Specification in terms of interactional properties as a way to optimize
the representation of spatial expressions
Viktor Pekar
Bashkir State University
Okt.Revolutsii 3a
450000 Ufa, Russia
vpekar@ufanet.ru
Abstract
The results of the study demonstrate
that numerous object-specific
restrictions on the use of projective
prepositions in English and Russian are
predicted by their interactional
(functional) semantic properties.
Object-independent perceptual
properties (such as distance between
objects, direction of their motion, etc)
that seemingly guide the use of the
expressions, are also found to be
presupposed by their interactional
properties. Based on these findings, it
is suggested that in addition to a basic
geometrical specification, the semantic
representation should contain
functional information. A
computational procedure of matching
an expression with a spatial scene
should thus include detection of the
interactional properties of the scene.
They can be determined through (1)
retrieval of information about
interactional properties of specific
objects and (2) determining
functionally relevant object-
independent perceptual properties of
the scene.
1 Introduction
By now a number of computational models of
spatial semantics have been developed, which
aim to generate spatial references (e.g. Gapp,
1994; Logan and Sadler, 1996; Regier, 1996). In
these models, spatial meaning is represented in
terms of geometric constructs such as shapes,
center of mass, distance, overlapping between
shapes, etc. The models are able to appropriately
match an expression with a novel spatial
arrangement of shapes. However, the great
disparity of real-world scenes a spatial
expression can refer to presents a serious
problem for this approach. There seems to be a
virtually illimitable number of object- and even
situation-specific restrictions on the usage of a
particular expression (Herskovits, 1986).
Consider, for example, the preposition in, the
meaning of which is often represented in terms of
the mathematical notion "inclusion". A scene
where an overturned bowl is placed over a potato
cannot be described by in (*the potato in the
bowl), even though the potato is within the
physical boundaries of the bowl. The spatial
relation must be described by under: the potato is
under the bowl. Hence, the lexical entry for in has
to contain a comment that the preposition is not
used when the Ground is a concave object
positioned with its concavity opening
downwards. On the other hand, a bulb, being
within the boundaries of a socket, which
concavity does open downwards, is said to be in
the socket, but not under it. This, in its turn, has
to be registered in the lexical entry as well.
Taking into account the fact that the restrictions
are imposed on specific orientation of specific
objects, such comments in semantic
representations should proliferate infinitely.
In a number of lexical semantics studies
(Miller and Johnson-Laird, 1976; Herskovits,
1986; Cuyckens, 1993; Coventry, 1998; Malyar
and Seliverstova, 1998), these restrictions are
accounted by the fact that spatial meaning
reflects not only perceptual experience of the
referent scenes, but also their interactional
(functional) conceptualization. For example,
Miller and Johnson-Laird (1976) argue that the
usage of the English preposition at cannot be
predicted by such notions as "contiguity" or
"juxtaposition". There are situations, where
these types of relations hold, but the preposition
cannot be used: *The chair is at the ocean liner.
*Bill is at Australia. To define the meaning of
at, they introduce the notion "region" of an
object x
1
 � a portion of space "where x can
interact with y socially, physically, or in
whatever way x�s conventionally interact with
y�s". The notion of  "interaction" explains
inappropriateness of at in the two sentences: a
chair and an ocean liner, as well as a person and
a big body of land normally do not interact with
each other.
However, it remains unclear how the
perceptual and functional properties relate to
each other. Malyar and Seliverstova (1998) for
some English and Russian prepositions propose
that function is a factor complementing
geometry in predicting the usage: in those uses,
where the available geometrical semantic
information does not correctly indicate the
Figure's position, it is delineated by the notion
"function" of the Ground. Cuyckens' (1993)
analysis of the Dutch in similarly suggests that
in most cases its meaning can be represented by
geometric constructs like "three-dimensional",
"porous", "bounded", etc; and in cases, where
geometric specification fails to explain the
usage, the notion "function" is employed
(notably for the case with the overturned bowl
and potato). This solution, however, seems
counter-intuitive: it requires that some portion of
uses is determined by geometry and some by
function and thus the meaning representation
still has to explicitly encode specific cases,
where geometrical description is inappropriate.
From the computational perspective, this
representation is also hardly plausible.
                                                          
1
 Miller and Johnson-Laird (1976) use �x� to refer to the
object denoted by the left argument of the preposition and
�y� for the object denoted by the right argument of the
preposition. In the present paper to designate these entities
the terms �Figure� and �Ground�, respectively, will be used.
 The present study attempts to verify the
hypothesis that a functional property of a
preposition presupposes its different perceptual
properties. If the hypothesis is verified, the
finding will explain why numerous perceptually
diverse uses of a preposition fall under one
linguistic category. The meaning of a
preposition could then be specified in terms of
function while omitting the many restrictions
necessary in a geometry-based semantic
representation.
The paper focuses on projective prepositions
� the English above and over and the Russian
впереди and перед
2
. Projective prepositions
present an interesting subject matter in the
context of study of spatial reference. Coventry�s
(1998) analysis of a number of synonymic pairs
of English projective prepositions (including
above and over) demonstrated that function
plays a significant role in their semantics. The
present study is to check if the usage of the
Russian prepositions is also influenced by
function. Comparison between semantics of the
vertical and frontal prepositions may reveal
certain cross-domain regularities of correlation
between perceptual and functional semantic
properties.
2 Methodology
The first stage of the study was concerned with
formulation of hypotheses about particular
character of perceptual and functional properties
of the prepositions. For this purpose examples of
the authentic usage of the prepositions in
electronic corpora (the Brown corpus, the
Lancaster-Oslo-Bergen corpus, the British
National Corpus, the Times (March 1995)) were
collected. The corpus data were supplemented
by usage examples found in literary English and
Russian texts. This stage revealed important
distributional characteristics of the prepositions.
For example, it was found that over very rarely
combines with verbs denoting an upward
motion, such as rise, raise, lift, heave, soar,
while above often does. Hypotheses about a
given preposition were formulated in terms of
properties of referent scenes that tend to be
described by this preposition. The hypotheses
                                                          
2
 The both prepositions denote the Figure's position on the
frontal axis of the Ground.
were tested in experiments with native speaking
subjects.
During the experiments subjects' judgements
about appropriateness of the use of the
prepositions in selected contexts were obtained.
The methodology is based on the assumption
that an expression is judged to be semantically
acceptable in a context, if this context possesses
semantic features that are either the same as
those of the expression or do not contradict
them; the expression is unacceptable, if the
context contains semantic properties,
contradicting those of the expression. Thus,
presence of a semantic property in the meaning
of a preposition was verified in the following
manner. In the context, which possessed the
examined semantic property, first one and then
the other of the contrasted prepositions were
placed. If there was a statistically significant
difference in distribution between subjects'
evaluations of the two sentences, presence of the
property in the semantics of a preposition was
taken to be verified. The use of linguistic data in
the experiments is particularly suited for the
purposes of the study, because it allows for
dealing with non-perceptual semantic properties,
as opposed to obtaining linguistic responses to
purely perceptual stimuli, e.g. pictures of
geometric shapes.
23 English-speaking subjects participated in
the experiments. They represented the American
and British varieties of English (20 and 3
subjects, respectively). Their age ranged
between 25 and 60. All of them were college
graduates. As Russian-speaking subjects, 45
graduate and undergraduate students of the
English Language Department of Bashkir State
University (Ufa, Russia) were recruited, their age
ranging between 18 and 30.
During the experiment the subjects were
presented with questionnaires, each containing
about 30 pairs of identical sentences, which
differed only in the prepositions used. The
sentences used were edited authentic examples
of the use of the prepositions. The subjects were
instructed to evaluate appropriateness of the use
of the prepositions in the sentences according to
a 5-degree scale. In case they perceived a
sentence as ambiguous, they were asked to point
it out and leave it unevaluated.
The difference between the pairs of sentences
thus formed was analyzed in terms of the
Student t criterion and the chi-square criterion.
The difference in evaluations between the
sentences (and hence between the semantics of
the prepositions) was taken to be established, if
the α value was smaller than 0.05. In the
following discussion, paired sentences with
α<0.05 are used as examples, with the
preposition having smaller mean of evaluations
marked by an asterisk.
3 Perceptual Properties
The section describes the revealed perceptual
semantic properties of the four prepositions,
which do not depend on specific objects and
namely those properties which pertain to motion
of the Figure, distance between the Figure and
the Ground and choice of reference frame
3
. The
usage of over and перед, one the one hand, and
above and впереди, on the other, was found to
be sensitive to largely the same perceptual
properties of referent scenes.
3.1 Choice of Reference Frame
The prepositions впереди and above were found
to be used when the position of the Figure is
described in the egocentric reference frame:
(1) Впереди стола стоит стул. �There is a stool
ahead of the table.�
(2) The roof of my school could be seen above
(*over) those trees.
Example 1 implies that the stool and the table
are located on the frontal axis of the observer,
the table being closer to the observer than the
stool (Figure1) (compare: Перед столом
стоит стул. �There is a stool in front of the
table.� which does not imply the presence of the
observer). In 2 the position of the Figure roof
relative to the Ground trees is described
simultaneously in the absolute reference frame
(relative to the gravity axis) and the egocentric
reference frame: the roof is not directly over the
trees; the roof and the trees are vertically co-
related only from the point of view of the
                                                          
3
 Strictly speaking, reference frame is not a perceptual
property of a scene, but a strategy of organizing the
perceptual input. For our purposes, it is important that
descriptions in different reference frames invoke different
percepts. For example, John is to the left of Mary in the
egocentric reference frame denotes different spatial
relations than the same sentence in the intrinsic reference
frame.
observer, whose position is implied � it is on
one horizontal line with positions of the trees
and the school (Figure2).
Figure 1. Egocentric reference frame in the
usage of впереди in (1).
Figure 2. Egocentric reference frame in the
usage of above in (2).
The prepositions перед and over are used
when the position of the Figure is described in
the intrinsic reference frame:
(3) Почтальон перед почтовым ящиком. �The
postman is in front of the mailbox.�
(4) He held the hammer over the nail.
In 3 the position of the postman is defined
relative to the frontal axis of the mailbox; the
position of the observer is not implied � he or
she can in principle be viewing the scene from
any point (Figure 3). In 4 the position of the
hammer is defined relative to the gravity axis
and the vertical axis of the nail, also irrespective
of the observer�s position (Figure 4).
Figure 3. Intrinsic reference frame in the
usage of перед in (3).
Figure 4. Intrinsic reference frame in the
usage of over in (4).
3.2 Motion of the Figure
The preposition over is found to be used to
denote Goal (i.e. the end-point of a trajectory) of
a downward motion of the Figure toward the
Ground (5). It can also denote Source (i.e. the
starting point of a trajectory) of an upward
motion of the Figure away from the Ground (6):
(5) He pulled his cap down over (*above) his eyes.
(6) The executioner removed his sword from over
(*above) Peter�s head.
The preposition above, on the contrary, is
used to denote Goal of an upward motion of the
Figure away from the Ground (7) and Source of a
downward motion of the Figure toward the
Ground (8):
(7) He raised his cap above (*over) his eyes.
(8) A meteorite falling from above (*over) us.
In Russian to denote Goals and Sources of
the Figure�s motion on a horizontal plane the
prepositions к (Goal of motion toward the
Ground), от (Source of motion away from the
Ground), вперед (Goal of motion away from the
Ground) and спереди (Source of motion toward
the Ground) are used. However, the prepositions
перед and впереди have different degrees of
acceptability when different Paths (i.e.
trajectories) of the Figure�s motion along the
Ground�s frontal axis are in question. The
preposition перед is preferred, when motion is
toward the Ground (9) and впереди when
motion is away from the Ground (10):
(9) Из-за угла прямо на него вылетела машина и
остановилась только перед ним (*затормозила
только впереди него). �A car raced from around the
corner and stopped just in front of him.�
(10) Впереди меня лыжники стали быстро
удаляться (*удаляться передо мной). �The skiers
ahead of me started to quickly enlarge the gap.�
Thus, перед, like over, emphasizes Goal of
the Figure�s approaching the Ground, while
впереди, like above, emphasizes Goal of the
Figure�s departing from the Ground.
3.3 Distance between the Figure and the
Ground
The prepositions впереди and above are used
when distance between the Figure and the
Ground is conceptualized as great.
(11) Дерево, стоящее далеко впереди нас (*далеко
перед нами). �A tree standing far ahead of us.�
(12) Keep the grill high enough above (*over) the fire!
The prepositions can be used when between
the Figure and the Ground there are some other
objects of a size, comparable to that of the
spatially co-related objects.
(13) He lives three floors above me (*three floors
over me).
(14) Он встал в очередь и заметил, что через три
человека впереди него стоял Владимир (*через
три человека перед ним). �He took a place in the
line and saw Vladimir standing three people ahead of
him.�
Presumably the presence of such objects
between the Figure and the Ground motivates
conceptualization of distance / remoteness
between them. Of conceptualization of distance
between the Figure and the Ground in
occurrences of above and впереди also speaks
the fact that these prepositions, unlike their
synonyms, are used when degree of remoteness
of one object from the other is specified. These
are those cases when the prepositions are
combined with words and phrases like one inch,
several feet, five hundred meters, slightly, a little
(15 and 16)
4
, etc.
(15) She stuck the rose in her hair a little above the
left ear (*a little over the left ear).
(16) Чуть впереди Алексея бежал Владимир
(*чуть перед). �Vladimir was running a little ahead
of Aleksey.�
The prepositions перед and over are used
when the distance between the Figure and the
Ground is not conceptualized at all:
                                                          
4
 It is of interest to note that above and впереди can
combine with words like slightly or a little, but not with
very, too, considerably, quite: *quite above, *довольно
впереди.
(17) Перед ним лицом к лицу стоял Владимир
(*Впереди него лицом к лицу). �In front of him
face to face stood Vladimir.�
(18) His cap was low over (*above) his eyes.
That the prepositions are used when distance
is negligible is also seen from the fact that they
are inappropriate in cases when there are some
other sizeable objects between the Figure and
the Ground (13-14) or when degree of
remoteness is emphasized (15-16).
The prepositions over and перед are also
used to denote the point where the Figure is
traversing a projective axis of the Ground,
typically at such a distance from it, that
conceptualized as negligibly small and also not
excluding a contact between the objects
5
.
(19) Ребенок перебежал дорогу прямо перед
грузовиком (*� перебежал дорогу прямо впереди
грузовика.) �The child dashed across the street right
in front of a truck.�
(20) The ball flew over the fence. (*The ball flew
above the fence.)
Their synonyms cannot denote this point on a
projective axis of the Ground: впереди is
unacceptable in 19 and above in 20 conveys
information of the Figure�s moving along a
projective axis of the Ground away from it.
4 Functional Properties
The study revealed that both the Russian and the
English prepositions possess functional semantic
properties, and namely their meaning is
characterized by information about certain
interaction, currently taking place or anticipated,
between the spatially co-related objects. The
prepositions перед and over convey information
about functional interdependence between the
objects, whereas the prepositions впереди and
above � of functional separation or
independence of the objects.
The first type of functional information is
physical interaction between the Figure and the
Ground, which is taking place at the moment in
question. The result of this interaction is usually
change of some physical (integrity, temperature,
etc) or interactional (visibility, possibility to
manipulate, etc) characteristic of one of the
objects. One of the objects � which may be both
                                                          
5
 Such uses of over can be considered boundary cases
between the �above� and �across� senses of the preposition.
the Figure and the Ground � is seen as a source
of influence or an agent of an action directed at
its counterpart. Animate objects can act in the
role of the influencing object, as well as those
inanimate objects that are able to disperse light,
heat, etc or used as instruments:
(21) She bent over (*above) the puppies to see them
better.
(22) Мы грелись, стоя перед (*впереди) плитой. �We
were keeping warm standing in front of the stove.�
(23) Footsteps thumping heavily above (*over) the
boys.
(24) Впереди него ежеминутно разрывались
бомбы (*Перед ним ежеминутно разрывались
бомбы). �Bombs were constantly exploding ahead of
him.�
In 21 and 22 there are functional relations
between the objects. In 21 the Figure she is
directing the action of inspecting at the Ground
puppies. Note that here not a simple act of
perceptually spotting an object is implied, but an
active examination of it. In 22 the Figure мы
�we� experiences influence exerted by the
Ground плита �stove�. In 23 and 24 the objects
are functionally disjunct. In 23 the action of the
Figure footsteps does not effect the Ground the
boys, if above is used; and does so, if over is
replaced for above. In 24 the process
разрывались бомбы �exploding� is understood
as not effecting the Figure него �him�, cf. Он
был убит разорвавшейся перед ним бомбой.
�He was killed by a bomb that exploded in front
of him.�
Second, the prepositions can describe such
functional relations, whereby one object is
conceptualized as protecting the other one from
influence from without the functional unity:
(25) He carefully held his hat over (*above) the
candle to protect it from the rain.
(26) The fog over (*above) the river prevented
detection from airplanes.
(27) Скрывая лицо от фотокамер, он держал
папку перед собой (*впереди себя). �Trying to
conceal himself from the cameras he held his file in
front of his face.�
(28) Перед оратором держали пуленепро-
биваемое стекло (*впереди оратора). �A
bulletproof shield was held in front of the speaker.�
Third, the relations between objects can be
conceptualized in such a manner that one object
is seen as having a potential to establish an
influence over the other one; at the moment in
question, however, no influence is exerted. To
describe this type of relations the term
�functional potential� will be used, which was
introduced by Miller and Johnson-Laird (1976)
to designate a similar interactional property of
artifacts.
(29) Trying to threaten Peter, the executioner held his
sword over (*above) his head.
(30) A black stormy cloud over (*above) the farm.
(31) Перед ним поставили тарелку, подождав
немного, он взял ложку и начал есть (*Впереди
него поставили тарелку). �A plate was placed in
front of him, he waited a little, then took the spoon
and started to eat.�
(32) На моем рабочем столе передо мной лежит
письмо (*впереди меня). �There is a letter on my
desk, right in front of me.�
To sum up, the prepositions over and перед
are found to convey information of three
identical types of functional relations between
the Figure and the Ground: actual physical
interaction, protection, functional potential; the
prepositions above and впереди convey
information of absence / impossibility to
establish such functional relations. As is clear,
the functional properties presuppose perceptual
properties that are specific for particular objects.
5 Correlation between Functional and
Perceptual Properties
The study revealed that each of the three types
of the object-independent perceptual properties
of each of the prepositions can be present in one
referent scene simultaneously together with the
functional property of this preposition, but not
with the one contradicting it. This regularity is
established from subjects� acceptability
judgements of sentences where information
about either presence or absence of functional
relations is added to information about a
particular object-independent perceptual
property.
The study replicated results of Carlson-
Radvansky and Irwin (1993), who demonstrated
correlation between presence of functional
relations and choice of the intrinsic reference
frame, on the one hand, and between absence of
functional relations and choice of the egocentric
reference frame, on the other. For example, in 3,
where, as it was shown, choice of the intrinsic
reference frame necessitates the use of перед,
the postman�s position is such that allows
functional interaction between him and the
mailbox (the postman may be taking mail out of
the mailbox). If it is manifestly shown that the
postman cannot interact with the mailbox,
впереди (or some other preposition like около
�near�) is preferred to перед:
(37) Почтальон стоял впереди / около почтового
ящика, разговаривая с дворником. (*Почтальон
стоял перед почтовым ящиком, разговаривая с
дворником.) �The postman was standing ahead of /
near the mailbox, talking to a roadsweeper.�
In 4, where the intrinsic reference frame is
also chosen, the position of the hammer is such
that allows its functional interaction with the
nail. Both in 3 and 4 the Figures (the postman
and the hammer) and the Grounds (the mailbox
and the nail) are conceptualized as facing each
other by their functionally relevant sides.
In uses of впереди and above, absence of
functional relations between the Figure and the
Ground can combine with choice of the
egocentric reference frame. In 1 the stool and
the table do not necessarily face each other by
their functional sides, the two objects do not
have to constitute a functional unity. For
example, the stool may be at such a distance
away from the table that a person seated on it
cannot interact with the table. The co-position of
the trees and the roof described in 2 does not
allow any sort of interaction between them.
The Figure�s approaching the Ground (38a)
and an insignificantly small distance between
the two objects (39a) are found to correlate with
the emergence and the presence of functional
relations between them, correspondingly.
(38a) He pulled his lamp down over his sheets to see
the scheme better.
(38b) *He pulled his lamp down over his sheets so
that it does not obstruct the view.
(39a) The helicopter was hovering low over the boat
to save the crew.
(39b) *The helicopter was hovering low over the
boat in order not to be detected.
The Figure�s departing from (40a) and a big
distance between the two objects (41a) correlate
with discontinuation and absence of functional
relations between them.
(40a) To let the sun rays play on his face he pulled
his cap up above his eyes.
(40b) *To conceal his face from the sunrays, he
pulled his cap up above his eyes.
(41a) She sat on a branch high above the lions so that
they could not get at her.
(41b) *She sat on a branch high above the lions and
fed them.
Examples 38b, 39b, 40b and 41b show that
the opposite is not possible. In a given scene,
perceptual properties, corresponding to those of
a given preposition, cannot combine with the
functional properties that contradict those of this
preposition. As is easily seen, this regularity is
not just a peculiarity of the prepositions, but
rather a matter of common sense. Removing the
prepositions and expressing the idea in any other
words cannot make the sentences semantically
well-formed: *The helicopter was hovering low
in order not to be detected from the boat. *She
sat high on a tree branch and fed the lions. It
can be expected that other prepositions, which
possess the same functional properties, also
possess corresponding perceptual properties.
From the correspondences between the
object-independent perceptual properties of a
preposition and its functional property, one can
conclude that the two types of semantic
properties presuppose each other. The
perceptual properties can be said to be
functionally relevant, that is, perceiving these
properties, the observer forms an idea about the
functional aspect of the scene. For example, one
object�s approaching some other one
automatically triggers conceptualization of a
possibility that the former influences the latter.
6 Conclusion
The English vertical above and over and the
Russian frontal перед and впереди are found to
possess similar object-independent perceptual
properties, which pertain to motion, distance,
and choice of the reference frame. All the four
prepositions are also found to have similar
functional properties � their usage is sensitive to
(1) interaction between the Figure and the
Ground that is currently taking place; (2) the
Figure�s preventing the Ground from being
physically influenced (�protection�); (3)
potential interaction between the objects
(�functional potential�). Conceptualization of
interaction in these cases hinges on experiential
knowledge about functionality of specific
objects. For example, a human is usually
conceptualized as (potentially) acting upon an
object, located near him/her. The fact that
specific objects are perceptually different, but
have the same functional status, explains object-
specific restrictions necessary in a geometry-
based semantic specification.
The object-independent perceptual properties
of referent scenes that determine the usage of
the prepositions are found to be functionally
relevant, i.e. by perceiving these properties the
observer is able to form an idea about the
functional aspect of the scene. That is why
functional relations are conceptualized even in
those cases when the spatially correlated objects
do not have any inherent function (i.e. "natural
kind objects" like clouds, fog, or rocks). These
are such cases when, for example, small distance
triggers off conceptualization of potential
interaction between objects, or great distance -
impossibility of interaction.
Thus, the object-specific and object-
independent perceptual properties of each of the
four prepositions are presupposed by its
functional property. The established correlation
between the perceptual and functional properties
allows not to keep geometry and function
distinct in the lexical entries, and thus to avoid
the necessity to explicitly specify cases that are
determined by geometry and cases that are
determined by function. On this account, an
optimal semantic representation will include
only functional semantic properties and
information about the particular projective axis
on which the Figure is located.
Based on these findings, a computationally
plausible procedure of matching a preposition
with a referent scene may be proposed. The
procedure should include detection of the
functional properties of the scene. They can be
determined through (1) retrieval of interactional
information about specific objects, e.g. their
functionally relevant sides; (2) functionally
relevant object-independent perceptual
properties of the scene, e.g. distance between
objects, direction of their motion, etc. After that
the scene is described by that preposition that
possesses the corresponding functional semantic
property.
The conducted study, however, does not
allow one to think that meanings of the vertical
and the frontal prepositions are entirely
identical. The frontal prepositions впереди and
перед, unlike the vertical prepositions above and
over, cannot denote Goal and Source of the
Figure�s motion: there are special prepositions
to denote these entities. Nonetheless, such cases
are not numerous and can be presented as
exceptions in the lexical entries without making
the semantic representation too bulky and
unmanageable.

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