Towards Invariant Meanings of Spatial Prepositions and Preverbs
1
Jean-Pierre Desclés
Paris-Sorbonne
LaLIC
96, bd. Raspail
75006 Paris, France
Jean-
Pierre.Descles@paris4
.sorbone.fr
Ewa Gwiazdecka
2
Paris-Sorbonne
LaLIC
96, bd. Raspail
75006 Paris, France
Ewa.Gwiazdecka@paris4.
sorbonne.fr
Azucena Montes-Rendon
3
Paris-Sorbonne
LaLIC
96, bd. Raspail
75006 Paris, France
Azucena.Montes-
Rendon@paris4.sorbonne
.fr
                                                          
1
 The research was granted by Projet Cognitique "Espaces, langues et cognition" Ministère de la Recherche, Paris, France.
2
 Granted by the scholarship of French Government.
3
 Granted by ANUIES-SUPERA, Mexican Government.
Abstract
This work presents the semantical
analysis of the two spatial prepositions
and associated prefixes, the French
sur, sur- (on) and the Polish przez,
prze- (across). We propose a theory of
abstract places (loci), as a method of
description which helps to build an
invariant meanings of the two
linguistics units.
1 Introduction
Natural languages encode spatial and temporal
representations in many various ways (deictics,
prepositions, verbal lexicon and preverb). This
article presents analyses of the two prepositions
and associated preverbs, the French sur, sur- (on)
and the Polish przez, prze- (across). We are
particularly interested in the way the preposition
and preverb determine a place.
It is interesting to note that from a diacronical
view point (Bally, Meillet, Witkowska-
Gutkowska) spatial prepositions become
preverbs. Two problems arise : Is the meaning of
the preverb composed with the meaning of
lexical predicate? Does the meaning of the
preverb have a prepositional origin? It is
however impossible to present in this short
article the results of our analysis; we show only
the methods by means of two mentioned
examples. We note that the work on other
prepositions and preverbs in French, Polish and
Spanish are in progress.
Many linguists (Benett, Culioli, Pottier,
Talmy…) have recognized the necessity of
quasi-topological analysis for studying space
encoded by languages. However, it seems to us
that the elementary topology as defined for
mathematical analysis, does not capture exactly
the linguistic problems in an adequated way. For
instance, the idea of boundary as expressed by
languages does not always refer to a point or
limit. On the other hand, the understanding of a
place cannot be reduced to the spatial notion.
Indeed, from the cognitive point of view, natural
languages use more abstract notion while
referring to the place. Thus, we represent spatial
place but also temporal and notional as, for
instance, in Pottier's approach (Pottier:1992).
We propose a theory of abstract places called
"Abstract Loci Theory". This theory uses
operators like in Kuratowski's algebra for
elementary topology (Engelking: 1989).
However, in this article, the operators of
interiority, exteriority, closure and boundary are
defined with new properties such that we obtain
a "quasi-topological" structure: the interiority
and exteriority operators are not idempotent and
the interiority of the boundary is not always
empty. We note respectively INT, EXT, FRO,
FER, the new operators of interiority, exteriority,
boundary and closure in this Abstract Loci
Theory. We propose to give an informal
approach to the main aspects of this theory as it
is in progress.
The notion locus refers to abstract place ( spatial
or temporal or notional). Let ℜ be a referential
domain and let the locus LOC be a part of ℜ.
This locus LOC builds a partition of ℜ
composed of three parts (see figure 1):
INT (LOC): interior locus of LOC;
EXT(LOC): exterior locus of LOC;
FRO(LOC): boundary locus of LOC between
EXT(LOC) and INT (LOC).
The interior locus of LOC in Abstract Loci
Theory has the following properties:
INT(INT (LOC)) ⊆ INT (LOC) ⊆ LOC
If LOC
1 
⊆ LOC
2
 then INT (LOC
1
) ⊆ INT(LOC
2
)
∀ LOC, INT(LOC) ≠ ∅
The exterior locus of LOC is such that it is
included in the complement of LOC.
The closure locus of LOC is defined as:
FER(LOC) = INT(LOC) ∪ FRO(LOC)
with the following property:
FER(FER (LOC)) ⊇ FER (LOC) ⊇ LOC
Inside FRO(LOC) we distinguish two other loci,
internal boundary and external boundary, such
that : FRO-int(LOC) = LOC \ INT(LOC)
FRO-ext(LOC) = FER(LOC) \ LOC
The boundary locus is then defined as:
FRO(LOC) = FRO-int(LOC) ∪ FRO-ext(LOC)
We introduce the "anchoring relation" (French:
repérage) between the "anchored entity" (repéré)
and the "anchor entity" (repère). This relation is
in general non-symmetric (Desclés, Froidevaux:
1982, Culioli: 1990). The analysis of the
meaning of the preposition is done by means of
Abstract Loci Theory and anchoring relation,
where the preposition determines an anchor
(Flageul: 1997, Desclés: 1998a).
Our hypothesis is that it is possible to exhibit an
invariant meaning in abductive process. We
understand this invariant as cognitive
representation which does not occur in natural
languages (Desclés and alii: 1998).
We consider the syntactical compositionality as
an application of verbal prefix to verbal predicate
in order to build a complex predicate (e.g. sur-
applies to veiller for building a complex
predicate surveiller) (Desclés: 1998a). However,
on the representational level, the
compositionality between the meaning of the
preverb and that of the verb forms a new
semantical construct; the result that cannot be
described by a simple function, but is rather
conceived as complex interaction between
semantical units.
2 Sur and Sur- in French
2.1 The French preposition sur (on)
Let us analyze the prepositional examples by
means of the above explained method. In the
example below:
(1) Le livre est sur la table
The book is on the table
the preposition sur expresses the position of the
entity the_book (anchored) to the surface of
the_table (anchor) according to the high-low
gradient (gravity) which is orthogonal to the
INT(LOC)
EXT(LOC)
FRO-int (LOC)
FRO-ext (LOC)
FRO (LOC)
LOC
ℜ
Figure 1
anchor. There is a contact between these entities.
The preposition sur indicates the external
boundary locus- FRO-ext (the_table) of
anchoring.
(2) L’affiche est sur le mur
The poster is on the wall
(3) La mouche est sur le plafond
The fly is on the ceiling
The preposition sur in (2) indicates the anchoring
relation between the_poster (anchored) and in (3)
FRO_ext of the_wall (anchor), the_fly and
FRO_ext of the_ceiling. There is contact in these
examples. The gradient is determined by some
other kind of force, which is not gravity.
(4) Les ponts sur la Moselle
The bridges on the Moselle river
We can analyze the preposition sur in (4) like in
(1) that is, we have the anchoring relation to
FRO_ext of the_river according to the high-low
gradient, without contact.
(5) Luc appuie sur une touche du piano
Luc presses a key of the piano
Luc controls the action considered as an oriented
movement establishing a contact between
his_hand and the FRO_ext of the piano_key The
gradient is determined by the action expressed
through the verb appuyer (to press).
(6) Le regard de Jean tombe sur sa fille
The glance of Jean falls on his daughter
Jean controls the oriented movement of his
glance. This movement is directed to the external
boundary locus of the visibility determined
around his_daughter. Hence a gradient is
determined by the orientation of the movement
of his glance.
(7) Je l’attends sur les onze heures
I’m waiting for him around eleven o’clock
This is a temporal example where eleven_o’clock
is an interval considered as anchor. The global
vision of this temporal locus explains the
meaning of the preposition sur, glossed as:
“being over (FRO_ext) the locus
around_eleven_o’clock”.
We can describe the invariant meaning of the
preposition sur as anchoring relation of an entity
to the external boundary locus, FRO_ext(LOC),
according to an orthogonal gradient. We note
that the contact between the entities is not
necessary.
2.2 The French Preverb sur-
The same analysis as for preposition is applied to
the preverb sur-.
(8) L’avion survole Paris
-> The plane flies over Paris
The complex predicate survoler (to overfly) in
(8) provides two pieces of information: one is
related to the verb voler (to fly) and the other, to
the preverb sur-. This preverb indicates that the
position of movement of the_plane is localized
to the FRO_ext of Paris, according to the high-
low gradient. There is no contact.
(9) Pierre surélève la table
-> Pierre raises the table over something
In this example, the preverb sur- indicates that
the_table is put on the external boundary of a
higher place (FRO_ext).
(10) La lanterne surmonte la porte
-> The lantern is over the door
In (10), the glance of any observer starts from the
low part of the_door and rises up, to visualize
the_lantern which is on the FRO-ext of the
superior part of the_door. Here, we have to do
with static description.
(11) Le magasin surbaisse les prix des vêtements
-> The shop lowers the prices beyond a threshold
The preverb sur- in (11) indicates that the action
expressed by the verb baisser (to lower) is
realized beyond the established threshold, that is,
the verb is realized on the external boundary
locus (FRO-ext of_threshold), the notional locus
being organized by the prices.
(12) Emilie suralimente son bébé
-> Emilie feeds her baby over the threshold
In (12), the process indicated by the
accumulative verb alimenter (to feed) continues
 towards a boundary of accomplishment, this
boundary being beyond a threshold (correct
feeding of a baby). The preverb sur- indicates
that the boundary is "above" the threshold.
Consequently, the process goes over this
threshold.
(13) Luc surmonte ses problèmes
-> Luc overcomes his problems
We analyze the meaning of (13) as follows: Luc
is anchored to the abstract locus (the activity
"being affected by problems"). The verb monter
(to rise up) is used to show that Luc becomes less
and less affected by his_problems, until he
becomes completely unaffected.
The spatial use of the preverb sur-, is oriented
according to the high-low gradient (gravity)
(8,9,10) and the position above the external
boundary of an anchor. In the other cases
(11,12,13), the preverb sur- indicates a position
above the external boundary of locus, organized
according to some gradient. The cognitive
representation (see figure 2) shows the net
meaning of preposition sur and preverb sur-, as
well as the common invariant meaning of them.
3. Przez and Prze- in Polish
3.1 Polish Preposition przez (across)
The preposition przez in the example below
expresses the idea of crossing the locus:
(14) Sekwana płynie przez Paryż
Seine to flow across Paris
The Seine flows through Paris
Parts of river pass through the locus Paris. We
consider in (14) five salient phases of the
passage: at the beginning of the process, the parts
of river are localized to the exterior EXT(LOC),
then to the boundary FRO(LOC), they arrive in
the interior INT(LOC), passing again the
boundary FRO(LOC), and coming out to
EXT(LOC). The double passage through the
boundary locus presupposes an orientation of this
locus, imposed here by the flow of the river.
(15) Słońce zagląda przez okno
sun to come in across window
The sunshine comes in through the window
This example introduces an intermediate locus
IME(LOC) inside the FRO(LOC) with FRO-ext
and FRO-int, considered as locus of
communication between EXT(LOC) and
INT(LOC). The passage implies three salient
phases of the movement. We note that
spatial temporal
spatio-
temporal
contact
no contact (4)
gravity (1) force
(2),  (3)
(7)
action (5) observ. (6)
invariant: orthogonal gradient
to external boundary
spatial
high-low gradient
no spatial
(11)
no contact
(8)
contact
(9)
static (10)
(13)
accumulative
verbs (12)
invariant: orthogonal gradient
to external boundary
movement
threshold
Net of prepositional meaning sur Net of preverbal meaning sur-
Figure 2
IME(LOC) is encoded in natural languages as
the privileged passage (door, window…).
(16) Darek nie przychodził przez cały miesiąc
not to come across whole month
Darek has not come for the whole month
The meaning "crossing a locus" is present in (16)
considering miesiàc (the month) as a locus of
temporal nature. We pass through the boundary
FRO(LOC) through interior INT(LOC) to the
second boundary FRO(LOC), the locus being
temporally oriented.
(17) Przez ciebie zmęczyłam się
across you to get tired
I got tired because of you
We analyze (17) using the intermediate locus
IME(LOC), but on a more abstract level. Let us
consider a domain related to the notion
"tiredness". The exterior EXT(LOC) is related to
"not being tired", while the interior INT(LOC),
to "being tired". To pass from EXT(LOC) into
INT(LOC), we need to cross IME(LOC), which
refers to a notional locus "you". Consequently,
three salient phases are taken into account.
(18) Rozmawiałam z nim  przez  telefon.
to speak with him across phone
I spoke to him over (across) the phone
We need to "cross" an instrument the_phone to
reach another person, thus we also refer to the
intermediate locus IME(LOC) in the domain of
communication.
We have so far discussed the examples taking
into account the meaning of the Polish
preposition przez in regard to the proposed
concepts of the Abstract Loci Theory. We may
now structure those examples. On the one hand,
we distinguish spatio-temporal, temporal and
notional loci, and on the other hand, we have
shown two related representations of the
prepositional meaning: the one refers to crossing
a locus, the other uses an intermediate locus
while crossing. Based on these analyses, we
consider an invariant meaning of the preposition
przez as crossing a boundary locus.
3.2 The Polish Preverb prze-
We will now establish a similar analysis of
preverbal examples prze-, in order to show an
invariant meaning of the complex predicate. To
simplify our study we omit the aspectual
consideration of the preverb, taking into account
only the relationship to the meaning of the
preposition.
(19) Przeszedł przez ulicę
across-to walk across street
He walked across the street
We encounter here "crossing" the locus ulica
(street) expressed by compositionality between
the preverb prze- and the lexical predicate iÊç (to
walk). Five salient phases are considered in (19):
a passage from the exterior EXT(LOC) to the
boundary FRO(LOC), then to the interior
INT(LOC), next to another boundary FRO(LOC)
for going out, to the exterior EXT(LOC). The
locus ulica (street) is temporally oriented.
(20) Przelał wino z beczki do butelki
across-to pour wine  from  barrel to bottle
He poured wine from the barrel into the bottle
The semantic description of (20) appeals to an
intermediate locus IME(LOC), which is not
specified here. The compositionality between
prze- and laç (to pour) means that the entity
(wine) is localized to exterior locus (barrel) and
crosses the intermediate locus IME(LOC) to be
localized to the interior INT(LOC) (the_bottle).
(21) Anna przeczytała książkę
across-to read book
She read the book "across"/ She achieved her reading
The compositionality takes into account not only
the preverb prze- and the predicate czytaç (to
read), but also the object ksià˝ka (the book). The
action of reading is thus simultaneous to
"crossing" the object the_book conceived as a
locus. Thus, we consider three salient phases:
boundary FRO(LOC) (the beginning of the
book), interior INT(LOC) and boundary
FRO(LOC) (the end of the book and the end of
reading, in the sense achievement of this action).
(22) Przemalowała ściany na zielono
across-to paint wall into green
She has repainted the wall in green
The example (22) expresses the property change
affecting an objet. In the domain related to
colors, we consider the first color as an exterior
EXT(LOC). "To reach" the other color,
considered as interior INT(LOC), we need to
cross an unspecified intermediate locus
IME(LOC). Changing the property is oriented in
time.
(23) Matka przekarmiła dziecko
mother across-feed baby
The mother overfed the baby
Some accumulative verbs (to salt, to cook) imply
a change towards a threshold. The prefix prze- in
connection to the predicate karmiç (to feed),
indicates the passage from the exterior
EXT(LOC), to which we associated the meaning
“not enough”, through intermediate locus
IME(LOC). The amount of food in IME(LOC) is
accurate. "Passing" into interior INT(LOC) is
interpreted as “too much”. The amount of food
organizes these locus.
(24) Jan  przegrał wszystkie pieniądze w kasynie
across-toplay all money in casino
"Jan has played across all his money"
Jan has lost all his money in casino
The domain is related here to the game. We
consider the passage from EXT(LOC) (having
enough money) through the intermediate locus
IME(LOC) (still having money) into the interior
INT(LOC) (having no money). The bet organizes
the locus.
We organize now the preverbial examples in the
way we did it for the preposition. We note that
the preverb introduces a dynamic change while
composed with the predicate. This is due to its
perfectivizing role that we do not develop in this
article. The examples (19) to (22), express the
meaning "crossing" a locus or "crossing it
through an intermediate locus". We encounter as
well the explicit idea of going over a threshold
(23 & 24). The invariant meaning for the preverb
composed semantically with a predicate is thus
crossing the boundary locus, the same as in the
prepositional case. Given the analysis of
preposition and the associated preverb, we can
now establish the relation between the nets of
meanings (see figure 3)
3 Conclusion
The analysis of prepositional examples of sur,
led us to establish an invariant meaning, which
corresponds to anchoring to the external
boundary locus with a gradient. The invariant
meaning of the preposition sur corresponds to
the invariant meaning of the preverb sur-.
This result seems more general than the analysis
of C. Vandeloise (Vandeloise: 1985), as the
resemblance family porteur-porté established in
his work does not explain the examples (5)-(7) of
sur. As for the Polish preposition przez and its
associated preverb prze-, we managed to
establish the same invariant meaning for the two
linguistic units: it refers to "crossing the
boundary locus". However, this analysis does not
crossing
the
locus
(14)
crossing
the
locus
(16)
preposition  przez
spatial locus temporal
locus
notional
locus
interme
diate
locus
(15)
intermedia
te locus
(17), (18)
invariant : crossing the boudary
locus
spatial
change
crossing
the
locus:
(19)
interme
diate
locus:
 (20)
invariant : crossing the boudary
locus
prze-(verbe)
object
change
property
change
crossing
the boudary
locus
crossing
the
object:
 (21)
crossing
interme
diate
place:
(22)
going over
threshold
(23),(24)
Net of prepositional meaning przez
Figure 3
Net of preverbal meaning prze-
take into account the aspectual consideration of
the prefix, which in Polish has a perfectivizing
role; the same approach will be used in the
semantical studies of aspect in Polish. Our results
may be compared to the analyses for the
preposition przez and preverb prze- obtained in
the framework of the Langacker's grammar
(Dabrowska: 1996), but the latter does not use
any topological approach.
We claim that the invariant meaning is not
universal across natural languages. Each natural
language organizes its own cognitive
representations (Desclés: 1998b) as it was
shown, for example, by Bowerman (Bowerman:
1996), who compared different meanings of the
preposition across few languages:
apple in bowl, b. handle on pan, c. bandaid on
leg, d. right on finger, e. fly on door.
abcde
Englishin onononon
French dans de sur à sur
Dutch aan op om op aan
If we look now at the following sentences in
English, Spanish, Polish and French:
 (i) The book is on the table
(ii) El libro esta en la mesa
(iii) Książka jest na stole
(iv) Le livre est sur la table
The prepositions on, na, en in these examples are
translated by the French sur. And yet, the
analogues of sur in English, Spanish and Polish
correspond only to a particular meaning of sur,
the value given in (1). The invariant meanings of
on, na, en are always defined within respective
languages.
If we consider the preverbal examples:
(12) Emilie suralimente son bébé
-> Emilie feeds her baby over the threshold
 (23) Matka przekarmiła dziecko
The mother overfed the baby
we notice that the two sentences have the same
state of affairs, but their cognitive construal is
related to each language (French or Polish).
Thus, in (12) the prefix sur- indicates the process
that continues up to the degree situated over the
threshold, while (23) indicates the passage from
“not enough” to “going over the threshold”. This
passage is present in (12), however it is
considered as a secondary effect.
In Fregean words: (12) and (23) have the same
Sinn, but differ in Bedeutung.

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