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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