ON THE SPATIAL USES OF
Linguistics
PREPOSITIONS
Annette Herskovlts
Department, Stanford U n i v e r s i t y
At f i r s t
glance, the s p a t i a l uses of prep o sit io n s seem
to
constitute
a
good
semantic
domain
for
a
computational
approach.
One expects such uses w i l l
r e f e r more or less s t r i c t l y
to a closed, e x p l i c i t , and
p r e c i s e chunk o f world knowledge. Such an a t t i t u d e Is
e x p r e s s e d in the f o l l o w i n g statement:
comprehension,
"Given d e s c r i p t i o n s of the shape of two objects, given
t h e i r l o c a t i o n ( f o r example, by means ox coordinates in
Some system o f r e f e r e n c e ) , and, In some cases, the
l o c a t i o n o f an observer, one can s e l e c t an appropriate
preposition."
Objects
identical
in
shape
may
be
"conceived m
differently,
f o r instance as surface or as enclosure.
This may be a choice a v a i l a b l e to the speaker to
emphasize c e r t a i n aspects (inlon t~$e rug), or I t may be
d e t e r m i n e d f o r the category of the reference o b j e c t (on
see [Boggess 1979]).
Ot h e r c h a r a c t e r i s t i c s
These i n c l u d e :
are
not
deducible
from
shape.
1. 1, ALTERNATE GEOM~'I'RIC DESCRIPTIONS
tAe football field).
This
paper
shows the
fallacy
of
this
claim.
It
addresses the problem of i n t e r p r e t i n g and generating
"locative
predications"
(expressions made up of two
noun-phrases g o v e r n e d by a p r e p o s i t i o n used s p a t i a l l y ) .
It
identifies
and
describes
a
number of
object
characteristics
beyond shape (section I) and contextual
factors
( s e c t i o n 2) which bear on these processes.
Drawing
on
these d e s c r i p t i o n s ,
the t h i r d
section
proposes
core
meanings
for
two
categories
of
p r e p o s i t i o n s , a n d describes some of the t r a n s f o r ~ t t o n s
t h e s e core meanings are subject to in context. The l a s t
section
outlines
the
main d i r e c t i o n s
of
Inquiry
suggested by the examples and observations in the
paper.
In under t/te aJater, t h e w a t e r stands for tAe upper free surface
of tAn ruater; in in the water, i t .is conceived as a volume. A
whole
category of objects
f o l l o w s t h is
rule:
see
( u n d t r l l n ) tan (snowllakeloceanlsan41.). Such objects tend to be
viewed o n l y as volumes w i t h "underneath': undcrn~A fat
lake i s g e n e r a l l y i n t e r p r e t e d as meaning "under the
l o w e r s u r f a c e o f t h a t body o f w a t e r ' .
In tan crack In tan 6~wl, the crack Is In the volume defined
by the normal surface o f the bowl in I t s uncracked
s t a t e . In tan milk in tat b o w l , the milk Is In the volume
e n c l o s e d by the bowl and l i m i t e d upward by a plone
t h r o u g h the rim.
1.2.
FUNCTION
1. ~BJECT CHARACTERISTIC~
T hroughout the paper, I use the term " o b j e c t ~, meaning,
strictly
speaking,
the
object
together with
some
lextcal
label.
In e f f e c t ,
the choice of p r e p o s i t i o n
depends on the l e x i c a l
c a t e g o r y associated w i t h the
o b j e c t by the noun-phrase used to r e f e r to I t . And such
a c a t e g o r y i s n o t u n i q u e l y defined. There are d i f f e r e n t
levels
In
the c a t e g o r i z a t i o n
hierarchy
(e.g.
"end
table",
"table",
"piece
of
furniture'),
but
also
different
perspectives
on the o b j e c t .
Cons i de r t he
p i c t u r e below.
,~,
,
~,
One says in ran disk and on the tray though these objects u y
be
essentially
Identical
in
shape.
One w i l l
not
ordinarily
say tan cat Is in :At t ~ e , but u n ~ r tan t ~ e , even
w i t h the c a g e - l i k e t a b l e below.
/oAn is et X Often means t h a t John Is using I as one
n o r m a l l y uses i t
(JoAn is at his desk). I f normal use
implies
being on or m X, then at Is not used (John is in
o r on the bed, but not at). And to the right of the chadr Is
d e f i n e d by r e f e r e n c e to a t y p i c a l user of the chair.
1.3.
That patc h o f grass could be r e f e r r e d to a l t e r n a t e l y as
a front.yard, a larun, grass, a patch of pass, e t c . (to assume
t h a t these phrases r e f e r to the sane object, one must
see the grass as a metonymlc s u b s t i t u t e f o r tMs patcA of
grass, and the front.yard as some " a r e a " r a t h e r than a
"slice"
l n c l u d l n ~ a i r above and ground under; n e i t h e r
v i e w i s unreasonable). The permissible prepositions,
and t h e i r
interpretation,
vary with each r e f e r r i n g
phrase: compare in/on the ~ass, ~nion tA~ patcA of ~as~, inK*on)
tan front.~:rd, onl(*~n) the /reran [ F i l l m o r e 1971]. With t h i s
warning,
I
will
go
on
speaking
of
"object
characteristics',
" o b j e c t i d e n t i t y " , etc.
Some o f the o b j e c t c h a r a c t e r i s t i c s used in production
and i n t e r p r e t a t i o n
can be computed from the shape of
t h e o b j e c t s - - the axes of symmetry (needed f o r across tan
road and along tan ro~d), the "top s u r f a c e " (on t&e label), the
~outllne"
(tA, #ird in t ~ tree), e t c . (for a d e s c r i p t i o n of
some o f these characteristics, and of their ro le In
TYPICAl, PHYSICAl, OR GEOMETRICAL CONTEXT
When using in w i t h areas, i t Is not s u f f i c i e n t th a t the
r e f e r e n c e o b j e c t be two-dimensional; t h a t o b j e c t must
be p a r t o f a su rf a ce d i v i d e d i n t o c e l l s . One does not
draw a l i n e in a blackboard; but in tat nlargin is acceptable,
because the margin is a subdivision of a page. In the
same f a s h i o n , ' g e o g r a p h i c a l areas (England, tat county,
e t c . ) a re s e c t i o n s of a d ivid e d surface. Some objects
are exclusively
conceptualized as parts of a " c e l l
structure"
and c a n n o t t he n f o l l o w at (*at his room, *at
England). O t h e r o b j e c t s can be conceptualized both as
e l e m e n t s o f a c e l l s t r u c t u r e (in the village), or as one of
a s e t o f s e p a r a t e places (at tat ~illage). Or consider ~ard:
when 1~ is a p a r t o f the grounds of a house, one is
r e s t r i c t e d to In. But o f somebody working In a Junkyard,
one c o u l d say he is at the )¢rd, r e f l e c t i n g a view of the
y a r d as one o f a set o f separate lo ca t io n s.
If
a door
is
in
its
typical
context,
i.e.
part
of a
wall,
then interpretation
o f m tk~ right of Me d~r must be
based on t h e d o o r ' s own axes. Otherwise ( I n a hardware
store
for
example) an o b s e r v e r ' s l i n e of s i g h t m y
override
the door's cross-axis.
1.4.
RELATIVE MOBILITY
The m o b i l i t y
of the reference object relative
to the
located
object
influences
the o r d e r o f the nominals
around the preposition:
the more mobile o b j e c t n o r m a l l y
precedes the preposition.
One w i l l not say t/ur ~&,n~ bot~t
i~ tam one in a cap, b u t tke one ~ d k a ~ p on it. Following Tally
(1978a],
I will call the l o c a t e d o b j e c t the " F i g u r e " ,
and t h e r e f e r e n c e o b j e c t the "Ground", when d i s c u s s i n g
t h e o r d e r o f t h e nominals.
Human b e i n g s
t e n d t o p l a y havoc w i t h the r e l a t i v e
mobility
rule,
either
because they are the preferred
topic
(flee man i~ a Nu~ coat), or - - a s c e n t e r o f t h e
universe
-- preferred
r e f e r e n c e o b j e c t (tke EmpOe 3t~e
building i~ in f r o n t of me).
Typicality
p l a y s an i l p o r t a n t
r o l e in d e t e r l l n l n g
an
appropriate
locative
predication
(and no doubt o t h e r
types of expressions).
The choice o f expression tends
to
depend
not
on
particular
(non
prototypicaI)
attributes
o f the o b j e c t s considered,
but r a t h e r on
typical
attributes
o f t h e c a t e g o r y t o which they are
assigned
by
the
linguistic
expression.
If
typical
conditions
do n o t o b t a i n ,
t h e y tend t o be ignored,
u n l e s s one has s o l e s p e c i a l reason to b r i n g a t t e n t i o n
to the atypical
conditions.
I f f o r Instance the cap o f
a bottle
were g l u e d t o the w a l l , one would s t i l l
say tk~
bo~tit wLtk a cap on it. Even I f a t r a y has v e r y high sides,
one w i l l
say on the tr¢7. Consider a l s o the t a b l e p i c t u r e d
above.
I m a g i n e the space under i t p r o g r e s s i v e l y more
solidly
e n c l o s e d ; t h e r e I s s p o i n t a t which one might
be s t r u c k by t h i s and say in tat t<d~le. But t h i s p o i n t is
rather
f a r a l o n g ; even w i t h a t a b l e w i t h a s o l i d sheZt
at floor
level,
people c o n s i s t e n t l y d e s c r i b e o b j e c t s on
t h a t s h e l f a s u n d e ~ t k t ta~e.
2.
~QHTEXTUAL FACTORS
The c h o i c e o f an a p p r o p r i a t e l o c a t i v e p r e d i c a t i o n 4 1 s t
d e p e n d s on v a r i o u s
a s p e c t s o f the c o n t e x t .
Some o~
these contextual
characteristics
are discussed In t h i s
s e c t i o n as. i f t h e y were n e a t l y separable; in f a c t , a l l
are
interdependent
in
complex
ways,
and
these
lnterrrelations
must become c l e a r b e f o r e we can design
models o f comprehension and p r o d u c t i o n .
2. I .
The m o b i l i t y
rule
I s I n f a c t a consequence o f the
principle
t h a t t h e o b j e c t whose l o c a t i o n is a t Issue
s h o u l d p r e c e d e t h e p r e p o s i t i o n . The Ground is t y p i c a l l y
bigger
and l e s s mobile than the Figure, since those
objects
whose l o c a t i o n
is most commonly a t issue are
t h o s e w h i c h move around, and a good r e f e r e n c e o b j e c t i s
one whose l o c a t i o n
can be I n f e r r e d from I t s name, and
t h u s had b e t t e r be the sase o v e r some time.
What I s a t
i s s u e in t u r n depends on t h e s p e a k e r ' s
purpose in constructing
the l o c a t i v e p r e d i c a t i o n ,
and
how I t f i t s
I n t o h i s / h e r o v e r a l l d i s c o u r s e plan.
2. 3.
VARYING V|EWPO[NT ON THE OBJECT
Mainly
this
I n v o l v e s the c o n t r a s t between a c l o s e - u p
and a remote v i e w o f t h e o b j e c t s . Most o f t e n , t h i s is
n o t a B a t t e r o f a c t u a l d i s t a n c e , but s way o f viewing
an o b j e c t f o r a g i v e n purpose: one Jay choose to ignore
one o r more d i m e n s i o n s , or l n t e r n a l c h a r a c t e r i s t i c s
of
the object.
For example, a road u y be seen as a s t r i p
(a truck On tke ro¢d), o r a l i n e (a oUlateon Mr r o ~ L ~ d o n ) .
N o r m a l l y beMnd tar kouJt v i i i
be based on the house's own
a x e s . B u t when l o o k i n g from some d i s t a n c e , one M y use
one's line of sight as axis.
Another aspect of viewpoint,
is the bounded/unbounded
distinction.
Compare w ~ n g
f~rougk versus across the ~at~
[Talmy 1978b]: in t h e former the boundaries of the body
o f w a t e r a r e I g n o r e d , b u t in the l a t t e r ,
the e x t e n s i o n
of
t h e body o f w a t e r from one end to another i s
involved.
2.4.
RELEVANCE
Give= the pictures
b e l o w , one w i l l
bomt, b u t r h t bulb in Mt s ~ k ~ .
s a y t/~ ~ , ~ d u n ~ r tat
CONTEXT DEPENDENT PARAMETERS.
These
Include
the l o c a t i o n
o f an observer,
for
deictic
uses o f some p r e p o s l t l o n s ~n fro~t oJ'lkt t r y ) ,
an
implicit
(fuzzy)
distance
threshold
for
prepositions
i n d i c a t i n g p r o x i m i t y (Denofsgy 1975].
the
and
the
] n the g a s - s f a t ~ ~s at fat freta~rJ, an i m p l i c i t c r o s s - p a t h is
assumed.
To say t h a t " f r e e w a y " occurs as a l e t o n y l i c
substitute
for
" a t the i n t e r s e c t i o n
of a c r o s s - r o o d
w i t h t h e f r e e w a y " i s not v e r y u s e f u l , since no general
rule
o f metonymy w i l l p r e d i c t t h i s one (as n a t u r a l a s
such a s u b s t i t u t i o n
may sound to E n g l i s h speakers, i t
i s n o t a c c e p t a b l e in French: see ~ t poste ~es~tct ~ t ~ la
route).
2.2.
and fA, ¢kurcA n ~ r tat kouJt. BUt the assigment must a l s o
respect the relative mobility.rule.
TAt kouJe n ~ r far ~urck
is reversible
because b o t h house and church are e q u a l l y
immobile;
b u t tam ~cycle near tam ¢ku~h Is not. When one
w i s h e s t o l o c a t e a l e s s mobile o b j e c t w i t h respect to a
more m o b i l e one, : t h e r e are a number of p e r i p h r a s t i c
devices
-o n e " being the use o f " w i t h ~ as in the
earlier
example (tat bottlt with ¢ ~ p on ~t); " w i t h " , not
being
basically
locative,
Is n o t
subject
to
this
relative
mobility
r u l e . See a l s o t/~ / ~ s e is n ~ r wk~t tat
~ ¢ ~ t Is ( b u t *tat ko~e is ne¢r the ~¢')cie ~ a l m y 1978aj); t h i s
t u r n s b~jc/e I n t o an immovable e n t i t y , namely a piece.
F}GURE/GROUND AS 1GNM~T
The a s s i g n m e n t
of
the r o l e s
of
Figure and Ground
depends p r i ~ r i l y
on which o f the two o b j e c t s ' l o c a t i o n
Is at issue.
The o b j e c t whose l o c a t i o n is a t issue
precedes the preposition:
compare the tenue nt~zr tam cku~k
The s o c k e t i s s t i l l
f u n c t i o n i n g as a socget when f a c i n g
down,
t h e bowl n o t as a bowl.
I f f u n c t i o n is the
relevant
aspect,
i t I s o f no I n t e r e s t to d i s t i n g u i s h
between situations
where b u l b and socket are as above,
and t h e i r
u p s i d e down v e r s i o n s .
With the bowl, t h i s
distinction
matters.
Similarly,
the
normally
useful
A
pear in 6 is m tke ~ I .
It is not
to distinguish
between s i t u a t i o n A and
E
For t h e two examples J u s t d e s c r i b e d , one could c o n t r i v e
Contexts
i n w h i c h the d i s t i n c t i o n s
norsally
ignored
w o u l d be i m p o r t a n t .
And c e r t a i n l y
adequate lOdels of
language should account f o r t h i s p o s s i b i l i t y .
A
locative
expression
may describe
the
general
i n t e n t i o n of a per}on over some time, rather than his
p r e c i s e l o c a t i o n at the tlme of speaking. I could say
L~nn is.at.t~e store even if l knew .Lynn might still be on
her way. But t h i s may not be appropriate (e.g. i f I
know the addressee is at the s t o r e ) .
Relevance
is
i m p o r t a n t f o r Grlcean inferences.
For
instance, from /on is near his desk, one can generally infer
i o n t~ not at his desk. I f however I asked a f r i e n d on the
phone "are you near your desk? could you look up the
address...",
an a p p r o p r i a t e answer is "yes", even if my
f r i e n d is a t h i s / h e r desk. In ~hls context pro xim it y is
the r e l e v a n t aspect, and "near" becomes appropriate.
2.5.
SALIENCE
The book below l e f t is on the table, the l i d ( r i g h t ) is
n o t , because the i n t e r v e n i n g r e l a t i o n between the l i d
and the jar is salient. Such salience Is not primarily
a u m t t e r o f the size of some intervening object.
~#.book
(One c o u l d however say here: A ls to the right and behind B, or
A is ~agonally to the right of B. This suggests th a t even in
t h e presence of C, A is to the algae of B is true, but
"uncooperative"
[Grice
1974].
However,
It
is
"uncooperative"
precisely because of some intrinsic
property
o f the concept to the right - - l.e. because
".closer to the axis" is in some sense a better way tO
r e a l i z e to the right. Even I f one grants some usefulness to
the semantic/pragmatic distinction, i t does not neatly
apply here.)
A similar use of c o n t r a s t can be seen with the ch.,~r is In
the corner in the f i g u r e below. I t is not appropriate
u n l e s s the armchair be removed.
~5'l~lid
,@.-.cha i r
One g e n e r a l l y s a y s t h a t X is tn eke field and in the ~mi,
whenever field or bowl contain X. One ~ay however say
the dust on the ~ml, and the fertilizer on the ~eid. An adhering
thln lamina brings attention to c o n t a c t rather than
inclusion.
The co n ce p t o f a " c o r n e r " has b u i l t In that In the corner
becomes less a p p r o p r i a t e as one gets further from the
vertex itself,
2.6.
Many uses o f the p r e p o s i t i o n s cannot be explained in
terms o f any of the above f a c t o r s . One then needs a
d e s c r i p t i o n o f the c o n t e x t of use a t a rather s p e c i f i c
level.
Consider f o r example the contexts in which one
will say Suzy is at the playground versus in the playp'ound. In
would be ( i ) p r e f e r r e d i f t h e speaker can see Suzy,
(il)
r e q u i r e d I f the addressee expects Suzy to be Just
o u t s i d e the playground, ( t i t )
required i f the speaker
h e r / h i m s e l f I s in the playground (an analogous c o n t r a s t
exists
between at the be~k and on the beach). These
conditions
"suggest" a close-up view, and th a t the
speaker's
knowledge is
precise;
by contrast,
"at"
s u g g e s t s a remote view, and imprecise knowledge. But
" t o suggest" is not to imply: one cannot i n f e r these
c o n d i t i o n s o f use from the ideas of a remote versus a
c l o s e - u p view.
HIGHLIGHTING SOME BACKGROUND ELEMENT
The c h o i c e between expressions is often a matter of
b r i n g i n g attention to some. background element ra t h e r
than s i g n a l l i n g d i f f e r e n c e s of f a c t . Thus to tke right, as
c o n t r a s t e d w i t h on the rigM, tends to h i g h l i g h t the
d i s t a n c e between the two objects, and to evoke t r a v e l
away from the r e f e r e n c e object; the contr a st cannot
always be described in terms of o b j e c t i v e d i f f e r e n c e s
in the situations ( i t sometimes is: thus i f a t h i r d
o b j e c t o f the same kind Is between the two considered,
o n l y to the right is a p p r o p r i a t e ) . And on the right side of the
bu~lW~ng as c o n t r a s t e d w i t h on the rigkt ~ the b~l~ng brings
attention
to the w a l l . Consider also Bogota is melon the
equator; " a t " will be p r e f e r r e d I f one wishes to signal
the presence of some transverse l i n e (e.g. a t r a v e l
traJectory~.
2. 7.
INDETERMINACY
Most
spatial
relations
are
t r u e given a c e r t a i n
t o l e r a n c e . The t o l e r a n c e has a lower l i m i t defined by
t h e n a t u r e of the o b j e c t s ; i t s e f f e c t i v e value depends
on o n e ' s purpose, and the p r e c i s i o n of one's knowledge.
Thus, the angular p r e c i s i o n with which ~ r ~ t l y to the ~gM
i s d e f i n e d v a r i e s w i t h s i l v e r w a r e on the table, chess
p i e c e s on a board, or houses on a block.
2.8.
CONTRAST
" P o l a r concepts", i.e. terms like to the ngkG may behave
l l k e i m p l i c i t comparatives. In some sense, to the right is
b e t t e r r e a l i z e d the c l o s e r the located object i s to the
" r i g h t axis". Thus, i f I said put the ckair to the righ! of tke
desk, I would expect you to put it more or less on the
r l g h t a x i s o f the desk. And, in the f i g u r e below, A ls to
tAe right of B only in the absence of C. The location of A
must be c o n t r a s t e d w i t h that of s i m i l a r objects in the
r e l e v a n t part of space.
2. 9. (~THERS
3. COR~ M E A N I N ~
With
most
of the examples given,
the explanation
suggested f o r the choice of a p re p o sit io n assumes the
e x i s t e n c e o f a "core meaning". This core meaning is
basically
a
geometrical
relationship
between
geometrical
entities.
Thus,
in
a given
context,
" g e o m e t r i c a l d e s c r i p t i o n s " (say a point, l i n e , surface,
volume, lamina, e t c . ) are mapped onto the subject and
object of the preposition. Strictly speaking, the core
meanings are -- at best -- true only of these geometric
descriptions.
In f a c t , they may not even hold f o r any
such g e o m e t r i c d e s c r i p t i o n - - see the pear in ¢ ~ml
example above, assuming the natural core meaning for
"lne,
i . e . " i n c l u s i o n " . Yet, the core meaning is then
present as "prototype".
Here a r e i n f o r m a l d e f i n i t i o n s o f the core meanings f o r
two
categories
of
prepositions,
designated
as
"topological"
(at. on. in), and " p r o j e c t i v e " (to the right,
be~nd, e t c . ) .
Topological
prepositions:
in:
partial
i n c l u s i o n o f a g e o m e t r i c a l c o n s t r u c t in a
v o l u m e , an a r e a , o r a l i n e .
on:
contiguity,
a d j a c e n c y of a g e o m e t r i c a l c o n s t r u c t
with a surface,
or a l i n e .
~ : c o i n c i d e n c e o f a p o i n t w i t h a p o i n t in s p a c e .
context,
inclusion,
contiguity,
and
c o i n c i d e n c e need not be true. Thus the book on top of a
p i l e o f books on the t a b l e can be said on tie ta~e, and
M a r ~ ts eJ the gate when very close to It. But the r e l a t i o n s
r e p r e s e n t the " i d e a l " around which p a r t i c u l a r instances
gravl'tate.
Thus at I m p l i e s
the c l o s e s t
reasonable
relationship
between two o b j e c t s , and coincidence where
sensible
(tie c e n t ~ o f t k e drclems attkeint~s~t~onoftke a x e ) . Of
course,
the
core
meanings are not s u f f i c i e n t
to
d e t e r m i n e the c o n d i t i o n s of use of a given p r e p o s i t i o n :
one must a l s o know p r e c i s e l y which d e v i a t i o n s from the
ideal
are permitted.
One p r i n c i p a l process J e d l a t t n g
between core meanings and a c t u a l c o n d i t i o n s of use Is
the
mapping o f o b j e c t s onto p o i n t s ,
surfaces, and
volumes.
In
actual
am n o t saying t h a t the core meanings presented here
a r e t h e o n l y p o s s i b l e ones. Only when core meanings are
I n c o r p o r a t e d in a g l o b a l e x p l a n a t o r y system w i l l I t be
possible
to
make r i g o r o u s
arguments f o r a l t e r n a t e
c h o i c e s . Those proposed here represent a good s t a r t i n g
point.
I
Projective
prepositions:
Each o f these p r e p o s i t i o n s involves - - through f a c t ,
supposition,
o r metaphor - - a " p o i n t o f o b s e r v a t i o n ' , k
point
of
observation
c o n s i s t s of two vectors,
one
Indicating
the intrinsic v e r t i c a l
of the o b s e r v e r (it
will
n o t be the g r a v i t a t i o n a l
v e r t i c a l I f the observer
I s l y i n g down, o r not In the g r a v i t a t i o n a l f i e l d ) , and
t h e o t h e r o r t h o g o n a l to the f i r s t
along the l i n e o f
sight.
These
two
vectors
completely
specify
four
c o p l a n a r o r t h o $ o n a l h a l f - l i n e a x e s associated with the
p o i n t o f o b s e r v a t i o n : the " f r o n t " , " r i g h t " , "back", and
"left"
a x e s , in c l o c k w i s e o r d e r .
In t h e c o r e meaning d e f i n i t i o n
of these p r e p o s i t i o n s ,
r e f e r e n c e and l o c a t e d o b j e c t s are p o i n t s . Given a p o i n t
of observation,
one can s p e c i f y axes aSSOCiated w i t h
t h e r e f e r e n c e o b j e c t - - the "base axes" ( r i g h t , l e f t ,
front, and back) by r e f e r e n c e to which to the ri~w,kt,be~nd,
etc.,
will
be d e f i n e d .
These axes o r i g i n a t e at the
reference object.
If the p o i n t of observation (PObs)
coincides
w i t h the r e f e r e n c e o b j e c t (PRef) ( f i g u r e A
below),
the base axes are I d e n t i c a l to those o f the
point of observation.
I f the p o i n t o f observation Is
away from the r e f e r e n c e o b j e c t ( f i g u r e B), the base
axes
are
a mirror
i M g e of those o f t h e p o i n t of
observation
t h e segment
object.
--
from/pRef
!eft4='il~'~
the
joining
right
bmCk~pot~ s
mtzror plane being the b i s e c t o r of
point o f o b s e r v a t i o n to reference
ba~//P"" f
Deft@right
fr?nt
B
There a r e thus two p o s s i b l e orders of the base axes, as
shown I n A and B.
I wlll
define
the core meaning of each p r o j e c t i v e
preposition
as f o l l o w s :
given a punctual reference
object
(PRef), punctual l o c a t e d o b j e c t (PLoc), and a
point
of observation,
base axes can be c o n s t r u c t e d
a c c o r d i n g t o the procedure o u t l i n e d above: PLoc Is to tie
left. o f
PRef
iff
it
Analogous d~finitions
e a s y to f o r m u l a t e .
is
located
f o r the
on
the
other
left
base
prepositions
axis.
are
A few examples w i l l
help understand how these co're
meanings
are
manifest
in the a c t u a l
uses of the
prepositions.
In in fremt of a r~ling st~me, the point of observation Is
"vlrtual"-l.e. It Is an hypothetical locatlon and
direction for vlewlng: the location is coincident with
the
stone,, and
the direction
Is the direction of
movement. One must o f course assume - - as w i t h the
objects
In tit= examples t h a t f o l l o w - - t h a t the stone
I s a s l m i l a t e d to a point.
I n to tie ~gkt of tle char, the base axes may be s p e c i f i e d a s
those intrinsic
t o the c h a i r -o I . e . by reference to a
typical
user.
The
point
of
observation
is
then
coincident
with
the r e f e r e n c e o b j e c t o- namely the
chair.
C o i n c i d e n c e may be the case when the base axes
are not Intrinsic
to the r e f e r e n c e o b j e c t : f o r Instance
on the ri[M of the sto0/ lay be d e f i n e d w i t h respect to
somebody s i t t i n g
on i t ,
given a round stool w i t h no
intrinsic
front axis.
R e f e r e n c e o b j e c t and p o i n t of o b s e r v a t i o n are separated
I n the moon ~ k i n d the clou~[. They can a l s o be separated when
the base
axes are intrinsic
to t h e r e f e r e n c e o b j e c t :
wlth on t ~ r i [ k t side of tle closet, the p o i n t of o b s e r v a t i o n I s
d e f i n e d by a t y p i c a l user f a c i n g the c l o s e t .
A g a i n , one might d e f i n e the core meanings d i f f e r e n t l y .
In . p a r t i c u l a r
one could d e f i n e the core meaning of " t o
the
right"
say, a s implying
l o c a t i o n In the whole
right-hand
half-space
instead of on the axis.
The
c h o i c e adopted here r e f l e c t s the f a c t noted In e a r l i e r
e x a m p l e s t h a t the " i d e a l " r e a l i z a t i o n of to the ngkt is
with the located o b j e c t on the right base a x i s .
P r o c e s s e s o t h e r than the mapping of o b j e c t s onto p o i n t s
may m e d i a t e between core meanings and actual c o n d i t i o n s
o f use. The r e f e r e n c e o b j e c t amy r o t a t e : where is on t~e
right nd, r of the ~ n t i n g when the painting is tllted7 Tie tree
to tie ri@kt of tie ro(~ a c t u a l l y means " a t s o b p o i n t of the
r o a d " - - t h i n k o f a c u r v i n g r o a d ) , end the ~
~ n d tat
barbed wirefence assumes " i n t e g r a t i o n " along the length o f
t h e f e n c e (note one cannot say t / ~ t y to tie ntkt o f t k e f ~ c e
to the Same effect -- that is r e f e r r i n g In thls way to
t h e whole c i t y . The l i n e o f s i g h t I s a favored a x i s , as
compared t o r i g h t , l e f t , and hack axes).
4.
SOME CONCLUS|( .'S
Here are
suggested
the main problels and directions
by the examples in this paper.
of
inquiry
One c a n n o t
fully
explain
the use of a l o c a t i v e
predication
in a given s i t u a t i o n in terms of the core
meanings t o g e t h e r w i t h some i n f e r e n c e s from general
principles
involving
object
knowledge,
salience,
relevance,
the precision
desired,
etc.
T h e r e w111
always
remain
uses
involving
some
degree
of
arbitrariness
(most
uses
are
"motivated",
If
not
"compositional"
[Flllmore Ig?9] -- i.e. the morphemes
composing
the
appropriate
expression
are
normally
selected from "reasonable" candidates). Even where such
principles are at play, they may operate not at the
comprehension/production
level,
but
rather
at
the
p h y l o g e n e t i c l e v e l . To s o r t p r i n c i p l e d aspects o f use
from a r b i t r a r y
ones, and to understand e x a c t l y where
such p r i n c i p l e s
operate,
one must of course f i r s t
establish
t h e i r e x i s t e n c e and nature.
REFERENCES
Boggess, L o is C. 1979. Computational i n t e r p r e t a t i o n of
E n g l i s h s p a t i a l p r e p o s i t i o n s . PHO thesis, U n i v e r s i t y o f
Illinois,
Urbana.
In t e r m s o f knowledge of t h e p h y s i c a l world, I b e l i e v e
o n e importan~ step. toward a d e q u a t e representations is
t o p u t t h e e x p e r i e n c e r back i n t o t h e p i c t u r e . That i s ,
Denofsky, Murray E. 1 9 7 6 . How near is near: a near
specialist.
M.~.T. Artificial
I~telltgence Lab. memo
no. 344, Cambrldge, Mass.
I t i s not enough - - or even always necessary - - to know
where what o b j e c t s are; one must also consider how much
fits
into
one
field
opposed, to how
viewing distance,
of
view,
"are",
they
visibility,
how t h i n g s
"appear"
how t h i s changes
o b s t r u c t i o n , etc.
as
with
General p r i n c i p l e s o f salience should ue studied: how
some o b j e c t p a r t s or r e l a t i o n s are selected as most
i m p o r t a n t - - e i t h e r in a l l imaginable contexts, or in
some c o n t e x t s .
Salience underlies many Instances of
metonymy (in at t~e front of tAe t~atre, " t h e a t r e " a c t u a l l y
r e f e r s to the p a r t occupied by the audience).
Fillmore,
Charles J. 1971. Santa Cruz lectures on
detxls,
presented a t the U n i v e r s i t y of C a l i f o r n i a ,
Santa
Cruz.
Mimeographed,
Indlan~
University
L i n g u i s t i c s Club, Bloomington.
,
linguistics.
Llnguls~
1979.
Innocence:
a second i d e a l i z a t i o n
for
Pr~ecdings. FlftA Annual Mitring, Btrkel~
3oci¢~,
63-76.
University
of
California,
Berkeley.
Grice,
1974. Logic and conversation. 3~ntaz and
3, ed. by Peter Cole and J e r r y
41-$8. New York: Academic Press.
H. Paul.
Semantic: ~pe~A o~ts, vol.
M a n y ' q u e s t i o n s revolve around the issue of "relevance"
- - of "what matters, to whom, in what circumstances"
r a t h e r than the t r a d i t i o n a l concern with what is true.
All
existing
artificial
I n t e l l i g e n c e programs have
i g n o r e d t h i s problem by using a l i m i t e d vocabulary In a
limited
domain,
so t h a t the question of se le ct in g
r e l e v a n t u t t e r a n c e s never arises.
Relevance i s l i n k e d to the speaker's purpose, as u n y
o f the c o n t e x t u a l f a c t o r s described in t h i s paper - indeterminacy,
Gricean
inferences,
highlighting
of
background elements, determination of the Figure/Ground
relationship,
etc. The set of " e x p r e s s i b l e " 8oals is
c o n s t r a i n e d by t h e " p o t e n t i a l " of the language, i . e . by
a semantic system w i t h f i n i t e l y many options. One can
o n l y want to say what can be said, and said in a
reasonable
amount o f time.
Clearly,
" p l a n n i n g " for
natural
problem.
language
processing
is
a
very
Important
Purpose however, w i l l not explain everything one says.
Simple
associative
mechanisms
must
sometimes
be
responsible
f o r what one says. For instance,
some
background element may be h i g h l i g h t e d - - provided Some
l i n g u i s t i c means to do so e x i s t s - - only because some
p a s s i v e a s s o c i a t i v e l i n k has brought i t to a t t e n t i o n .
Once general p r i n c i p l e s are b e t t e r understood, I t Is an
open q u e s t i o n whether they are used by speakers, or
whether t h e i r e x p l a n a t o r y power Is at the phyiogenettc
l e v e l (and w i l l thus be only I m p l i c i t in the s t r u c t u r e
of
the
knowledge
representation).
For
instance,
a l t h o u g h t h e r e is a general p r i n c i o l e t h a t the l o c a t e d
o b j e c t should be more mobile than the reference object,
p r o d u c t i o n may not proceed by inferences from t h i s
g e n e r a l p r i n c i p l e together with scenarios Involving the
two o b j e c t s . The l i n g u i s t i c expression (or p a t t e rn f o r
e x p r e s s i o n s ) may be attached to some representation of
a "situation
type" i n v o l v i n g the two objects (or two
superordinate objects).
And although " a t " generally
i m p l i e s the c l o s e s t reasonable r e l a t i o n s h i p between two
objects,
such a d e f i n i t i o n
may never be used by a
speaker
-or
used
only
In
the
creation
or
u n d e r s t a n d i n g o f novel types of expressions, metaphors,
witticisms,
etc.
What
speakers
do,
and what conputer
models
of
comprehension and production processes should be made
to do, are two d i f f e r e n t things: the l a t t e r depends on
the c o n s t r u c t e r ' s goals, which should be subjected to
some s c r u t i n y .
A c o m p u t a t i o n a l treatment of the use of pr e p o sit io n s
will
r e q u i r e much g r e a t e r s o p h i s t i c a t i o n than naive
r e p r e s e n t a t i o n theory would lead us to expect.
L. Morgan,
Talmy,
beonard~ 1978a. Figure and ground in complex
se n t e n ce s. Unluttsals of Human Language, vol. 4, ed. by
Joseph H. Greenberg e t ' a l ,
625-649. "Stanford, Col:
Stanford Univ..Press.
1978b. The R e l a t i o n o t ' g r a m u r to c o g n i t i o n
- - a synopsis. T~rtt~allssuts In Natur~ Language Pr~sin~2.
14-24.
Coordinated
Science
Lab.,
University
of
illinois,
Urbana-Champatgn.