ON THE SPATIAL USES OF PREPOSITIONS 
Annette Herskovlts 
Linguistics Department, Stanford University 
At first glance, the spatial uses of prepositions seem 
to constitute a good semantic domain for a 
computational approach. One expects such uses will 
refer more or less strictly to a closed, explicit, and 
precise chunk of world knowledge. Such an attitude Is 
expressed in the following statement: 
"Given descriptions of the shape of two objects, given 
their location (for example, by means ox coordinates in 
Some system of reference), and, In some cases, the 
location of an observer, one can select an appropriate 
preposition." 
This paper shows the fallacy of this claim. It 
addresses the problem of interpreting and generating 
"locative predications" (expressions made up of two 
noun-phrases governed by a preposition used spatially). 
It identifies and describes a number of object 
characteristics beyond shape (section I) and contextual 
factors (section 2) which bear on these processes. 
Drawing on these descriptions, the third section 
proposes core meanings for two categories of 
prepositions, and describes some of the transfor~ttons 
these core meanings are subject to in context. The last 
section outlines the main directions of Inquiry 
suggested by the examples and observations in the 
paper. 
1. ~BJECT CHARACTERISTIC~ 
Throughout the paper, I use the term "object ~, meaning, 
strictly speaking, the object together with some 
lextcal label. In effect, the choice of preposition 
depends on the lexical category associated with the 
object by the noun-phrase used to refer to It. And such 
a category is not uniquely defined. There are different 
levels In the categorization hierarchy (e.g. "end 
table", "table", "piece of furniture'), but also 
different perspectives on the object. Consider the 
picture below. 
,~, , ~, 
That patch of grass could be referred to alternately as 
a front.yard, a larun, grass, a patch of pass, etc. (to assume 
that these phrases refer to the sane object, one must 
see the grass as a metonymlc substitute for tMs patcA of 
grass, and the front.yard as some "area" rather than a 
"slice" lncludln~ air above and ground under; neither 
view is unreasonable). The permissible prepositions, 
and their interpretation, vary with each referring 
phrase: compare in/on the ~ass, ~nion tA~ patcA of ~as~, inK*on) 
tan front.~:rd, onl(*~n) the /reran \[Fillmore 1971\]. With this 
warning, I will go on speaking of "object 
characteristics', "object identity", etc. 
Some of the object characteristics used in production 
and interpretation can be computed from the shape of 
the objects -- the axes of symmetry (needed for across tan 
road and along tan ro~d), the "top surface" (on t&e label), the 
~outllne" (tA, #ird in t~ tree), etc. (for a description of 
some of these characteristics, and of their role In 
comprehension, see \[Boggess 1979\]). 
Other characteristics are not deducible from shape. 
These include: 
1. 1, ALTERNATE GEOM~'I'RIC DESCRIPTIONS 
Objects identical in shape may be "conceived m 
differently, for instance as surface or as enclosure. 
This may be a choice available to the speaker to 
emphasize certain aspects (inlon t~$e rug), or It may be 
determined for the category of the reference object (on 
tAe football field). 
In under t/te aJater, the water stands for tAe upper free surface 
of tAn ruater; in in the water, it .is conceived as a volume. A 
whole category of objects follows this rule: see 
(undtrlln) tan (snowllakeloceanlsan41.). Such objects tend to be 
viewed only as volumes with "underneath': undcrn~A fat 
lake is generally interpreted as meaning "under the 
lower surface of that body of water'. 
In tan crack In tan 6~wl, the crack Is In the volume defined 
by the normal surface of the bowl in Its uncracked 
state. In tan milk in tat bowl, the milk Is In the volume 
enclosed by the bowl and limited upward by a plone 
through the rim. 
1.2. FUNCTION 
One says in ran disk and on the tray though these objects uy 
be essentially Identical in shape. One will not 
ordinarily say tan cat Is in :At t~e, but un~r tan t~e, even 
with the cage-like table below. 
/oAn is et X Often means that John Is using I as one 
normally uses it (JoAn is at his desk). If normal use 
implies being on or m X, then at Is not used (John is in 
or on the bed, but not at). And to the right of the chadr Is 
defined by reference to a typical user of the chair. 
1.3. TYPICAl, PHYSICAl, OR GEOMETRICAL CONTEXT 
When using in with areas, it Is not sufficient that the 
reference object be two-dimensional; that object must 
be part of a surface divided into cells. One does not 
draw a line in a blackboard; but in tat nlargin is acceptable, 
because the margin is a subdivision of a page. In the 
same fashion, ' geographical areas (England, tat county, 
etc.) are sections of a divided surface. Some objects 
are exclusively conceptualized as parts of a "cell 
structure" and cannot then follow at (*at his room, *at 
England). Other objects can be conceptualized both as 
elements of a cell structure (in the village), or as one of 
a set of separate places (at tat ~illage). Or consider ~ard: 
when 1~ is a part of the grounds of a house, one is 
restricted to In. But of somebody working In a Junkyard, 
one could say he is at the )¢rd, reflecting a view of the 
yard as one of a set of separate locations. 
If a door is in its typical context, i.e. part of a 
wall, then interpretation of m tk~ right of Me d~r must be 
based on the door's own axes. Otherwise (In a hardware 
store for example) an observer's line of sight my 
override the door's cross-axis. 
1.4. RELATIVE MOBILITY 
The mobility of the reference object relative to the 
located object influences the order of the nominals 
around the preposition: the more mobile object normally 
precedes the preposition. One will not say t/ur ~&,n~ bot~t 
i~ tam one in a cap, but tke one ~dk a ~p on it. Following Tally 
(1978a\], I will call the located object the "Figure", 
and the reference object the "Ground", when discussing 
the order of the nominals. 
Human beings tend to play havoc with the relative 
mobility rule, either because they are the preferred 
topic (flee man i~ a Nu~ coat), or -- as center of the 
universe -- preferred reference object (tke EmpOe 3t~e 
building i~ in front of me). 
Typicality plays an ilportant role in deterllnlng an 
appropriate locative predication (and no doubt other 
types of expressions). The choice of expression tends 
to depend not on particular (non prototypicaI) 
attributes of the objects considered, but rather on 
typical attributes of the category to which they are 
assigned by the linguistic expression. If typical 
conditions do not obtain, they tend to be ignored, 
unless one has sole special reason to bring attention 
to the atypical conditions. If for Instance the cap of 
a bottle were glued to the wall, one would still say tk~ 
bo~tit wLtk a cap on it. Even If a tray has very high sides, 
one will say on the tr¢ 7. Consider also the table pictured 
above. Imagine the space under it progressively more 
solidly enclosed; there Is s point at which one might 
be struck by this and say in tat t<d~le. But this point is 
rather far along; even with a table with a solid sheZt 
at floor level, people consistently describe objects on 
that shelf as unde~tkt ta~e. 
2. ~QHTEXTUAL FACTORS 
The choice of an appropriate locative predication 41st 
depends on various aspects of the context. Some o~ 
these contextual characteristics are discussed In this 
section as. if they were neatly separable; in fact, all 
are interdependent in complex ways, and these 
lnterrrelations must become clear before we can design 
models of comprehension and production. 
2. I. CONTEXT DEPENDENT PARAMETERS. 
These Include the location of an observer, for the 
deictic uses of some preposltlons ~n fro~t oJ'lkt try), and 
an implicit (fuzzy) distance threshold for the 
prepositions indicating proximity (Denofsgy 1975\]. 
\]n the gas-sfat~ ~s at fat freta~rJ, an implicit cross-path is 
assumed. To say that "freeway" occurs as a letonylic 
substitute for "at the intersection of a cross-rood 
with the freeway" is not very useful, since no general 
rule of metonymy will predict this one (as natural as 
such a substitution may sound to English speakers, it 
is not acceptable in French: see ~t poste ~es~tct ~t ~ la 
route). 
2.2. F}GURE/GROUND AS 1GNM~T 
The assignment of the roles of Figure and Ground 
depends pri~rily on which of the two objects' location 
Is at issue. The object whose location is at issue 
precedes the preposition: compare the tenue nt~zr tam cku~k 
and fA, ¢kurcA n~r tat kouJt. BUt the assigment must also 
respect the relative mobility.rule. TAt kouJe n~r far ~urck 
is reversible because both house and church are equally 
immobile; but tam ~cycle near tam ¢ku~h Is not. When one 
wishes to locate a less mobile object with respect to a 
more mobile one, : there are a number of periphrastic 
devices -- one" being the use of "with ~ as in the 
earlier example (tat bottlt with ¢ ~p on ~t); "with", not 
being basically locative, Is not subject to this 
relative mobility rule. See also t/~ /~se is n~r wk~t tat 
~¢~t Is (but *tat ko~e is ne¢r the ~¢')cie ~almy 1978aj); this 
turns b~jc/e Into an immovable entity, namely a piece. 
The mobility rule Is In fact a consequence of the 
principle that the object whose location is at Issue 
should precede the preposition. The Ground is typically 
bigger and less mobile than the Figure, since those 
objects whose location is most commonly at issue are 
those which move around, and a good reference object is 
one whose location can be Inferred from Its name, and 
thus had better be the sase over some time. 
What Is at issue in turn depends on the speaker's 
purpose in constructing the locative predication, and 
how It fits Into his/her overall discourse plan. 
2. 3. VARYING V|EWPO\[NT ON THE OBJECT 
Mainly this Involves the contrast between a close-up 
and a remote view of the objects. Most often, this is 
not a Batter of actual distance, but s way of viewing 
an object for a given purpose: one Jay choose to ignore 
one or more dimensions, or lnternal characteristics of 
the object. For example, a road uy be seen as a strip 
(a truck On tke ro¢d), or a line (a oUlateon Mr ro~L~don). 
Normally beMnd tar kouJt viii be based on the house's own 
axes. But when looking from some distance, one My use 
one's line of sight as axis. 
Another aspect of viewpoint, is the bounded/unbounded 
distinction. Compare w~ng f~rougk versus across the ~at~ 
\[Talmy 1978b\]: in the former the boundaries of the body 
of water are Ignored, but in the latter, the extension 
of the body of water from one end to another is 
involved. 
2.4. RELEVANCE 
Give= the pictures below, one will say t/~ ~,~d un~r tat 
bomt, but rht bulb in Mt s~k~. 
The socket is still functioning as a socget when facing 
down, the bowl not as a bowl. If function is the 
relevant aspect, it Is of no Interest to distinguish 
between situations where bulb and socket are as above, 
and their upside down versions. With the bowl, this 
distinction matters. 
Similarly, the pear in 6 is m tke ~I. It is not 
normally useful to distinguish between situation A and 
A E 
For the two examples Just described, one could contrive 
Contexts in which the distinctions norsally ignored 
would be important. And certainly adequate lOdels of 
language should account for this possibility. 
A locative expression may describe the general 
intention of a per}on over some time, rather than his 
precise location 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 this may not be appropriate (e.g. if I 
know the addressee is at the store). 
Relevance is important for Grlcean inferences. For 
instance, from /on is near his desk, one can generally infer 
ion t~ not at his desk. If however I asked a friend on the 
phone "are you near your desk? could you look up the 
address...", an appropriate answer is "yes", even if my 
friend is at his/her desk. In ~hls context proximity is 
the relevant aspect, and "near" becomes appropriate. 
2.5. SALIENCE 
The book below left is on the table, the lid (right) is 
not, because the intervening relation between the lid 
and the jar is salient. Such salience Is not primarily 
a umtter of the size of some intervening object. 
~#.book ~5'l~lid 
One generally says that 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 contact rather than 
inclusion. 
2.6. HIGHLIGHTING SOME BACKGROUND ELEMENT 
The choice between expressions is often a matter of 
bringing attention to some. background element rather 
than signalling differences of fact. Thus to tke right, as 
contrasted with on the rigM, tends to highlight the 
distance between the two objects, and to evoke travel 
away from the reference object; the contrast cannot 
always be described in terms of objective differences 
in the situations (it sometimes is: thus if a third 
object of the same kind Is between the two considered, 
only to the right is appropriate). And on the right side of the 
bu~lW~ng as contrasted with on the rigkt ~ the b~l~ng brings 
attention to the wall. Consider also Bogota is melon the 
equator; "at" will be preferred If one wishes to signal 
the presence of some transverse line (e.g. a travel 
traJectory~. 
2. 7. INDETERMINACY 
Most spatial relations are true given a certain 
tolerance. The tolerance has a lower limit defined by 
the nature of the objects; its effective value depends 
on one's purpose, and the precision of one's knowledge. 
Thus, the angular precision with which ~r~tly to the ~gM 
is defined varies with silverware on the table, chess 
pieces on a board, or houses on a block. 
2.8. CONTRAST 
"Polar concepts", i.e. terms like to the ngkG may behave 
llke implicit comparatives. In some sense, to the right is 
better realized the closer the located object is to the 
"right axis". Thus, if I said put the ckair to the righ! of tke 
desk, I would expect you to put it more or less on the 
rlght axis of the desk. And, in the figure below, A ls to 
tAe right of B only in the absence of C. The location of A 
must be contrasted with that of similar objects in the 
relevant part of space. 
(One could however say here: A ls to the right and behind B, or 
A is ~agonally to the right of B. This suggests that even in 
the 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 of the concept to the right -- l.e. because 
".closer to the axis" is in some sense a better way tO 
realize to the right. Even If one grants some usefulness to 
the semantic/pragmatic distinction, it does not neatly 
apply here.) 
A similar use of contrast can be seen with the ch.,~r is In 
the corner in the figure below. It is not appropriate 
unless the armchair be removed. 
,@.-.cha i r 
The concept of a "corner" has built In that In the corner 
becomes less appropriate as one gets further from the 
vertex itself, 
2. 9. (~THERS 
Many uses of the prepositions cannot be explained in 
terms of any of the above factors. One then needs a 
description of the context of use at a rather specific 
level. Consider for example the contexts in which one 
will say Suzy is at the playground versus in the playp'ound. In 
would be (i) preferred if the speaker can see Suzy, 
(il) required If the addressee expects Suzy to be Just 
outside the playground, (tit) required if the speaker 
her/himself Is in the playground (an analogous contrast 
exists between at the be~k and on the beach). These 
conditions "suggest" a close-up view, and that the 
speaker's knowledge is precise; by contrast, "at" 
suggests a remote view, and imprecise knowledge. But 
"to suggest" is not to imply: one cannot infer these 
conditions of use from the ideas of a remote versus a 
close-up view. 
3. COR~ MEANIN~ 
With most of the examples given, the explanation 
suggested for the choice of a preposition assumes the 
existence of a "core meaning". This core meaning is 
basically a geometrical relationship between 
geometrical entities. Thus, in a given context, 
"geometrical descriptions" (say a point, line, surface, 
volume, lamina, etc.) 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 fact, they may not even hold for any 
such geometric description -- see the pear in ¢ ~ml 
example above, assuming the natural core meaning for 
"lne, i.e. "inclusion". Yet, the core meaning is then 
present as "prototype". 
Here are informal definitions of the core meanings for 
two categories of prepositions, designated as 
"topological" (at. on. in), and "projective" (to the right, 
be~nd, etc.). 
Topological prepositions: 
in: partial inclusion of a geometrical construct in a 
volume, an area, or a line. 
on: contiguity, adjacency of a geometrical construct 
with a surface, or a line. 
~: coincidence of a point with a point in space. 
In actual context, inclusion, contiguity, and 
coincidence need not be true. Thus the book on top of a 
pile of books on the table can be said on tie ta~e, and 
Mar~ ts eJ the gate when very close to It. But the relations 
represent the "ideal" around which particular instances 
gravl'tate. Thus at Implies the closest reasonable 
relationship between two objects, and coincidence where 
sensible (tie cent~oftke drclems attkeint~s~t~onoftke axe). Of 
course, the core meanings are not sufficient to 
determine the conditions of use of a given preposition: 
one must also know precisely which deviations from the 
ideal are permitted. One principal process Jedlattng 
between core meanings and actual conditions of use Is 
the mapping of objects onto points, surfaces, and 
volumes. 
I am not saying that the core meanings presented here 
are the only possible ones. Only when core meanings are 
Incorporated in a global explanatory system will It be 
possible to make rigorous arguments for alternate 
choices. Those proposed here represent a good starting 
point. 
Projective prepositions: 
Each of these prepositions involves -- through fact, 
supposition, or metaphor -- a "point of observation', k 
point of observation consists of two vectors, one 
Indicating the intrinsic vertical of the observer (it 
will not be the gravitational vertical If the observer 
Is lying down, or not In the gravitational field), and 
the other orthogonal to the first along the line of 
sight. These two vectors completely specify four 
coplanar ortho$onal half-line axes associated with the 
point of observation: the "front", "right", "back", and 
"left" axes, in clockwise order. 
In the core meaning definition of these prepositions, 
reference and located objects are points. Given a point 
of observation, one can specify axes aSSOCiated with 
the reference object -- the "base axes" (right, left, 
front, and back) by reference to which to the ri~w,kt, be~nd, 
etc., will be defined. These axes originate at the 
reference object. If the point of observation (PObs) 
coincides with the reference object (PRef) (figure A 
below), the base axes are Identical to those of the 
point of observation. If the point of observation Is 
away from the reference object (figure B), the base 
axes are a mirror iMge of those of the point of 
observation -- the mtzror plane being the bisector of 
the segment joining point of observation to reference 
object. 
from/pRef 
!eft4='il~'~ right 
bmCk~pot~ s 
ba~//P"" f 
Deft@right 
fr?nt 
B 
There are thus two possible orders of the base axes, as 
shown In A and B. 
I wlll define the core meaning of each projective 
preposition as follows: given a punctual reference 
object (PRef), punctual located object (PLoc), and a 
point of observation, base axes can be constructed 
according to the procedure outlined above: PLoc Is to tie 
left. of PRef iff it is located on the left base axis. 
Analogous d~finitions for the other prepositions are 
easy to formulate. 
A few examples will help understand how these co're 
meanings are manifest in the actual 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 of course assume -- as with the 
objects In tit= examples that follow -- that the stone 
Is aslmilated to a point. 
In to tie ~gkt of tle char, the base axes may be specified as 
those intrinsic to the chair -o I.e. by reference to a 
typical user. The point of observation is then 
coincident with the reference object o- namely the 
chair. Coincidence may be the case when the base axes 
are not Intrinsic to the reference object: for Instance 
on the ri\[M of the sto0/ lay be defined with respect to 
somebody sitting on it, given a round stool with no 
intrinsic front axis. 
Reference object and point of observation are separated 
In the moon ~kind the clou~\[. They can also be separated when 
the base axes are intrinsic to the reference object: 
wlth on t~ ri\[kt side of tle closet, the point of observation Is 
defined by a typical user facing the closet. 
Again, one might define the core meanings differently. 
In .particular one could define the core meaning of "to 
the right" say, as implying location In the whole 
right-hand half-space instead of on the axis. The 
choice adopted here reflects the fact noted In earlier 
examples that the "ideal" realization of to the ngkt is 
with the located object on the right base axis. 
Processes other than the mapping of objects onto points 
may mediate between core meanings and actual conditions 
of use. The reference object amy rotate: where is on t~e 
right nd, r of the ~nting when the painting is tllted7 Tie tree 
to tie ri@kt of tie ro(~ actually means "at sob point of the 
road" -- think of a curving road), end the ~ ~nd tat 
barbed wirefence assumes "integration" along the length of 
the fence (note one cannot say t/~ty to tie ntkt oftkef~ce 
to the Same effect -- that is referring In thls way to 
the whole city. The line of sight Is a favored axis, as 
compared to right, left, and hack axes). 
4. SOME CONCLUS|( .'S 
Here are the main problels and directions of inquiry 
suggested by the examples in this paper. 
One cannot fully explain the use of a locative 
predication in a given situation in terms of the core 
meanings together with some inferences from general 
principles involving object knowledge, salience, 
relevance, the precision desired, etc. There 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 
phylogenetic level. To sort principled aspects of use 
from arbitrary ones, and to understand exactly where 
such principles operate, one must of course first 
establish their existence and nature. 
In terms of knowledge of the physical world, I believe 
one importan~ step. toward adequate representations is 
to put the experiencer back into the picture. That is, 
It is not enough -- or even always necessary -- to know 
where what objects are; one must also consider how much 
fits into one field of view, how things "appear" as 
opposed, to how they "are", how this changes with 
viewing distance, visibility, obstruction, etc. 
General principles of salience should ue studied: how 
some object parts or relations are selected as most 
important -- either in all imaginable contexts, or in 
some contexts. Salience underlies many Instances of 
metonymy (in at t~e front of tAe t~atre, "theatre" actually 
refers to the part occupied by the audience). 
Many'questions revolve around the issue of "relevance" 
-- of "what matters, to whom, in what circumstances" 
rather than the traditional concern with what is true. 
All existing artificial Intelligence programs have 
ignored this problem by using a limited vocabulary In a 
limited domain, so that the question of selecting 
relevant utterances never arises. 
Relevance is linked to the speaker's purpose, as uny 
of the contextual factors described in this paper -- 
indeterminacy, Gricean inferences, highlighting of 
background elements, determination of the Figure/Ground 
relationship, etc. The set of "expressible" 8oals is 
constrained by the "potential" of the language, i.e. by 
a semantic system with finitely many options. One can 
only want to say what can be said, and said in a 
reasonable amount of time. Clearly, "planning" for 
natural language processing is a very Important 
problem. 
Purpose however, will not explain everything one says. 
Simple associative mechanisms must sometimes be 
responsible for what one says. For instance, some 
background element may be highlighted -- provided Some 
linguistic means to do so exists -- only because some 
passive associative link has brought it to attention. 
Once general principles are better understood, It Is an 
open question whether they are used by speakers, or 
whether their explanatory power Is at the phyiogenettc 
level (and will thus be only Implicit in the structure 
of the knowledge representation). For instance, 
although there is a general princiole that the located 
object should be more mobile than the reference object, 
production may not proceed by inferences from this 
general principle together with scenarios Involving the 
two objects. The linguistic expression (or pattern for 
expressions) may be attached to some representation of 
a "situation type" involving the two objects (or two 
superordinate objects). And although "at" generally 
implies the closest reasonable relationship between two 
objects, such a definition may never be used by a 
speaker -- or used only In the creation or 
understanding of 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 different things: the latter depends on 
the constructer's goals, which should be subjected to 
some scrutiny. 
A computational treatment of the use of prepositions 
will require much greater sophistication than naive 
representation theory would lead us to expect. 
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Boggess, Lois C. 1979. Computational interpretation of 
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Illinois, Urbana. 
Denofsky, Murray E. 1976. How near is near: a near 
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, 1979. Innocence: a second idealization for 
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