Path Based and Node Based Inference in Semantic Networks

YAI WBAStC

ANU

NUUt-BAStU

1NPtKtNLt

IN

StMAN

i I C

NETWORKS

S t u a r t C. _{S h p p i r o}

9

partment of Cornpyter S c i e n c e S t a t e n i v e r s i t y of New York a t B u f f a l o

Amherst, New Y o r k 1 4 2 2 6

A b s t r a c t

Two styles of performing i n f e r e h c s i n semantic networks are p r e s e n t e u and c o m - pared. P a t h - b a s d i n w x e n c e allows a n a r c

or a p a t h of

arcs

between two given-nodes t o be i n f e r r e d from t h e e x i s t e n c e

of

an- o t h e r s p e c i f i e d p a t h between t h e same two

nodes. Path-based i n f e x e n c e r u l e s may be w r i t t e n u s h g a b i n a r y relational c a l c u l u s

n o t a t i o n . Node-based i n f e r e n c e a l l o w s a s t r u c t u r e o f nodes t o be i n f e r r e d from t h e e x i s t e n c e of a n i n s t a c c e of a p a t t e r n of node s t r u c t u r e s . Node-based i n f e r e n c e

riles can be c o n s t r u c t e d i n a semantic network u s i n g a v a r i a n t o f ' a p r e d i c a t e c a l c u l u s n o t a t i o n . Path-based i n f e r e n c e i s more e f f i c i e n t , w h i l e node-based i n f e r - e n c e i s more g e n e r a l . A method i s de- s c r i b e d o f combining t h e t w o s t y l e s i n a s i n g l e system i n order t o take advantage o f t h e s t r e n g t h s of each. App&ications of path-based i n f e r e n c e r u l e s to t h e r e p r e - s e n t a t i o n of $he ex-sional e q u i v a l e n c e o f i n t e n s i o n a l c o n c e p t s , and t o t h e e x p l i - c a t i o n of i n h e r i t a n c e i n h i e r a r c h i e s are

sketched.

1. I n t r o d u c t i o n

Semantic networks have developed

s i n c e the mid s i x t i e s [ t o ; 11

I

as a formal- i s m for t h e r e p r e s e n t a t i o n of knowlEage. Methods have a l s o been developing f o r per-

forming d e d u c t i v e i n f e r e n c e on t h e knowl- edge r e p r e s e n t e d i n t h e network. I n t h i s p a p e r , w e w i l l compare t w o s t y l e s o f i n - ference t h a t are used i n semantic networks, path-based i n f e x e n c e and node-based i n f e r - ence. Xn sections 2 and 3, t h e s e terms w i l l be e x p l a i n e d and r e f e r e n c e s to sys-

tems tibt use them w i l l be provided. Xn s e c t i o n s 4 and 5 , t h e advantages and dis-

advantages o f e a c h w i l l be discu8sed.

Section% 6 , 7 and 8 w i l l show how they can be used t o complement

each

o t h e r i n a s i n - g l e semantic network system, how path- b a s e d c k f e r e n c e c a n f a l p represent t h e ex- t e n s f a n a l e q u i v a l e n c e of i n t e n s i o n a l con- cepts, and how a f o r m a l i s m for writing

path-based i n f e r e n c e r u l e s c a n be used to

e x p l i c a t e t h e n o t i o n of " i n h e r i t a n c e a i n a semantic network.

2. Path-Based I n f e r e n c e

Let: u s r e f e x t o a r e l a t i o n (pegf~xce

b i n a r y ) t h a t - i s r e p r e s e n t e d by a n arc in a

network as a n

-

a r c - r e l a t i o n . I f R i s an a r c - r e l a t i o n , an

arc

l a b e l l e d R from node a t o node b r e p r e s e n t s t h a t the r e l a t i o n -

ship aRb h o l d s . I t may be t h a t this arc

is n o t p r e s e n t i n t h e network, b u t aRb may

be i n f e r r e d from other i n f o r m a t i o n p r e s e n t i n t h e network and one o r more i n f e r e n c e r u l e s . I f t h e other i n f o r m a t i o n i n t h e network is a specified path o f arcs ftom a t o b , w e w i l l r e f e r t o the i n f e r e n c e as path-based. The ways i n which such p a t h s may be s p e c i f i e d w i l l be developed as this

paper proceeds.

The two clearest examples of the gen- e r a l use of path-based i n f e r e n c e are i n

SAMENLAQ X I [ I 8 1 and P r o t o s y n t h e x I11 [13].

Both t h e s e systems use what might be c a l l -

ed " r e l a t i o n a l " networks

rather

t h a n

"semantic" networks s i n c e a r c - r e l a t i o n s i n c l u d e c o n c e p t u a l r e l a t i o n s as well as s t r u c t u r a l r e l a t i o n s (see [ 1 4 1 for a d i s - c u s s i o n of the difference)

.

For example,

i n Protoaynthex I11 t h e r e is a n arc label-

led COMMANDED from t h e node r e p r e s e n t i n g Napoleon t o t h e node r e p r e s e n t i n g t h e

French army, and i n SAMENLAQ I1 a n arc l a - belled EA$T.OF goes f r o m the node for

Albany to t h e node' for Buffalo. Both sya

t e m s u s e r e l a t i o n a l c a l c u l u s e x p r e s d i o n s

to form path-based - i n f e r e n c e r u l e s . The f o l l o w i n g r e l a t i o n a l operators are employ- ed (we h e r e u s e a v a r i a ' n t of t h e earlier n o t a t i o n s ) :

1. R e l a t i o n a l Converse

--

I f R i s a A

r e l a t i o n , R~ i s i t s c o n v e r s e . C

SO, V X , ~ ( X R <-, ~ R x ) ,

2 , R e l a t i o n a l Corn s i t i o n

--

If R

and S are re

T=--r

atxons R / S is R

composed with S, So,

V x , y ( x R / S y <-> a a ( x R x 5 a s p ) ) .

3 . Domain Restriction

--

If R and S

are r e l a t i o n s , (S a 1 R &a t h e re-

l a t i o n R w i € h V i t s domain re- stricted to those objects that b e a r t h e - r e l a t i o n S

t o

s. SO,

Vz,y,.(z(S s)Ry <-> (zS. C l z ~ ~ ) ) .

axe r e l a t i o n s , R (S s) is t h e re-

l a t i o n R w i t h i t s range restrict- t o t h o s e o b j e c t s t h a t b e a r t h e r e l a t i o n S t o

r .

So,

e e , g g ( + P ( S a ) # <-> (xRy 6 r s r l ) . 5. ~ e l a t i o n a l 1nter8;;ction

--

I f R

and S are r e l a t i o n s , R&S i s t h e i n t e r s e c t i o n o f R and S. So,

=,y ( x R Q S ~ <--> (XRY & ESY) )

Notice t h a t V Q , R , S , X , ~ ,x (XR(Q- a)/Sy <->

xR/ (Q a ) Sy ) so w e can u s e t h e n o t p t i o n

R

(4

a 1 S unambiguously:

I n SAMENLAQ 11, path-based i n f e r e n c e r u l e r s ~ a r e e n t e r e d by u s i n g the r e l a t i o n a l o p e r a t o r s t o g i v e a1 t e r n a t e d e f i n i t i o n s o f simple a r c labels. For example (again i n a v w i a n e n o t a t i o n ) t

EAST ,OF 4 EAST.OF/EAST .OF

d e c l a r e s t h a t EAST .OF i.8 transitive

SOUTH .OF 4 NORTH .OF= declares t h a t

Y X , ~ (gNORTH.OFx + xSOUTH.OFr/)

FATHER.OF +- (GENDER MALE)PARENT.OF d e c l a r e s t h a t a f a t h e r is a male p a r e n t .

S I R [ l f ] i s a n o t h e r r e l a t i o n a l n e t -

work system th* Wes path-based inference. Although the o r i g i n a l expressed i n f e r e n c e

r u l e s i n the form of general. LISP func- t i o n s , the reproduction

i n

[16, Chap. 7 ) u s e s the n o t i o n of p a t h granunars. The re* l a t i o n o p e r a t o r s l i s t e d above are augment- e d with R*, meaning z e r o or more occur- r e n c e s of R composed w i E h i t s e l f , R + ,

meaning one o r more occu r e n c e s o f R corn-

B

posed w i t h k t s e l f , and R S, meaning the

union of R and S. The following r e l a t i o n s

are used:

x EQUIV y means x and y are

t h e same i n d i v i d u a l x SUBSET y means x i s a s u b s e t

of Y

x MEMBER y means x i s a member

o f t h e set

3: POSSESS y means z owns a mem-

b e r of t h e set y x POSSESS-BY-EACH y means every member

o f t h e set x owns a member o f t h e set 8 ,

To determine if x POSSESS y , t h e -Work is searched u s i n g the following r u l e :

POSSESS

*

EQUIV*

/(POSSESS

~ ( M E M B E R / ~ ~ B ~ E T * / P O ~ ~ E S S ~ B Y - E A C H ) )

/SUBSET*

The widest u s e of path-based afer- ence i s i n ISA h i e r a r c h i e s , Fig. 1 i s based on pxobably the most famous ISA h i e r a r c h y , t h a t of C o l l i n s and Q u i l l i a n

121

.

The two important r u l e s h e r e a r e ISA + ISA*

and PROP 4 ISA*/PROP

A s McDermott 18) p o i n t s o u t , ISA h i e r a r -

c h i e s have been abused as w e l l as used.

I n

S e c t i o n 8 , w e w i l l propose a xnethod

[image:2.862.73.445.85.1067.2]

authQrtJ c&O us9 t o delscribe t h e i r h i e r - chies p r q c i s e l y .

FIGURE 1: ISA hierarchy based on t h a t of Collins

and Quxlllan

3. Node-Based Xnference

~ e v e r a i semantic network systems i n - c o r p o r a t e methods of r e p r e s e n t i n g general

r u l e s i n a s e m n t i c network v e r s i o n of predicate c a l c u l u s . Among t h e s e systems

are t h o s e of Shapiro [14;15;17], Kay [71, Hendrix 161

,

Schubert [ I 2)

,

and F i k e s and ~ e n d r k x [ 3 ] . Figure 2 shows such a n e t - work d e d u c t i o n r u l e r e p r e s e n t i n g

-

vx

[=EMAN +' 3 y (y WOMAN 6 xL0VESy)'l a,

Figqre 3 shows a r u l e f o r ~ ~ [ ~ E T R A N S I T I V E +

Yx,y ,a ( x r y 5 yra + x r a ) 1

.

FZGURE - 2 : A semantic network deduction rule for

YxIxEMAN + ay(ycW0MAN 6 d O V E S y ) ]

for

8 m y be deduced., Q u a n t i f i c a t i o n i s

represented i n t h i s n o t a t i o n by an arc-re- l a t i o n between a r u l e node and t h e v a r i - able nodes bound i n t h e r u l e . For ex-le,

3: i s bound by a univexsall q u a n t i f i e r i n R2

[image:3.862.74.374.109.434.2] [image:3.862.74.393.490.880.2]

and p

ie

bound by an e x i s t e n t i a l q u a n t i - f i e r i n R 1 .

FIGURE 3: A semantic network deductlon rule for

VrlrcTRANSITIVE + Vx,y,a(xry t y r z + s p a ) 1

To see how a node-based i n f e r e n c e

proceeds, consider t h e n e t w k of Fig- 4

i n conjunction w i t h t h e r u l e of F t g u r e 3 , and say that we w i s h t o decide i f

4 S U P P ~ R T S C. The network t h a t would rep- r e s e n t t h a t A SUPPORTS C matches P7 w i t h t h e v a r i a b l e binding [%/A, r/SUPPORTS, a/C]. P4 i n t h e binding [r/SUPPORTS] i s matched a g a i n s t t h e network and is found

t o s u c c e s s f u l l y match

MI.

P5 [x/A,

r/SUPPORTS, y/u] and P6 [y/u, r/SUPPORTS, a / C ] are then both matched a g a i n s t t h e qetwork and each succeeds with a consis- t e n t binding of 41 t o

B.

The r u l e t h u s succeeds and A SUPPORTS C is deduced.

( D e t a i l s

nf

t h e bindings and the match r o u t i n e are given i n [I 51

.

)

FIGURE 4: A network data base asserting that

A SUPPORTS 0 , B SUPPORTS C and

SUPPORlS T R A N S I T I V E ,

It should be noted t h a t set i n c l u s i o n was represented by an arc ( I S A ) i n Section 2 , b u t s e t membership i s being represented by a node (with a MEMBER, CLASS "case

frame")

i n t h i s s e c t i o n , The nodal repre- s e n t a t i o n fs required by node-based i n f e r - ence r u l e s and i s c o n s i s t e n t w i t h t h e no- t i o n t h a t everything t h a t t h e hetwork

"knows", and every concept t o which t h e

Yo

network can

refer

is xepresented by - - a

node

.

4. Advantaqes of Node-Based I n f e r e n c e

The adfaFtZgees

or

node-base.# i n f e r - ence s t e m from t h e g e n e r a l i t y of t h e syn- t a x

of

node-based i n f e r e n c e r u l e s , Path- based r u l e s are limited to b i n a r y r e l a - t i o n s , hav6 a r e s t r i c t e d q u a n t i f i c a t i o n

s t r u c t u r e and r e q u i r q t h a t an

arc

between t w o nodes be implied by a path between t h e same t w o nodes. Rule R 2 of I!'iguree2 could n o t be w r i t t e n as a path-based r u l e , and, although t h e t r a n s i t i v i t y of SUPPORTS could be expreaaed b

_I

a path-based r u l e

(SUPPORTS + SUPPORTS )

,

t h e "second o r d e r "

r u l e R4 of Figure 3 could n o t .

L e t us b r i e f l y c o n s i d e r how r u l e R4 i s constructed, whether it r e a l l y i s o r i s n o t a second oeder r u l e , and why it could n o t be expressed as a path-based r u l g . Rule R4 s u p p l i e s a r u l e for use

with

t r a n s i t i v e r e l a t i o n s . I n o r d e r to assert t h a t a r e l a t i o n i s t r a n s i t i v e (e.g. a s s e r - t i o n node M 1 of Figure 4 ) , the r e l a t i o n

must be r e p r e s e n t e d as a node, rather than

as an

arc.

This a l s o allows quantifica-

t i o n over such r e l a t i o n s , s i n c e i n a l l node-based i n f e r e n c e r u l e formalisms v a r i - ables may onLy be substituted f o r nodes, n o t for arcs. Since t h e r e l a t i o n i s a node, another node must be used to show t h e r e l a t i o n s h i p of t h e r e l a t i o n t o its arguments (e,g. nodes M2 and M3 i n Figure

4): Thus, R 4 i s r e a l l y a f i r s t order r u l e deri.ved from t h e second o r d e r r u l e

~ ~ [ P E T R A N S I T I V E

+ y x r g r a (srg 5 y r a + xra)

1

by reducing r t o an i n d i v i d u a l v a r i a b l e and intzoducing a h i g h e r order relation,

AVO, whose second argument i s a conceptual r e l a t i o n and whose o t h e r arguments

are

conceptual i n d i v i d u a l s . So R4

is

nore

a c c u r a t e l y seen as t h e f i r s t o r d e r rule

I n t h i s view, t h e p r e d i c a t e s of semantic networks a r e n o t the nodes r e p r e s e n t i n g

conceptual r e l a t i o n s , b u t t h e d i f f e r e n t case frames. Rule R4 cannot be repreaent-

ed as a path-based rule because it is a r u l e qbout t h e r e l a t i o n AVO, and AVO is a t r i n a r y , r a t h e r t h a n a binary r e l a t i o n .

Although some node-based i n f e r e n c e r u l e s cannot be expressed by path-based i n f e r e n c e r u l e s , it is easy to see t h a t any path-based i n f e r e n c e r u l e can be ex-

pressed by a node-based inference rule, as long as w e a r e w i l l i n g to r e p l a c e some a r c - r e l a t i o n s by nbdes and h i g h e r o r d e r p r e d i c a t e s .

5. Advantages of Path-Based I n f e r e n c e The major advantage of path-based in- ference i s e f f i c i e n c y , Carrying

out

a pith-based i n f e r e n c e involves merely

perhaps, 8ome s i d e paths t o s p e c i f i e d

nodes required by domain and range

rrsstric-

t i o n a ) . This f s a

well

understood and

re-

l a t i v e l y e f f i c i e n t operation, e s p e c i a l l y compared

to

t h e backtracking, i n t e r s e c t i o n , o r u n i f i c a t i o n operations required t o

W c , k the consistency of v a r i a b l e s u b s t i - t u t i o n e nin notSEX2seT

r?iference

rules,

Moreover, path following seems t o many people

t o

be what semantic networks

were

o k f g i n a l l y designed

for.

The major search algorithm of Q u i l l i a n ' s Semantic

Memory

is

a

b i - d i r e c t i o n a l search

for

a

path connecting

two

nodes (1 0 , p. 2491.

Also, t h e a b i l i t y t o do path t r a c i n g i s a motivation underlying I SA h i e r a r c h i e s , and

is why t h e C o l l i n s and Q u i l l f a n r e s u l t s

121 gained such a t t e n t i o n . Theae ef f i- c i e n c i e s a r e lost by replacing path-based

inference r u l e s by node-based inference

rules.

6 % Combining Path-Based and Node-Based Inference _{- - --- - --}

We

begin the t a s k of unifying path- basad and node-based inferences by noting t h e formal equivalence between an arc-re-

l a t i o n and a trro

case

c a s e frame

.,

Figure 5 illustrates t h i s using ISA vs. SUB-SUP. Figure 5a shows t h e use of t h e ISA arc-re- l a t i o n t o r e p r e s e n t t h a t c a n a r i e s are

-

b i r d s . Figure 5b r e p r e s e n t s t h e sama

re-

l a t i o n s h i p by a SUB-SUP c a s e frame, and

has

t h e advantage that t h e r e l a t i o n s h i p is

represented by a node, M4. Figure 5c is a redrawing of Sb, using t K e a r c l a b e l

SUB-

t o r e p r e s e n t the r e l a t i o n SUBC. ( I t i s

generally understood i n semantic network fonnalisma t h a t whenever-an a r c represent- i n g

a

r e l a t i o n R goes frod so- node n t~ some node m , t h e r e i s a l s o an a r c repre- s e n t i n g RC going from m

_{t o}

n)

.

Figure Sc

c l a r i f i e s t h e notion t h a t w e may t h i n k o f a0 i n l t a n c e of a two case c a s e frame (such

as M4) a s both an a r c and

a

node i f we

are

w i l l i n g t o r e c a l i b r a t e t h e measurement of t i m e it t a k e s t o follow one a r c - r e l a t i o n

to be t h e time it takes t o follovf %wo

arcs. We

can

replace a l l i n s t a n c e s 6% ISA i n t h e path-base8 Anterenee r u l e s of

Section 2 by t h e composition SUBn/SUP and still have v a l i d rules except t h a t w e now

have paths on t h e l e f t of t h e "+" syaabgl.

&

CANARY CANARY

0

FIGUPE 5: An L l l u s t r a t i o n of the e q u i -

valence o f an a r c - r e l a k i o n to a two case

case frame. a) I b p r e s e n t i n g s e t member-

s h i p as the 1 SA arc-relation. b) Repre-

s e n t l n g set membership as a SUB-SOP case frame. c ) Redrawulg (b) so it looks l i k e

( a ) .

Let

u s , t h e r e f b r e , extend our syntax

of

path-based inference

rules

t o

allow

a

41

path of a r c compositions on t h e l e f t of

t h e "+" symbol. The r u l e I S A + 1 SA*

states t h a t whenever t h e r e

is

a path o f "

1 _{a r c s}

from

m d e n t o mode m, w e can in- fer a " v i r t u a l n I S A arc d i r e c t l y f r o m n t o

m which we may, if wkwish, a c t u a l l y add

to t h e network. S;tm&lply, let the r u l e SUB-/SUP 4- (SUB-/SUP)* s t a t e tnat whenever

a path of a l t e r n a t i n g SUB- and SUP a r c s goes from node n t o node m, w e can i n f e r a

" v i r t u a l n node with SUB

t o

n and SUP

t o

m

which w e may, if we Wish, a c t u a l l y add to t h e network.

We now have a formalism f o r specify- ing path-based inference r u l e s i n a nskt work formalism t h a t r e p r e s e n t s binary con- ceptual relations by two c a s e c a s e frames. This would allow, f o r example, for a more u n i f i e d r e p r e s e n t a t i o n i n t h e SNIFFER system [31,

i n

which node-based inference

rules

a r e implemented

and

b u u l t - i n path based inference r u l e s

are

used f o r set membership and set i n c l u s i o n , both of which a r e represented only by arc-rela-

t i o n s . The formalism presented here

would allow set membership and set inclu- s i o n a s s e r t i o n s t o be represented by

nodes, permitting o t h e r a s s e r t i o n s t o reference them, without g i v i n g up t h e e f f i c i e n c y of b u i l t - i n r o u t i n e s to imple- ment t h e set i n c l u s i o n h i e r a r c h i e s .

We d e s i r e , however, a

more

general u n i f i c a t i o n of path-based and node-based inferences. There are two b a s i c r o u t i n e s used t o implement node-based inferences

(although s p e c i f i c implementations may

d i f f e r ) . One i s t h e match r o u t i n e t h a t i s given a p a t t e r n node a n d f i n d s i n s t a n c e s of it i n t h e network, and t h e o t h e r i s t h e r o u t i n e t h a t intrtrpsets t h e q u a n t i f i e r s ana connectives to c a r r y o u t t h e a c t u a l deduction. The match r o u t i n e can be en-

hanced

t o

make use of path-based

inference

r u l e s . Consider a t y p i c a l match r o u t i n e used i n t h e dedubtion i n Section 3 of

A SUPPORTS C

from

the network of Figure 4 and t h e r u l e of Figure 3, q d l e t u s fn- troduce t h e n o t a t i o n t h a t i f P i s a path of arcs and n i s a node, P [ n ] r e p r e s e n t s t h e set of nodes found by following t h e p a t h P from t h e node n. I n t h e example,

the match r o u t i n e was given t h e p a t t e r n

P 4 t o match i n t h e binding [rjSUPPORTS 1. I t waS 93;rle t o f i n d M 1 by i n t e r s e c t i n g

CLASS^

ITRANSITIVEI

w i t h

M E M B E R ~ ~ S U P P O R T S I

.

Now, l e t u s suppose t h a t t h e path-basea

inference rule CLASS f CLASS/ (SUB-&UP)

*

has been declared i n such a way tha t h e match r o u t i n e could use it. T t e match

[image:4.862.428.747.79.283.2]

nodes. This completes the general unifica- tion of path-based and node-based infer- egce we desired, Since path-based infer- ence is embedded in the match routine, while node-based inference requires the quantifier and connective interpreter, the diffexence is reminiscent of the differ- ence between subconscious inference and conscious reasoning,

7. Application to Extensional

- . Equivalence - of

Intensional Concepts

A basic assumption of semantic,net- works is that each concept is represented by a single node and that all information about a concept is reachable from its node.

Y e t , since Woods' discussion [ 2 0 ] , mast Semantic network authors have agreed that a node represents an intensional, rather than an extensional concept. How should we handle the inf~rmation that two differ-

ent intensional concepts are extensionally equivalent?

Let us illustrate this by a story (entirely fictiafial). For the last year we have heard of a renowned surgeon in

town, Dr. Smith, known for his brilliance and dexterity, who saved the life of the famous actress Maureen ~e'lt by a difficult heart transplant operation. ~ e a n w ~ i l e , at several social gatherings, we have met someone by the name of ~ o h n Smith, about five feet, six inches tall, black hair and beard, generally -d$sheveled and clumsy. We now discover, much to our ama~ement that John Smith and Dr. Smith are one and the samef In our semantic netwokk, we have one node for Dr. Smith connected to his attributes, and another for John Smith connected to his attributes. What are we

to do? Although we now know that John Smith saved the life of Maureen Gelt and that Dr. Smith has black hair, surely we cannot retrieve that infarmation as fast, as that Dr. Smith is a surgeon and that John Smith is 5 ' 6 " tall, If ye were to combine the two nodes by taking all the arcs from one node, tying them to the other and throwing away the firbt, we would lose this distinction, We dpust in-

troduce an assertion, say an E Q U I ~ E Q U I V

case frame, that represents the fact that

Dr. Smith and John Smith, different inten- sional concepts, are e x t e n s i ~ n ~ l y the same.1 Haw are we to use this assertion?

Ignoring for the moment referentially opaqtte contexts ("We didn't know that John Smith was Dr. Smith."), how can we express the ruledhat if n E Q U I V ~ / ' / E Q U I ~ m, than anything true of n is true of m? Our node based inference rules cannot express this rule because expressing "anything-true of

n n requires quantifying over those higher order case frame preaicates such as AVO

'lhe psychological plausibility of this discussion is supported by the experimees of Anderson and Hastie [ I ] and of McNabb

191

and

MEMBER'C~ASS.

One possibility is to

YZ

use lambda abstraction as Schubert does

f12J. Each n-ary htgher order predicate involving some node becomes a unary predi- cate by replacing that nodle by a lambda vaxiab7e. Thus, "Dx, Smith saved Maureen Gelt 's life" becotnes ,an instance of the

unary predicate X ( x ) [a saved Maureen

Gelt's life] applied to Dr. Smith. Using

a

PRED-ARG

case frame, it is easy to rep- resent the rule

The trouble with this solution is, how' are we to retrieve this information as a fact

about Maureen GeLt? Must we also store

A ( * ) [Dk. Smith saved x ' s life) (Maureen Gelt) 3

This duplication is unsatisfying, An al- ternative is to include in the path-based inference rule defining each arc-relation the path (EQUIV-/EQUIV)*. For example, AGENT +

AGENT/

(EQUIV-/EQUI V) % and CLASS

+ CLASS/( (EQUIV-/EQUIV)

*/

(SUB-/SUP)

*

1

*

.

Although this solution requires more rules than the lambda abstraction solution, and the rules look complichted, it avoids the duplication of the same assertion in dif-

ferent forms and the postulation of con-

ceptual predicates such as A (s) [ x saved Maureen Gelt's life].

Hays' cognitive networks [4;5] in- clude a scheme similar to the one proposed here. Each assertion about Dr, Smith

would refer to a different node, =each with an MST (manifestation) arc t o a common node. This node would represent the in tension of Dr. Smith, while the others represent Dr. Smith as surgeon, Dr. Smith as saviour of Maureen Gelt, etc. Presum- ably, when Hays' network learns of the identity of Dr. Smith with John Smith, a new node is introduced with MS arcs from both Dr. Smith and John Smith.3 Dr. Smith and John Smith are then seen as two mani- fes-tions of the newly integrated Dr. John Smith, Hays presumably uses an

M S T * / ( M S T ~ ) * path where we propose an (EQU 19-/EQUI V)

*

path.

~ l ~ c k i n g referentially opaque con- texts seems to require introducing rsZa-

tionaZ oempZemen*. For any pat4 P and

nodes xaand y, let x& hold just in case a path P from x to y does not exist in the network.

*

We miqht blocg referentially opaque contexts-by including the domain or range restriction

(OBJ'/VERB/MEMBER-/CLASS

OPAQUE) in the arc definitions.

8. Application, to the Explicatian of Inheritance

- -

As was mentioned in section 2, many

'~ctuall~, Hays' networks have not yet been implemented, and I have been warned

semantic networks i n c l u d e i n h e r i t a n c e

(ISA) h i e r a r c h i e s . Often t h e s e are a t best vague and a t worst i n c o n s i s t e n t . We

propose t h a t t h e i n h e r i t a n c e p r o p e r t i e s o f t h e s e h i e r a r c h i e s be c l e a r l y defined by path-based i n f e r e n c e r u l e s using t h e syn- tax we a r e p t e s e n t i n g h e r e or some o t h e r

w e l l

d e f i n e d syntax. We do n o t say t h a t

a l l

systems should be a b l e t o i n p u t and i n t e r p r e t such r u l e s , b u t only t h a t auth- ors use such r u l e s

t o

e x p l a i n c l e a r l y to t h e i r r e a d e r s how t h e i r h i e r a r c h i e s work.

Before thia proposal i s f e a s i b l e , w e

must

be a b l e to handle two more s i t u a t i o n s * The f i r s t i s the exception p r i n c i p l e ,

f i r s t expressed by Raphael [ ) 1, p.851 and s u c c i n c t l y s t a t e d by Winograd a s , "Any property t r u e of a concept i n t h e h i e r - archy i s i m p l i c i t l y t r u e of anything l i n k - ed below it, u n l e s s e x p l i c i t l y c o n t r a d i c t - ed a t t h e lower l e v e l n [19, p.1971. To allow f o r t h i s , l e t us i n t r o d u c e an e x c e p -

tton opera to^, X f P and Q are p a t h s and

x and y are nodes, l e t xP\Qy hold j u s t in

case t h e r e is a pa&h described by P from x

to y and no path of e q u a l o r s h o r t e r

[image:6.862.440.758.441.1029.2]

length d e s c r i b e d by Q from x t o y . T o see t h a t t h i s s u f f i c e s t o handle t h e e x c e p t i o n p r i n c i p l e , c o n s i d e r t h e h i e r a r c h y of

Figure 6 , where, to make t h i n g s more i n - t e r e s t i n g , w e have p o s t u l a t e d a v a r i e t y of f l y i a g penguins. W e have a l s o t a k e n t h e l i b e r t y of e x p l i c i t l y r e p r e s e n t i n g t h a t

CAN-FLY and

CAN-NOT-FLY

are negations o f each o t h e r . "The r u l e f o r i n h e r i t a n c e i n t h i s h i e r a r c h y i s

PROP *. (I SA*/PROP) \ ( I

SA*/PROP/NC~T).

FLY ING-PENGUI NS

An I S A hierarchy illustrating the exception

principle.

The o t h e r s i t u a t i o n w e must d i s c u s s

is "almost t r a n s i t i v e n r e l a t i o n s such as

SIBLING-

SIBLING

i s c e r t a i n l y symmetric, but it c a n n o t be t r a n s i t i v e s i n c e it is

i r r e f l e x i v e . Yet your s i b l i n g ' s s i b l i n g i s your s i b l i n g a s long a s he/she is n o t y o u r s e l f . T h i s is what w e mean by "almost t r a n s i t i v e . " N o t e t h a t f o r any r e l a t i o n )

R , R* S ( F ) i s t h e i d e n t i t y r e l a t i o n . Lel us c a l l it 1. Then for any r e l a t i o n P, let PR be Pf

f.

pR i s t h e i r r e f Z e x ~ v e

roetriotion of P W can u s e e this t o de-

f i n e

SIBLING

as

SIBLING

*

( S T B L I N G V S I B L I N G ~ )

We s u g g e s t t h a t t h e syntax f o r path- based i n f e r e n c e r u l e s is now complete

enough t o e x p l i c a t e the i n h e r i t a n c e rules

43

of v a r i o u s h i e r a r c h i e s . The complete syn-

t a x w i l l be summarized i n t h e n e x t s e c t i o n

W e have presented and compared two s t y l e s o f i n f e r e n c e i n semantic networks, path-basgd i n f e r e n c e and node-based i n f e r - ence, The former is more e f f i c i e n t , while t h e l a t t e r is more g e n e r a l . W e showed t h e equivalence o f an a r c - r e l a t i o n t o a two case c a s e frame, and d e s c r i b e d how path- based i n f e r e n c e could be i n c o r p o r a t e d i n t o t h e match r o u t i n e o f a node-based i n f e r - ence mechanism, thereby combining t b e s t r e n g t h s of t h e two i n f e r e n c e s t y l e s . We discussed t h e u s e of equivalence p a t h s

t o

r e p r e s e n t t h e e x t e n s i o n a l equivalence of i n t e n s i o n a l concepts. F i n a l l y , w e urged a u t h o r s o f i n h e r i t a n c e h i e r a f c h i e s t o ex- p l i c a t e t h e i r h i e r a r c h i e s by d i s p l a y i n g t h e path-based i n f e r e n c e r u l e s t h a t govern

i n h e r i t a n c e in them.

We a l s o presented a s y n t a x f o r path- based i n f e r e n c e r u l e s which can be summar-

i z e d a s follows:

1. A a t h i s e i t h e r an a r c - x e l a t l o n o r a

%-

p a t as d e s c r i b e d i n p a r t 2 enclosed i n parentheses. P a r e n t h e s e s may be o m i t t e d whenever an ambiquity does n o t r e s u l t .

2. I f P and Q are p a t h s and z, y

,

and a

are

nodes, p a t h s may be formed a s f o l l o w s :

a. Converse: i f P i s a p a t h from s

t o y , pd*is a p a t h from y t o x . b. Corn o s i t i o n : i f P i s a path from

-8 i s a path from a t o y

,

P/Q i s a p a t h from x t o y. c. Composition z e r o

or

e r e t i m e s :

I f P composed w i t h i t s e l f z e r o

o r

more t i m e s d e s c r i b e s a p a t h from x

to g , PS is a p a t h ftgm x t o y .

d, Composition one o r more t i m e s : I f

P composed with itself

one

o r more

times-$.sea pach from x t o y , P+ i s a p a t h from x . t o y.

e. Union:

-

If P i s a p a t h from x t o y or Q is a path from x to y , Pv6j is a p a t h from x t o y ,

f. I n t e r s e c t i o n : If P is a p a t h from x

t o

y and Q is a p a t h from x t o y , P&Q is a path from x bo y e

g. Corn leraent: I f t h e r e i s no p a t h P

by,

P

i s a path from r t o

h. t r r e f l e x i v e restriction: I f P is

a p a t h from x t o y and x$y, pR i s a p a t h from x t o y.

i, Exce t i o n : If P is a p a t h from x *there is

no

p a t h Q of l e n g t h e q u a l t o

or

less t h a n t h e l e n g t h of P, P \ Q i s a p a t h from x

t o y.

Psychology Program, Department crf Psv- chology, I n d i a n a U n i v e r s i t y ,

~ i o o m i ~ g t o n , I N . August, 1 9 7 7 . * p a t h from s to # and'

Q is

a p a t h

f r o m x t o s, (Q s ) P is a fiath from

x t o y .

k, Range r e a t r i a t i o n : I f P

is

a path from 3t t o 8 and

4

is a p a t h f r o m y

t o a , P ( Q r ) i s a path from x t o Y o

10. Q u i l l i a n , M.R. Semantic memry.

I n

M. Ninkay, ed. Semantic Information P r o c e s s i n

,

MIT Press, Camb

d 2 7 0 . rid*, MA,

A path-based i n f e r e n c e r u l e i s of t h e

form < d e f i n e d path> + < d e f i n i n g paths

where <defining p a t h > i s any p a t h de-

scribed by p a r t s 1 or 2 above, and < d e f i n e d path> i s e i t h e r a) a s i n g l e a r c - r e l a t i o n , or b) a composition of n arc relations

for

q r a e

fixed n, i.0. u s i n g o n l y "/*, n o t

"*"

o r

"+".

The r u l e i s i n t e r p r e t e d t o mean t h a t i f t h e < d e f i n i n g p a t h , goes from some node x t o some node y t h e n : a ) t h e

azc

t h a t id the < d e f i n e d p a t h > i a i n f e r r e d t o e x i s t from x t o #; b) t h e n arcs

t h a t are t h e <def.tnsd path, and n-1 new i n t e r m e d i a t e nodes a r e i n f e r r e d t o e x i s t f r o m x t o y.

l l . Raphael, B. SIR: s e m a n t i c informa- t i o n r e t r i e v a l . I n M. Minsky, ed.

S e m n t i c Information

Pkooesainy,

MIT

P r e s s , Cambridge, MA., 1968, 3 -145.

12. Schubert, L o K * Extending t h e expws- s i v e p o w e r o f semantic networks.

13. Schwarcz, R.M., Burger, J . P . , and Simmons, R.F. A d e d u c t i v e q u e s t i o n - answerer f o r n a t u r a l lanuuaqe i n f e r - ence. CACM 1 3 , 3 (March; 1570), 167-

183.

14. Shapiro, S .C. A

nett

s t r u c t u r e for semantic i n f o r m a t i o n storage, deduc- t i o n and r e t r i e v a l , Proc e - Second I n t

.

Jt,. Conf,

on

A r t i f i c i a l I n t e l l i g e n c e , The BritYsh Computer Society, frondon, References

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F i k e s , R. and Hendrix, G. A network-

based knowledge r e p r e s e n t a t i o n and i t s _{17. Shapiro, S.Ce The SNePS semantic n e t -}

n a t u r a l d e d u c t i o n system. Proc. F i f t h

I n t . J t . Conf. on A r t i f i c i a k I n t e l l i - ~ o r k _ed. p r o c e s s i n g system. _{Associative N e t w o r k s} I n

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un-

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185-210. Hendrix, G.G. Expanding t h e u t i l i t y

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Int. J t . Conf

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h

McNabb, S.D. The e f f e c t s of encoding s t r a t e g i e s and age on t h e memory re- p r e s e n t a t i o n for s m t e n c e s c o n t a i n i n g p r o p e r names and -hit@ d e s c r i p t i o n s