As a notauionai device, a semanuc network can iteeil he given a semantics, That is, the arcs, nodes, and rules of a semantic network representational svstem cum be given interpretations
Trang 1MEINONGIAN SEMANTICS FOR PROPOSITIONAL SEMANTIC NETWORKS
William J Rapaport Department of Computer Science University at Buffalo State University of New York Buffalo, NY 14260 rapaport% buff aloecsnet-relay
ABSTRACT
This paper survevs several approaches to semanuc-network seman-
tus that have not previously been treated in’ the Alor
computational dinguistics literature, though there is a targe phrlo-
sophical literature investigating them in some detail In particular,
propositional semantic networks (exemplihed by SNePS) are dis
cussed, it is argued that ondv a fully nntensional (®Mfeinanpran”)
seMUNCes IS appropriate tor them, and several Xieinoapian svstems
are presented
1 SEMANTICS OF SEMANTIC NETWORKS
Semantic networks have proved to be a useful date structure
for representing information, Le u “hnowledge” representation svs
tem (A better terminology is “belief” representation system: cf
Rapaport and Shapiro 1984, Rapaport 1984b) The idea is an old
one: dnheritance networks (Vip 1) like those af Quillian 1968,
Fig 1 An inheritance network
Robrow and Winograd’s ARI (1977) or Brachman’s KI OME,
(1979), bear strong family resemblances to “Porphyry’s Uree™ (hip
2)—a mediaeval device used to illustrate the Aristotelian theory of
definition by species and differentia (ui Kretymann 1966, Cho 2:
Kneale and Knesle 1966: 232) It has been pointed out that there ts
nothing essentially “semantic” about semantic networks (Hendrix
1979; hut cf Woods 1975, Brachman 1979), Indeed, viewed as a
data structure, it is arguable that a semantic network 18 a language
Cpassibly with an associated logic or inference mechanism) for
representing information about some domain and, us such, is a
purely svnractic entity ‘Vhey have come ta he called “semantic”
peimariiy because of there uses us wavs of representing the mean:
ings of lingurstic tems
As a notauionai device, a semanuc network can iteeil he given
a semantics, That is, the arcs, nodes, and rules of a semantic
network representational svstem cum be given interpretations in
terms of the entities they are used to represent Without such a
Semantics, a semantic network is an urhitrary notstitonal device
lable to musinterpretation fet Woods 1975; Brachman i977, 1983:
McDermott 1981) ‘The tasa of providing a semantics (or semantic
networks is more ukin to the task of providing a semantes for a
language than lor a dogic, since in the latter case, hue not in the
GENUS verre eee renee ern ee >
Differentia - >
< Principle of Individuation
~ <—- Individuals
Fig 2 Porphyry’s Tree:
A mediaeval inheritance network
former notions like areanent validity must be established und con- Nections must be made with axioms and rules of mberencte, cul-
mingling ideally in soundness and completeness theorems Hút
underlving the logie’s semantics there must be u semantics tor the logie’s undertving languaye, and this would be given ins terms of SUH ou notion as meaning Here, typically in interpretation fune tron ts established between svntuctical ilems trom the language / and ontological iems trom the “wortd” Wothae the language is to describe Phíx, tn turn wy usually accomplished by describing the
‘sorta in another language, Zand showing that / and / 4 are Netational variwats by showing that they are womorphic
Re-enrlv, linguists and philosophers have argued for the Importance of tntenstonald semantics for natural languages (ct Mon- tưyuc 19271, Parsons T98U, Kapunort T981) AE thế same tìme, com- putational linguists und other Ab researchers have begun to recog: nize the importance ol representing intenstonal entities Col Woods
1975, Brachman 1979, McCarthy 1979, Maida and Shapira 1982)
It seems reasonuble that a semantics for such a representational svs- tem should itself be an intensional semantics fn this paper, [ out- tine several fuily intenstonal semantics for intensional semantic networks by discussing the relations between a semantic-network
“language” /, and several candidates for £., Vor 4, 1 focus on Shapiro's propositional Semantic Network Processing Svstem (SNePS: Shapiro 1979), for which [tsrael (1983) has offered a possible- worlds semantics But) possible-worlds semantics, while countenancing intensional entities, are not fully intensional, since
they treat intensional entities extensionally The Ly s I discuss all
Trang 2have fully intensional components
2 SNePS
A SNePS semantic network (Fig 3) is primarily a propost-
Gach) property)
Fig 3 A SNePS representation for
‘A person named “John” has the property of being rich.’
tional network (see below) It can however also he used to
represent the inheritability of properties, ether by explicit rules or
by path-based inference (Shapiro 1978) It consists of labeled
nodes and labeled, directed ares satist ving (inter alia) the following
condition (cf Maida and Shapiro 1982):
(5) There is a 1-1 correspondence between nodes and represented
concepts
A concept is “anything about which information can he stored
and/or transmitted” (Shapiro 1979: 179) When a semantic net-
work such as SNePS as used to model “the belief structure of a
thinking, reasoning language using being” (Maida and Shapiro
1982: 296: cl Shapiro 1971b: 5123), the concepts are the obpects of
mental (1e intentional) acts such as thinking hebeving, wishing,
etc Such ohjects ure intensional (ut Rupaport 1978)
It follows trom CS) that the arcs da not represent concepts
Rather they represent hinary, structural relations between con-
cepes [f ic is desired to talk đÖou certain relations between con-
cepts, tnen those relations must be represented by nodes, since they
have inen become objects ot thought, 12 concepts In terms of
Quine’s dictum that “te be is to be the value of a (bound) variable”
(Quine 1980: 15; cf Shapirn 1971a: 79-80), nodes represent such
values, arcs do not That is, given a domain of discourse—including
items, 2 arv relations among them, and propositions—SNePS nodes
would be used to represent all members of the domain The ares
are used to Structure the items, relations, and propositions of rhe
domain inte (other) propastuons As an analogy, SNePS ares are to
SNePS nodes as the symbols ‘+' and “+ are to the symbols “SNE,
and ‘VP’ in the rewrite rule: S “P+ VP [tis because no propasi
tions are represented hv arcs that SNePS is a “propositional” seman-
tic network (cf, Maida and Shapiro 1982: 292)
When a semantic network such as SNePS is used to model a
mind, the nodes represent only intensional items (Maida and
Shapiro 1982; cf Rapaport 1978) Similarty if such a network
were to be used as a notation for a fully intensiona! natural-
language semantics (such as the semantics presented in apuport
1981), the nodes would represent only intensional items Thus, a semantics for such a network ought itself to be fully intensional, There are two pairs of types of nodes in SNePS; constant and variable nodes, and atomic (or individual) and molecular (or propo- sitional) nodes (Molecular individual modes are currently being implemented: see Sect 7 8 Vor a discusston of the semantics of vanable nodes, see Shamro £985.) Except for a few pre-defined arcs for use bv an inference package, all arc labels are chosen bv the user; such tabets are complerely arbitrary (albert often mnemonic) and depend on the domain being represented The “meanings” of the labels are provided (hy the user) only by means of explicit rule nodes, Which allow the retrieval or construction (by inferencing)
of propasilional nodes
3 ISRAEL'S POSSIBLE-WORLDS SEMANTICS FOR SNePS David) Israel's semantics for SNePS assumes “the general framework of Kripke-Montague stvle model theoretic accounts” (fsrael 19823: 3), presumably becuuse he takes it as “quite clear that
(Maida and Shaprrol View their formalism as a Montague tvpe
type theoretic, intensional svstem” (Israei 1983: 2) He introduces
“a domain 2 ot possible entities, a non empty set / 0 of possi hie worlds) and oo a distinguished element woot / to represent the real world” Csraeh 1983: 320 An indivéduad concept is a tune: fron te sf 2 A Tach constant individual SNePS mode is modefed
hy an ic; vartable individual nodes are handled by “ussipnments Telanve to such a model” However, predicates— which, the reader should recall, are also represented in SNePS by constant individual nodes—are modelled as tunctions “Lrom / inte the power set of the setoot individual concepts.” Propositional nodes are modelled bv
“functions from / into $7, Fd although Istued beets thuta “hyper: intensional™ logic would be needed in order to handle propositional attitudes
Israel has dithculty interpreting MEMBER, CLASS and ISA arcs in thus framework This is to be expected for twee reasons, Pirst, is arguably a mistake to éacer pret them (rather than yiving rưles for them), since Chev are arcs, hence arbitrarv and non- conceptual Secund, a purssinle- worlds semantics is mot the best approach (nor 1s it “clear” that thts is what Maida and Shapiro had
im mind—indeed, they explicitly reject it: cf Maida and Shapiro 1982: 397) Israel himself hints at the inappropriateness of this approach:
if one is focussing on propositional atuctudefs} it can seem like a waste of time to introduce model -theoretie ac- counts of intensionaliny atatl Phus the air of desperation about the foregoing attempt {Israel 1983: 8.) Moreover—and significantty—a possible-worlds approach is mịs- guided i ene wants to be able to represent impossible obwects, an one Should want to if one is doing natural -lanpuaye semantics (Rupa- port 1978, 1981: Routley 1979), A fully intensional semantic net- work demands a@ fully intensional semantics The main rival to
Montague-stvle, possible worlds semantics (as well as to its close Kin, situation semintcs (Barwise and Perry 19830) 1s Metnorngian
SOMUNLICS,
4 MEINONG'S THEORY OF OBJECTS
AJexius Memong’s (1904) theory of the objects of psvchologi- cal acts 1s a more appropriate foundation for a semantics of proposi- tional semantic networks as well as for a natural-language seman- tes, In brief, Meinong's theory consists of the following theses (cf Rapaport 1976, 1978):
(M1) Thesis of /ntentionality: Every mental act (e.g thinking, believing, judging, etc.) is “directed” towards an “obgect”
There are two kinds of Memongian objects: (1) objecta, the individual-like objects of such a mental act as thinking-of, and (2)
Trang 3objectives, the proposition-like objects ot such mental acts us
believing(-that) or knowing(-that) Eg the object of my act of
thinking of a unicorn ts: a unicorn; the object of my act of believ-
ing that the Earth ts flac ws: the Farth is flat
(M2) Not every object of thought exists (technically, “has being”)
(M3) It is not setf-contradictory to deny, nor tautologous to affirm,
existence of an object of thought
(M4) Thesis of Aussersein: All objects of thought are ausser-
seiend (“beyond being and non-being”)
For present purposes, Aussersein 1s most easily explicated as a
domain of quantification for non-existentially-louded quantifiers,
required by (M2) and (M3)
(MS) Every object of thought has properties (technically, “Sosetn”)
(Mo) Principle of independence: (M2) and (MS) are not incon:
sistent (For more discussion, of Rapaport 1984e.)
Corollary: Liven objects of thought that do not exist have
properties
(M7) Principle of Freedom of Assumption:
(a) Every set ot properties (Soseit) corresponds to oan object
af thought
(b) Every object ot thought can be thought of Crelative to
certain “performance” limitations)
(XI§) Some obgcts of thought are incompiete Cie undetermined
with respect to some properties J
(M9) ‘The meaning of every sentence and noun phrase is an object
ot thought
it should be obvious that there ts a close relauvionship between
Meinong’s theory and a fully intensional semantic network like
SNePS SNePS itself is much like Ausser sein; Shapiro (personai
communicauion) has said that all nodes are implicitly tn the net-
work all the time In particular, a SNePS base (Le atomic constant)
node represents um obctum, and a SNePS propositional node
represents an ohyective Phus, when SNePS is used us a model of a
mind, propositional nodes represent the obyectives of hetiets (cf
Maida and Shapiro 1982, Rapaport and Shapire 1984, Rapaport
1984bi and when SN¿PS is used tn a natural-language processing
system (cl Shapiro 1982, Rapaport and Shapiro 1984), individual
nodes represent the meanings of noun phrases und verb phrases, and
propositional nodes represent the meanings of sentences
Meinong’s theory was attacked by Herrrand Russell on
grounds of inconsistency: (1) According to Meinong, the round
sguare 15 both round and square (indeed, this is a tautatopgy): vet,
according to Russell, if it is round, then st es not square (2) Simi-
lirlv, the existing yolden mountnin must hate all Chree of tà
defining properties: being a mountain, heiny volden, and existing:
hut, as Russell noted it doesa existe, CCL Rapaport 1976, 1978 tor
Vhere have been several formatizavions af Mernongian
theories in recent philosophical literature, each of which overcomes
tnese problems In subsequent sections, | briefly describe three of
these and show their relationships to SNePS (Others, not described
here, include Routley 1979—cl Rapaport 1984a—and Zalta 1983.)
5 RAPAPORT’S THEORY
Qn my own reconstruction of Meinong’s theory (Rapaport
1976, 1978—wihich bears a concidental resemblance to McCarthy
1979), there are two types of objects: M-objects (ie the objects of
thought, which are intensional) and actual objects (which are extensional) There are (wo modes of predicatton of properties to these: M-objects ure constituted by properties, and both M- and actual obcts can exemplify properties For instance, the pen with which | wrote the manuscript of this paper ts an actual object that exem pli fies the property of being white Right now, when | think ubout that pen, the object of my thought is an M-object that is con- stituted (in part) by that property The M-object /an’s pen can be Tepresented as: <belonging to Jan, heing a pen> (or, for short as:
<J,P >) Being a pen is also a constituent of this M-obct: P c
<J, P >; and ‘Jan's pen is a pen’ is true in virtue of this objective
In addition, </, P > exemplifies (ex) the property of being constE- tuted by two properties There might be an actual object, say a, corresponding to </, ? >, that exemplifies the property of being a pen (cr ex I?) as well as (say) the property of being 6 inches long
ut being 6 inches lung? «J 1’ >
The M-object the round square, (RS °> 1s constituted bv pre- cisely two properties: hetny round (R) und beinp square CS): “The round square ts round’ is true in virtue of this, and “The round square is not square’ is false in virtue of it But <&, 5 > exemplifies neither of those properties, and “The round square is not square’ Is true im virtue of that Le is is ambhivuous
An Mobhreect o exists i there es an actual obect a that ts
“Semm-correlated” with HH enasts at JelaSCo] cử 3aV/[P có saeYx PĐƑ Note that incomplete obpeuts, such us
‘J, P >, can exist However the Meohject fhe existing golden mountain, «h.G, Moo, has the property of existing Cbecause Fc«+£,(, Ms) hụt does aot exist (hecuuse > Jala SC BOG, M >], as an empirical tact),
The intensional fragment of this theary can be used to pro- vide a semantics for SNe?S in much the same way that it can been used to provide a semanties tor natural lanyvuage (Rapaport 1981) SNePS base nodes can be taken to represent Mo obecta aad properties: SNePS propositional nodes can be tuken to represent Vi obectives
‘Two alternatives tor networks representing the three Moobjectives: Ree RSo SO RS +, and © RLS > en being impossible are show niin Pips Sand S (ihe second can he used to avoid “Clark's
5 a
roun (square) ( impossible) uare
Fig 4 A SNePS representation of
‘The round square is round’, ‘The round square is square’, and ‘The round square is impossibie’ on Rapaport’s theory
puradoa™, set Rapaport 1978, 1982.) Actual (he extensional) obyects however, should not be represented (ci Maida and Shaprro 1982: 395 98) To the extent to which such objects are essential to this Metnongian theory, the present theory is perhaps an inap- propriate one (A similar remark holds, of course, for MeCarthy
1979.)
6 PARSONS’S THEORY
Terence Parsons’s theory of nonexistent objects (1980; cf Rapaport 1976, 1978, 1985) recognizes only one type of object— intensional ones—und onÏv one mode of predication But it has two
Trang 4
Fig 5 An alternative SNePS representation of
‘The round square is round’, ‘The round square is square’,
and ‘The round square is impossible’ on Rapaport’s theory
types of properties: nuclear and extranuclear Vhe tormer includes
all “ordinary” properties such as: being red, being round, etc.; the
latter inchudes such properties us: existing, being imposstble, ete
Hur che distinction us blurry, since For each extranuclear property,
there is a corresponding nuclear one lor every set ot nuclear pro
perties, there iS a unique obwct that has only those properties
Existing vbpects must be complete (and, of course consistent)
though not all such obgcts exist For instance, the Morning Star
and the Hvening Star don’t exist (ib these are taken to consist,
roughly, of only two properties each) fhe round square, of course
is (and only is} both round and square and, so isn’t non-square:
though itis, for that reason, impossible hence not real As for the
existing golden mountuin, existence is extranuclear, so the set ot
these three properties deesn't have a corresponding obgct There vs,
however, a “watered down", nuclear Version of existence, und there
is un existing golden mountain that has that property: but if doesn’t
have the extranuclear property of existence, and, so it doesn’t extsé
Parsons’s Cheory could provide a semantics for SNePS, though
the use of two types of properties places restrictions on the possible
uses of SNePS On the other hand, SNePS could be used to represent
Parsons's theory (though a device would be needed for marking the
distinction between nuclear and extranuclear properties) and, hence,
tupether with Parsons’s natural languuye semantics, to provide a
Tool for computational linguistics, Fig 6 suggests how chs might
he done
Fig 6& A SNePS representation of
‘The round square is round, square, and impossible’
on Parsons’s theory
7 CASTANEDA'S THEORY
Hector-Neri Casitaredas theorv of “guises” (1972, 197Sa-c,
1977, 1979, 1980) is a better candidate It is a fully intensional
theory with one type of object: guises (intensional items
corresponding to sets of properties), and one type of property More
precisely, there are properties (e.g., being round, being square, being
biue, ), sets of these (called guise cores; ey being round, being square}) and an ontic counterpart, c, of the detinite-description operator, which is used to form guises: ep cibeing round, being Square} is the round square Guises can be understood, roughlv, as things-under-a-description, as “facets” of (physical and non- physical) objects as “roles” that objects play, or, in general, as obgects of thought
Guise theory has two modes of predication: internal and external In general, the guise ci # } is-internally # Fg the guise (named by) the round square is-internally only round and square The two guises the tallest mountain and Mt Everest ure related by an external mode of predication culled consubstantia- tion (C*) Consubstantiation is an equivalence relation that is used
in the analvses of (1) external predication, (2) co-reference, and (3) existence: Let aect F } be 4a guise and = let alG | “qự c({ .|OltŒH Then (124 iws-externally G (in one
sense) if C*(a, aÍG ]) For instance, ‘the Morning Star ts a planet’ is
true because C*(c{M.StciM,S, Pt): ie the Morning Star and the Morning Star that is a planet are consubstanuated (2) Guise a
“is the same as” guise 6 if and only if (*ab Vor instance, ‘the Morning Star is the same as the Evening Star’ ts true because CHUM OSG GELS And (3) a exists ound oniv if there isa guise & such that C*ud
Another external mode of predation is conmsoctuiiun (CC **),
‘This is also an equivalence relation, but one that holds between guises Chat a mind has “put together”) Le between guises ina
“belief space” lor instance, C'( Hlamlet, the Prince of Denmark ( * and C'* correspond almost exactly fo the use of the EQUIN are sn SNePS.0 Maida and Shapiro (P9822: 303b) use the EQUIV case-frame to represent co reference (which is whut (* ish hut, as [ have sugpesred in Rapaport 19&db, LOQUTY more property represents believed cu-reterence which is what €'* 1s It should
be clear hos purse theory can provide a semantics for SNePS Eig
7 Suppests bow this might be done Some problems remain how ever: in particular, the need to provide a SNePS Correlate for inter: nal predivation und the requirement of eaplicating external predica- tion oin terms of refutions ke Oo Note, too, that qodes mJ ms, und m& in bay 7 are “structured mdisiduals” -a sort of molecular base node
8 CONCLUSION
It is possible to provide a tully intensional, aon: possible worlds semantics for SNePS and stmilar semantic network Formal isms ‘The most strayhtiorward way is to use Memong’s theory of obeets, though this theory hus the disadvantage of not berg for: malized There ure severai extant formal Metnongian theortes that can be used, theugh cách has verunn disadvantages or problems Two tines of research ure currentty being investigated: (1) Take SNePS us is, und provide a new, formal Meinongian theory Vor tts semantic foundation This has not been discussed here, but the way
to do thix should be clear from the possibilities examined above, Myo oown cheery (stripped of tts extensional fragment) or oa mixliiccalen Of Castameda’s theory seem the most promising approacites, 62) Modaty SNePS so that one of the extant formal Mernoneien theories can be so used SNePS as in Fact, currently bering modihed by the SNePS Research Group lor independent
“TM wavs chat make TL closer to Castaneda’s vuise theory,
bv the introduction of structured indiytduals—- “hase nodes” wath descending arcs for indicating their “internal structure”
Feasts
ACKNOWLEDGMENTS
Yhis research was supported in part by SUNY Buifalo Research Devejupment Fund grant #150-9216-F I am grateful to Stuart C Shapiro, Hector-Neri Castaneda, and the members of the SNePS Research Group for comments and discussion.
Trang 5
4
(starlike) (Morning Stan) seen in
Fig 7 A SNePS representation of “The Morning Star is the Evening Star’ (m6)
and ‘The Morning Star is a planet’ (m9) on Castaneda’s theory
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