1976, 1978): (MI) Thes/s oj" Intentionality: livery mental act (e.g., thmkmg, believing, judging, etc.) is "directed" towards an "ob.)ect". 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) 44 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 believ- ing that the I~rth is flat is: the Earth is flat. (M2) Not every object of thought exists (technically, "has being"). (M3) It is not self-contradictory to deny. nor tautologous to al'firm. existence of an object of thought. (M4) Thesis of Au~sersein: All objects of thought are ausser- se/~nd ("beyond being and non-being"). For present pur~ Aussersein ts most easily explicated as a domain of quantification for non-existentially-loaded quanttfiers. required by (M2) and (M3). (MS) I!verv oblect of thought has properties (technically. "Sosein"). (M6) Principle of Independence: (M2) and (MS) are not incon- sistent. ( For more d,~'ux, c,on. if. Rapal~rt I984c.) ('atoll'dry: liven oblectx of thought that do not exist have properties. (M7) Principle of l"teedom of Assumption : (a) I!verv set ol properties (S, asein) ci~rres(~mds ti~ ,in ~hlect ~fl" thought. (b) livery oblet:t t~l thought can be thought ol (retatl'.e to certain "perfornlance'" 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. 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 net- work ,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,¢ 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. 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" ~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.) 5. RAPAPOIIT'S THEORY. 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 con- stitLaed (in part) by that property. The M-object Jan's pen can be represented as: <belonging to Jan. being a pen> (or. for short, as: *J. P>). Ileing a pen is also a constituent of this M-object: P c <J. P >; and 'Jan% pen is a pen' is true in virtue of this objective. [n addition. <J. P > exemplifies (ex) the property of being consti- tuzed by two properties. There might be an actual (abject, .say. ~. corresrxmding to <J. P >, that exemplifies the property of being a pen (iv ex /" ) as well as (say) the property of being 6 inches &rag. But being 6 inches long ¢ ('J. l" ",. "['he M-object the round square. • R. A' ",. IS c,nstntuted bv pre- cn~ly two properties: being round ( R ) and being ~uare (S): "The round square is round' is true m virtue of this. and 'The round ~uare ts not .~luare" ts fal~ ,n virtue of it. But (R, S > exemplifies neither of thine pn)pertles, and 'The round ~quare ts not ~uare" ts true In virtue of lhtll, i.e., 'I'~" Is .imhl~UOUS. An ~'| tlhleCt o eXl ls ill there is .n .ctu. I ,~hleCt tl th.t Is "'"kin-correlated'" wnh It: ,, extsrs lfl' 3(,[ t, %( "o] Iff" ]c~l"[l'" c o • ,tex 1'" 1. X, ole th.t tnct~nlplete oble~.ts, such am .Y. I'',. can ex,st. Ih~wever. the \t hle¢ t the existing golden mountain. < E. (i. M >, has the property t,l exnstnng ( hecause 1:" C , 1:'. (;, M >) hut does not exnst (because 3t~{t* S(7 • I:'. (;. M >]. as an empirical fat.t I. The mtensmnal fragment ol this theory can he used to pro- vnde 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). %Nel)9; hase nodes can t~ taken to represent \1 t~b~ecta and prl)pertles; %Nel)% prt}rx~ltlimal IIIM'kN L.n i've taken t(~ represent \1 oh~ectlves. Twu ,ilternatixe'~ ix,r networks, rcpre'-~:nIlnL, tile three \| ,ff~lectlves: R t. • R.S',. .%' L • R.S , rod ,R.S;, ex bein e iml~ible are ~,ho~.~. n in l:ig,~. 4 ,nil 5. Ir}le ,,¢.,Lolid Lan }~' it,ceil t()d~.iud "'('lark's Fig. 4. A SNePS repro~n~tion of "The round square is round', 'The round square is square', and "The round square is impossible' on Rapaport's theory. paradox"; ',.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 map- proprtate tree. (A similar remark holds, of course, l'or Mc('arthy 1979.) 6. PARSONS'S THEORY. Terence Parsons's theory of nonexistent oh]eeLs (1980; cf. Rapa~x~rt 1976. 1978. 198.5) recognizes only one type of ob]ect intenstonal ones and onl~" one m(xle of predlcatton. But it has two 45 Fig. 5. An alternative SNePS repreuncation o£ 'The round square is round', ~rhe round square is square', and "Tho round square is impossible' on Rapaport°s theory. types ill" properties: nuclea~ and extranuclea~. Tile tormer includes all "ordinary" properties such as: being red. being round, etc.; the latter includes such properties as: existing, being ~ml~t~sthJe. etc. I~u[ the thstlnctnon ts SlurrY, s, nce for each extranuclear pn~perty, there Is a ct)rresl~)ndlng nuclear one. J:or ever',' set ~d nuclear prtt pertles, there Ix a unique ohlect that has ~nls," rh,w,e prt~l~rt~es. Existing ohlects must he ct~mplete (and. ~tf ct~urse, ctmslstent). though not all such ohle~ts exist. For instance, the Morning Star and the I:'vening Slat don't exist (tl th~ are taken to ct)nsnst, roughly, of only two properties each). I'he ~ound square, of course. ts (and only ls~ hits round and square ,and. ~, ~sn't non-square; through tt is. for that rea~am, lmp~.xsd~le, hence not real. ks for the existing golden mountain, exintence ix extranuclear. ~l the set ~1 these three properties doesn't Ila~.e a cttrre.~p~mtlung ~)htect. There is, however, a "'watered do~ n". nuclear ~ersion ,~1 existence, and there is an ex=stm~ golden mountain that has Ihat property; hut it didn't ha',e the extranuclear property ~,1 existence, and. '~ ~t doesn't exist. Parstms's the~lrv could pn~ tdea semantics for SNeI>S. though the use of two types of properties pla~ restrictions on the po~tble uses of SNePS. On the other hand, SNePS could he used to represent Parsons's theory (though a device would be needed for marking the d~sttoctlon between nuclear and extranuclear properties) and, hence. tt~ether with I)arrams's natural language semantics, to provide a hX)t f(}r comptit:ttit)nal linguistics. Fig. h suggests how tilts might be d~me. Fi~. 6. A SNePS representation of The round square is round, square, and impossible' on Parsons's th~orT. 7. CASTANIrDA'S THEORY. Ilector-N~ri Castan'eda's theory of "guises" (1972, 1975a-c. 1977, 197q. 1980) is a better .~ndidate. It is a fully intensional theory with one type of oh!oct: guises (intensional items corr~ponding to ~t.q ,if properties), and one type of property. More prettily, there are properties (e.g., being round, being square, being blue ). ~ees of these (called guise cores: e.g., {being round, being squaret), and an ontic counterpart, c, or the detimte-descriptlon operator, which ns used to form guises; e.g c{being round, being square| is the round square. Guises can be understood, roughly, as things-under-a-descrtptmn. ~,s "facets" of (physical and non- physical) ob.l~t.s, as "roles" that ohjecr,s play, or, in general, as objects t)l" thought. Gui~ theory has two modes of predication: internal and external In general, the gui~ cl F } is-internally t'. I: g., the gut~ (named by) the round square is-mternally only round and square. The two guises the tallest mountain and &It. Everest are related hv an external mode of predication called consubstantia- lion (C'*). Consuh~tantmtnon is an equivalence relation that is u~d in the analyses of (I) external predication, (2) co-reference, and (3) existence: l,et a = c { /" } be a guise and let a[fi l =~f c({. . . 1" } u l(; }). Then(I)a ~s-externally(; (in one ,sense) if C~(a. a[G ]). For instance. "the Morning Star ts a planet' is true because C~( c t M. S }, c { M . S, P }): i.e the Morning Star and the Morning Star that is a planet are consul~tantlated. (2)Gut~ a "is the ~me as" gul~ b .I and ~mlv d" ('*ab. I:~r instance, 'the M~)rnlng Star tx tile ~me as the Evening Star" ~s true because ("(tIM.S}. ~.Jt",S}). \nd (31 ,t exists, tl ,Had ~niv H 'here I~ .t guise b such that (",lb. Amtther e\ternal nl,~e td' predt~atl~)n ~x ~,msociati, n (('"). This ts al~ an equivalence relalltm, hut t~ne that holds between gu0se~ that a m0nd has "put together". ~.e between gulwes m "behef space". I'(~r unsran~.e, (" "(llamlet. the Prm~,e ~f I)enmark J. (" anti C" ct~rre~p~md alm~sr exactly r(~ tile use ~t tile I'OUIV art sn 'q,NePS. \lalda and Shap~n~ ~I'IS2: );1131~ u.~ the I-{)UIV ca~-frame to represent t,o relerence f ~vhlch us ~hat ('" us), hut, .~s I have suggested In RapaI~rt lt~84h. I:(J('l\" m~re prnpertv repre~ntx believed ct~ relerence ~A,'hl~.h Is '~'ltat (''= IS. It sht~uld he clear h,~ gu:~ the~rv can pnw~de a ~mantncs It)r 'qNeP%. Ilg. 7 ";ugge'~ls h~v. thus m~t, ht h~ done. %~nle pn~hlems remain, ho,x ever: in p.lrtlcular, the need t~ pn:,tde ,= SXeP ~, ~t~rrel,te lt}r mter hal predt~,at~t~n and the retlu~renlent ~1 explicating external predica- tion In terms ~1 retatl~n~', like (" . Note. h~, tha! nt~des m3. mS. and m8 in F!y. 7 ;ire 'structured illdl~.ldtl.~ls '" -a ,~rt ~1 molecular h;~se nixie. g. CON(~L USION. It ~s p~,sthle rn provide a tully tntenslonal, nt)n-fx~,'~ahle- w(~rlds ~malltlCS for ~NePS and similar ,~emanttc net~.v~rk f(wmal tsms. "l he tnt~t strat~,htlttr~.vard way ,s h~ use ~,letmmg's thet~rv ~)l ohlects, though thus the~rv has tile dx.,,ad~antage ,~t not being f~,r- mah/¢d. There are several extant formal ~.|emon~lan theorte~ that can t~ u.sed, t|t~;u~h eaLh has L.ertaln dt~tdvantages or pn~hl~mr;. Two hnes ,ff ,e~earch are currently being inv,~;tlgate~d: (1) Take ~.Nel~F, as :s. and prnvide a nov,', formal Memonglan theory I',~r Its semanth.: ~~,u,'tdatl~)n. Thin has not been discussed here. hut the wav to do this sh~luid be clear: from the p~.s.slhtlittes examined ab~lve. My t~v,'n theory (strspped of Its exten~mnal IragmentJ ~)r a m(Cdl~;:il~n (~| (',istaRetia'y~ rllel~rv ~'enl tile me,st pronll~ln~ appn~:u.he~. {2~ Modnlv S~.eP% '~ that ~n~ ,,I the extant lormal \lenn~;n~.)an ttl,t~rtc.s can ~ ,a~ used. S3,eP~ ~s, nn fact, ~.urrentIv |~nn[. m,~dlhed hv tile SNePS Research [intup-lor independent rea a,l'.S - 'n v,'avN that make it cheer to ('.=,,talleda's guise theory, hv :he tnt."(xlUCtlon of structured mdt~,uduals "hase nodes" with descending arcs for indicating their "internal ~tructure". ACKNOWLEDGMENTS. This research was supported in part by ~ilSN'I' Buifalo Research DeveJupment Fund grant ~150-9216-F. I am grateful to Stuart C'. Shapiro, Hc,~tor-Nen Ca.stallreda. and the members of the SNePS Research Group for comments and discussion. 46 'r- (Evening Star) ~ ~ (Morning Sta~ ~ @_orning Star [plane't.~ Fig. 7. A SNePS representation o£ "l'he Morning Star is the Evening Star' (m6) and 'The Morning Star is a planet' (m9) on Castaneda's theory. 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SEMANTICS OF SEMANTIC NETWORKS. ~emantlc