Contextual processing of locative prepositional phrases

Nicolas DENAND & Monique ROLBERT Laboratoire d’Informatique Fondamentale de Marseille 163, avenue de Luminy - Case 901 F-13288 Marseille Cedex 9 France {Nicolas.Denand,Monique.Rolbert}@lif.univ-mrs.fr

Abstract locative uses is anaphorically linked to a NP. These uses were already studied (see, for exam- This paper deals with contextual aspects of loca- ple, (Ruwet, 1990)). tive preposition processing. Firstly, accordingly to a study on the referential behavior of the pronominal What about locative uses of the pronominal 1 adverb ”y” in its locative uses, we show that static adverb ”y” ? That is, when it is used to replace locative prepositions are functions, not only at the the locative prepositional complement of a verb conceptual level (as shown in previous studies), but (Locative Prepositional Phrase, or LPP), like also from a contextual point of view. Such functions in: introduce new objects in the discourse context, that (3)Cette ville est belle. J’y ai v´ecu autre- have to be taken into account in classical contex- fois.(This town is beautiful. I lived there tual processing tasks, such as reference resolution or formerly.) question answering. Then, we show how these phe- nomena can fit into contextual formalisms like DRT Here again, in a classical way, one can say that and DPL. ”y”/”there” refers to a ”place” introduced by a NP preceding the pronoun. We have a prob- 1 Introduction lem though, to rebuild the exact locative seman- tics of the pronominal sentence (here, something Most often, in a nominal anaphoric relation, a like ”in this town”). The situation gets even personal pronoun (like ”le”(clitic)/”him”) is in- more complicated when the antecedent of the volved in an anaphoric relationship with a nom- pronoun lies itself in a LPP, like in the follow- inal phrase (NP), located in the same sentence ing: as the pronoun or a previous one. The pronoun is therefore related to the discourse individual (4)J’ai pass´emes vacances dans le Gard. J’y referred to by the NP: ai v´ecuautrefois.(I spent my holydays in (1)Un homme est venu ce matin. Paul le the Gard. I lived there formerly.) connaissait.(A man came this morning. In this paper, we show that the pronominal Paul knew him.) adverb ”y” can be anaphorically linked to a In this example, the pronoun ”le”/”him” is LPP, locative preposition included. This leads anaphorically linked to the NP ”un homme”/”a us to the fact that some LPPs introduce indi- man”. The pronoun refers to the discourse en- viduals in the discourse context. We discuss tity introduced by the NP. the functional role played by locative preposi- The antecedent NP can be found in different tions in this process. Finally, we explain how syntactical configurations, without being neces- to account for these contextual functions within sarily related to the case of the pronoun itself. a discourse representation system such as DRT For instance, the personal pronoun ”elle”/”it” and DPL and its integration into processing a (subject) can be in anaphoric relation to a NP, subset of French. itself embedded in a complement (here, loca- tive): 1”y” is usually considered a pronoun for its non loca- (2)J’ai pos´emon portable sur la table parce tive uses (Ce vase est cass´e. N’y touche pas.(This vase qu’elle ´etait propre.(I put my laptop on is broken. Don’t touch it.)) and an adverb elsewhere the table because it was clean.) (Paul y va.(Paul goes there.)). (Grevisse, 1975) notes certain uses in which the status of ”y” is unclear. It is Similarly, the clitic pronoun ”y” in its non- then called ”pronominal adverb”. 2 Locative prepositions are contextual functions If we replace the pronoun with its antecendent, A lot of examples show that ”y”, as a pronom- we have: inal adverb, may have a NP as syntactical an- (10)Va chercher pr`esde la table, je crois que tecedent: ton ballon se trouve pr`esde la table.(Go (5)Je vois la table. Tu y as pos´etes clefs.(I look near the table, I think your ball is near see the table. You put your keys there.) the table.) If we replace the pronoun with its referent, we (11)Je suis all´ederri`ere la maison. Un v´elose have: trouvait derri`ere la maison.(I went behind (6)Je vois la table. Tu as pos´etes clefs sur the house. A bicycle was behind the house.) la table.(I see the table. You put your keys (12)Quand j’ai pos´e mon sac `a cˆot´e de la on the table.) tasse, ton portable se trouvait `acˆot´ede la But, differences appear between this last ex- tasse.(When I put my bag next to the cup, ample and a classical anaphoric relationship: your laptop was next to the cup.) first of all, the preposition ”sur”/”on”, appear- ing in the rebuilt LPP in (6) does not come from The difference between these examples and either the antecedent (since this one is a NP), (5) resides in the fact that, here, the prepo- or the verb (”sur”/”on” is not a mandatory sition employed in rebuilt examples (10), (11) preposition for the verb ”poser”/”put”, since and (12) is necessarily the same as the prepo- this one accepts other prepositions like in ”poser sition involved in the LPP of the previous sen- dans”/”put in” or ”poser sous”/”put under”). tence. We notice that the syntactical similar- Moreover, the coreference link between the pro- ity between the antecedent LPP and the rebuilt noun and its antecedent (usually generated by one does not come from a pure syntactic rela- the anaphoric relation) is unclear: can we re- tionship between the pronominal adverb and its ally assume that ”y”/”there” refers to the ob- antecedent. In addition, there really is a coref- ject designated by the NP ”the table”? A first erence relationship since, in example (10) for in- answer to these problems could be that there stance, both LPPs mention the same table and, is a kind of metaphoric interpretation of the in fact, the same ’place’. Therefore, we have object designated by the antecedent NP, which to account for the coreference link between pro- would allow it to designate also a place, for in- noun ”y” and a ’place’, described by the an- stance the location where it stands, or its inte- tecedent LPP. We must then consider that ”y” rior when the name of the object clearly sug- is anaphorically related to the LPP and, hence, gests an interiority feature. This approach was refers to an ’object’ introduced by this LPP and studied and approved by (Mackenzie, 2004) and different from that designated by the NP. similar ideas (though in the conceptual domain) Studying where-questions raises a valuable can be found in (Flageul, 1997). Nevertheless, analogy. For instance, let us consider a static we can notice that it is rare for the pronoun ”y” locative question like: to designate the place defined this way. In ex- (13)O`use trouve mon portable ?(Where is my ample (5), one cannot say that ”y” refers to the laptop?) place occupied by the table. Moreover, such an One possible answer to this question, within a interpretation of the involved phenomenon does universe described by example (9) above, is: not allow to account for the following examples: ` (7)Va chercher pr`esde la table, je crois (14)A cˆot´ede la tasse.(Next to the cup.) que ton ballon s’y trouve.(Go look near the table, I think your ball is there.) If we classically consider that the semantics of such questions (wh-questions) is the maximal (8)Je suis all´ederri`ere la maison. Un v´elos’y set of individuals satisfying the property corre- trouvait.(I went behind the house. A bicy- sponding to the question (on this subject, see cle was there.) (Van Rooy, 1999), (Groenendijk and Stokhof, (9)Quand j’ai pos´e mon sac 1984)), then we must admit that ”`acˆot´ede la `acˆot´ede la tasse, ton portable s’y trou- tasse”/”next to the cup” is an individual. As vait.(When I put my bag next to the cup, a matter of fact, the semantics of question (13) your laptop was there.) is: {x/se trouve(mon portable, x)}2 is therefore involved in a coreference relation- and one element of this set is therefore an object ship with another object than the one desig- that can be designated by the LPP ”`acˆot´ede nated by its antecedent. The semantics of this la tasse”/”next to the cup” (which is clearly a object depends on the antecedent NP and a (yet different object from the one designated by the undetermined) preposition. We notice that even NP ”la tasse”/”the cup”). if the antecedent NP is embedded in a LPP, the Thus, we conclude that LPPs introduce indi- preposition of the latter is not always referred viduals that can be viewed as answers to loca- to by the pronoun. The following example: tive questions. Then it appears that these in- (17)Max habite loin du parking mais j’y ai dividuals are precisely those that can be des- (quand mˆeme)gar´ema voiture.(Max lives ignated by adverb ”y” in situations similar to far from the carpark, but I (nevertheless) the examples given above. Other examples give left my car there.) support to this point of view. The anaphoric use of locative adverb ”l`a”/”there”3 or repeti- can be paraphrased by: tions by definite description show us other cases (18)Max habite loin du parking mais j’ai quand that require to assume the existence of LPPs- mˆeme laiss´e ma voiture dans le park- generated individuals: ing.(Max lives far from the carpark, but I (15)Je suis en face du cin´ema. On se retrouve (nevertheless) left my car in the carpark.) l`a.(I am in front of the cinema. Let’s meet In these situations, the preposition ”far from” there.) is not part of the anaphoric relation. We will (16)Je suis `adroite de l’arbre. L’endroit est say that the syntactic antecedent of the pronoun magnifique.(I am to the right of the tree. is the embedded NP (and not the LPP) and The place is beautiful.) we will introduce a new locative preposition to calculate the referent of ”y”/”there”. Therefore, we give the following rule: We notice that this process makes the inter- Some4 LPPs introduce/designate two pretation of pronoun ”y” potentially ambiguous individuals: one classical, given by the when this one refers to a LPP: the pronoun can contextual interpretation of the embed- indeed refer to the LPP or have the NP (embed- ded NP, the other given by the in- ded in the LPP) as an antecedent. The following terpretation of the LPP itself (that example shows such an ambiguity: is, by the compound [prep + NP]). (19)J’habite `acˆot´ede Paris et j’y travaille.(I The pronominal adverb ”y” may be live near Paris and I work there.) anaphorically linked to a LPP (that There are two possible interpretations for this is, precisely, to the phrase made of sentence: [prep+NP]), thus referring to the indi- vidual introduced by the complete LPP. (20)J’habite `acˆot´ede Paris et je travaille `a cˆot´ede Paris.(I live near Paris and I work Then, what happens when ”y” has a NP for near Paris.) an antecedent? The NP is its antecedent but it has no coreference relationship with it. On (21)J’habite `a cˆot´e de Paris et je travaille can think here that we are facing a relationship `aParis.(I live near Paris and I work in close to bridging anaphora (like ”la porte”/”the Paris.) door”...”la poign´ee”/”the handle”). But in- Finally, we notice that the behavior of relative stead of having a classical part/whole relation- sentences introduced by ”o`u”/”where”is similar ship between the two members of the anaphora, to the examples above, except the fact that the we have an underspecified (the preposition is antecedent is always a NP: missing) relationship of type object/place. ”y” (22)Je vois la table o`utu as pos´eton portable.(I 2There is no way to introduce the preposition ”next see the table where you put your laptop.) to” in this semantic formula from the surface form of the question. (23)Max habite loin du parking o`uj’ai laiss´e 3See the work of (Lorentzen, 1998) on the distinct ma voiture.(Max lives far from the carpark behaviors of ”ici”/”here” and ”l`a”/”there”. where I left my car.) 4We will see later that determining what LPPs are involved in this rule is a difficult question, unanswered The antecedent of the relative pronoun in this paper. ”o`u”/”where” is the NP which is embedded in the locative complement and its semantics must studies also highlight this role of locative prepo- be completed by a (implicit) locative preposi- sitions. V. Flageul (Flageul, 1997) considers tion (it could be replaced in surface forms by locative prepositions as conceptual-level opera- ”on which”/”in which”). tors, which turn a type object into a type place. Now that we showed that some LPPs in- A. Peyraube (Peyraube, 2003) describes the his- troduce/designate one discourse individual, we torical evolution of Chinese localizers and notes must have a closer look at the underly- that ”their main function in pre-medieval Chi- ing phenomenon. Many studies dealt with nese is to follow nouns and transform them into contextual effects of NPs (definite/indefinite, place words, tending to behave like functional generic/specific, etc. see, for instance, (Cor- words”. We take one step further and state that blin, 1987)). A summary of these can be found locative prepositions are contextual-level oper- in (Salmon-Alt, 2001). Where do LPPs fit in ators (or ”functions”, from a logical point of there? First of all, we notice that the situation view) which produce an object from another, is complicated since it depends obviously on the the former being the part of space cited before. nature of the NP which is embedded in the LPP The work of V. Flageul allows us to specify the and, for example, some cases of ”generic LPPs” conceptual type of this object according to the can be encountered, like in: involved preposition. (24)Habiter pr`esd’un cr´ematorium comporte Concerning LPPs that contain NPs quanti- ´egalement des risques : la mortalit´enatale fied by ’every’, the situation slightly differs: y est plus ´elev´eede 4%.(It is also risky to typically, such NPs imply universally quantified live near a crematorium: birth mortality is variables. We will get back on this point when higher by 4% there.) examining examples in the next paragraph. As a conclusion for the current section, we We will firstly focus on LPPs containing two state that in the situations described above: - types of NPs: indefinite with specific interpre- Some locative prepositions denote contextual tation and definite descriptions (or any refer- functions: they associate to one individual X ential expression, for instance pronominal). In from the context another one, noted f(X). - both cases we get, after the interpretation of the Some LPPs produce an object f(X) where f is embedded NP, an entity, either pre-existing the the function associated to the locative preposi- interpretation of the NP or newly created. This tion and X, the object designated or produced entity serves as a basis to determine the new en- by the embedded NP. tity generated by the interpretation of the LPP. Clearly, the other tool allowing to determine 3 Processing preposition functions this new entity is the locative preposition in- with DRT and DPL volved in the LPP: what is its status? Several studies on space representation give definitions We are now going to show how to integrate these (either qualitative or quantitative) of the part of functions when representing discourse and ref- space designated by a spatial function applied erential links. First of all, we show on exam- to an object or a place. These works usually ples6 how this works within DRT-like formal- focus on explaining the conditions under which ism. Then we show results obtained in a DPL one can say that a point of space (or an object) approach. is or not within such a part of space (see, for example (Vieu, 1991), (Schang, 1997)). This 2000). 6The examples we use here are simple on purpose and belonging is then most often represented by a may therefore seem odd or ill-formed. Nevertheless, we spatial relation (like to be on the right of) be- can give many others where ”y” refers to a LPP. A brief tween objects, which will be either true or false. search on the Internet allowed us to reveal examples of These processes do not highlight this part of various types: space that we aim to raise as a discourse object, (25)Nous nous sommes promen´espr`es d’un volcan et nous y avons trouv´edes roches int´eressantes.(We but they show the matching between some loca- had a walk near a volcano and we found interesting 5 tive prepositions and spatial functions . Other rocks there.)

5Here, again, it seems difficult to state that every (26)Les terrains primitifs, en faisant irruption dans les locative preposition matches a spatial function. This terrains primordiaux, y ont amen´eun certain nom- question will not be discussed in this paper. But, such bre de min´eraux int´eressants.(Primitive terrains, a study could probably rely on the classification of loca- when rushing into primordial terrains, brought a tive prepositions proposed in (Borillo, 1993) and (Borillo, certain number of interesting minerals there.) DRT ((Kamp, 1981)) is a theory proposing a x y z v w discourse representation formalism, essentially oriented towards (pronominal and others) ref- tree x erence problems. We show here with the cases studied in the previous section how a LPP and house y a referent to a LPP can be accounted for within z = behind(y) this formalism. is_located(x,z) (30)Un arbre se trouve derri`ere une maison. v = x Il y fait de l’ombre7.(There is a tree w = z behind a house. It casts shadow there.) casts_shadow(v,w)

Figure 2: DRS of example (30) (step 2)

Comments: classically, pronoun ”il”/”it” in- x y z troduces a new reference marker v linked to its antecedent by the equality v = x. ”y”/”there” tree x also introduces a new reference marker w linked house y to its antecedent by equality w = z. The fact that the antecedent z is itself linked to a func- z = behind(y) tional term is without consequence. is_located(x,z) (31)Si un arbre se trouve derri`ere une maison, il y fait de l’ombre.(If a tree is Figure 1: DRS of example (30) (step 1) behind a house, it casts shadow there.)

x y z v Comments: indefinite NPs ”un arbre”/”a tree x tree” and ”une maison”/”a house” classically house y v = z introduce two new individuals in the Discourse z = behind(y) casts_shadow(x,v) Representation Structure (DRS). The LPP in- troduces a new individual z, being the result of is_located(x,z) the application of function behind on reference marker y. Figure 3: DRS of example (31)

Example continuation: Comments: this example is equivalent to a don- key sentence. Thanks to its location inside the DRS, reference marker z is accessible from vari- able v. (27)Au moment du projet, la densit´e des moules z´ebr´ees,. . . , ´etait de faible `a mod´er´ee pr`es de (32)Un arbre se trouve derri`ere chaque maison Burritts Rapids, mais elle y augmentait rapide- et y fait de l’ombre.(A tree is ment.(At the time of the project, the density of ze- behind every house and casts shadow bra mussels,. . . , was low to moderate near Burritts Rapids, but it was quickly increasing there.) there.) (28)Durant le projet, c’est pr`esde chaque section qu’on a observ´eles plus bas niveaux de bact´eries E. Coli y z de toute la rivi`ere. Le niveau d’E. Coli y ´etait assez faible pour que la baignade y soit permise presque x y = behind(x) tous les jours.(During the project, the lowest levels of E. Coli bacteria in all the river were observed house x tree z near every section. The level of E. Coli was low is_located(z,y) enough there to permit swimming on most days.) casts_shadow(z,y) (29)Les gens pr´ef`erent acheter loin du centre ville car ils y trouvent des logements peu chers.(People pre- fer buying far from downtown because they find Figure 4: DRS of example (32) cheap residences there.) Comments: we chose here the interpretation DPL (Groenendijk and Stokhof, 1984) is an- in which the quantifier ”chaque”/”every” has other discourse representation system allowing a scope beyond the indefinite subject. We no- easy expression of referential links. To account tice that the quantification associated to vari- for our LPP processing, the language must be able y is existential (from its presence in the augmented with functions and functional terms right box of the implication) and not universal, (which raises a priori no problem). Here are like it would have been the case if variable y was some DPL formulas corresponding to the fol- present in the left box. This choice is not really lowing examples: important since the result of a function is, by (33)Un arbre se trouve derri`ere une maison.(A definition, unique. tree is behind a house.) Through these examples, we can see that rep- ∃x ∃y [tree(x) ∧ house(y) ∧ is(x, behind(y))] etitions of functional terms are always done (34)Il y fait de l’ombre.(It casts shadow there.) within the scope of the argument quantification: ∃x ∃y [tree(x) ∧ house(y) ∧ is(x, behind(y))] ∧ indeed, either both terms are introduced in the casts shadow(x, behind(y)) same box - at the same level - or the functional The occurrence of the variable in the functional term is introduced in the right box of an impli- term is linked by its quantifier, like in case of cation (it is therefore in the scope of the variable pronominal repetition without function. The introduced in the left box). To remain correct, well-formedness of formulas is therefore guar- every reference to this functional term will oc- anteed. cur in the same context. These processes are thus classical. Functional (35)Si un arbre se trouve derri`ere une maison, terms just have to be introduced in DRT no- il y fait de l’ombre.(If a tree is behind a tation. In the ”classical” DRT definition (like house, it casts shadow there.) it is presented, for instance, in (van Eijck and [∃x tree(x)∧∃y [house(y)∧is(x, behind(y))]] ⇒ Kamp, 1997), p. 191), terms are either con- casts shadow(x, behind(y)) stants or variables used as reference markers or In order to build these DPL formulas, discourse referents. We added functions in the we associate to locative prepositions the language. We assume that a set of function let- lambda-expression λv(behind v) of type < ters with their arities is given. Then the set of e, e >, and to LPPs the lambda-expression terms is augmented by functional terms. Prac- λP [NP λy[P [P rep Loc y]]] of type << e, T > tically, these functional terms are obtained by , T > ([ ] are used as application operator). applying functions on variables. These expressions are very close to those used Thus, a locative preposition corresponds to in DRT, apart from the fact that they do not a function from this language. One can see to introduce reference markers. In the absence of which typed lambda-expressions lexical items or these markers, the link between pronoun ”y” phrases must be associated to obtain the results and its functional antecedent is established by given above. According to notations from (van using the same variable appearing in the an- Eijck and Kamp, 1997) p. 217, we can state tecedent functional term and building a new that a locative preposition is of type < e, e > functional term from the same function. The and has as lambda-expression λv (behind v) if lambda-expression associated to ”y” then be- behind is the function associated to the prepo- comes λP [P [P rep Loc x]] where [P rep loc x] sition. The LPP causes the new individual to is the antecedent of ”y”. appear in the DRS. It is of type << e, T > , T > (like a NP) and its lambda expression is 4 Conclusion λP (ui;(NP λv(ui = (Loc P rep v) .P (ui)))) In this paper, we studied the contextual conse- where NP denotes the lambda-expression given quences of the referential interpretation of loca- from the LPP-embedded NP, Loc P rep is the tive prepositional phrases through references by lambda-expression of locative preposition given pronominal adverb ”y”. We stated that locative above and ui the reference marker introduced prepositions are functions at a contextual level by the LPP. Finally, pronoun ”y” will be asso- and that LPPs introduce new individuals into ciated to lambda-expression λP (P ui) where ui the discourse context. is its antecedent reference marker8. processing of our examples. The approach is classical 8We can not detail here the lambda-expressions as- and the reader can refer, for instance, to (van Eijck and sociated to other phrases or items required for complete Kamp, 1997) The results described here are used within A. Peyraube. 2003. On the history of place a platform (made by our team) allowing to words and localizers in chinese: a cognitive develop natural language understanding appli- approach. Space in languages: linguistic sys- cations featuring a syntactical analysis phase, tems and cognitive categories, february. a lambda-calculus-based representation of sen- N. Ruwet. 1990. En et y : deux clitiques tences and a contextual processing of discourse pronominaux antilogophoriques. Langages, (proforms and definite descriptions resolution). 97. Larousse. We use DRT to resolve references, then DPL for S. Salmon-Alt. 2001. R´ef´erence et dialogue a final discourse representation. finalis´e : de la linguistique `a un mod`ele Many difficult questions remain unanswered. op´erationnel. Ph.D. thesis, LORIA, Univer- First of all, it seems that only some LPPs pro- sit´eHenri Poincar´e,Nancy I. vide such a productive ability at a contextual D. Schang. 1997. Repr´esentation et in- level and that it depends on both the locative terpr´etationde connaissances spatiales dans preposition and the type of the embedded NP. un syst`eme de dialogue homme-machine. Classifying and characterizing these types of Ph.D. thesis, Universit´e Henri Poincar´e, NPs remain to be done. Dynamic LPPs should Nancy I. also be studied. Besides we could study the be- J. van Eijck and H. Kamp. 1997. Representing havior of other prepositional syntagms (tempo- discourse in context. 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