Fagard Benjamin

É vida, olha…: Imperatives as Discourse Markers and Grammaticalization Paths in Romance A diachronic corpus study

Keywords: grammaticalization, discourse markers, corpus study, spoken language, Catalan/French

. The lesser grammaticalization of French regarde could seem unimportant, but is in apparent contradiction with the now well-established fact that French is, of all Romance languages, the most grammaticalized. We try, in conclusion, to address this paradox: is French not so grammaticalized after all, or is this just an exception to the rule?

Introduction

What are you supposed to look at when your great-aunt tells you É vida, olha… ("Look, that's life…")? 1 Nothing, of course. There have been many studies on the grammaticalization of the imperative of verbs meaning "to look" or "to observe" into a discourse marker (hereafter DM) used to draw the addressee's attention not on an object but on discourse itself, and later on into a turn-taking device (for instance [START_REF] Brinton | From Matrix Clause to Pragmatic Marker: The History of Look-Forms[END_REF][START_REF] Dostie | Analyse sémantique et traitement lexicographique[END_REF][START_REF] Gallardo Paúls | Marcadores discursivos procedentes de verbos perceptivos en el discurso afásico[END_REF][START_REF] Marín | Verbos de percepción gramaticalizados como conectores: análisis constrastivo español-catalán[END_REF], Marín Jordà 2005[START_REF] Pons Bordería | Los apelativos oye y mira o los límites de la conexión[END_REF][START_REF] Rossari | Grammaticalization and Persistence Phenomena in Two Hybrid Discourse Markers: La preuve and Regarde[END_REF][START_REF] Waltereit | Different functions, different histories. Modal particles and discourse markers from a diachronic point of view[END_REF]. It is found in various languages: English look, Dutch kijk, Spanish, Galician and Catalan mira, Portuguese olha and Galician olla, Italian guarda, Romanian uite, Polish patrz, etc. We propose here to investigate specifically the development of imperatives of such verbs in French, Spanish, Catalan, Portuguese, Italian and Romanian: regarde, mira, olha, guarda and uite.

Three main issues are at stake: the status of DMs in general and the uses of the DMs we are investigating in particular; their development from (lexical) imperatives to DMs, and finally the place of French with respect to the other Romance languages, 2 since French regarde has a more restricted range of uses than the other items. 3 In the first part of this paper, Section 1 ("Theory and method"), we present a working definition of DMs, and list the corpora we used for the present research. In the next part, Section 2 ("The discourse marker uses of Romance look-forms"), we define and illustrate the main uses of the items under study, and show that only French regarde clearly differs from the others, having few DM uses. In Section 3 ("How they come about: the evolution of look-forms in Romance"), we address the question of the development of these DMs, with a diachronic corpus study of some of the items we chose to investigate, and argue against [START_REF] Waltereit | Imperatives, Interruption in Conversation, and the Rise of Discourse Markers: A Study of Italian guarda[END_REF] that they do constitute a case of grammaticalization, albeit not a prototypical one. These results bring to light a paradox: French is usually taken to be the most grammaticalized Romance language, and DM uses of Romance look-forms seem to be the result of a process of grammaticalization, yet the French look-form is the least grammaticalized. We will discuss this paradox in Section 4 ("Discussion: what about French?").

Theory and method 1.1 A working definition of discourse markers

As Traugott (2007a:141) points out, there are various definitions of DMs. Following mainly Schiffrin (1987:31, 323, 328), Hansen (1996:111), Waltereit and Detges (2007:63) and Traugott (2007a:144), we adopt here a broad definition of DMs as elements which operate at the discourse level. This implies that their meaning is non-propositional, and that they are functionally extrasentential: this feature of DMs, in turn, is made apparent by their relatively free distribution (i.e. syntactic position), specific prosodic contours, and variable scope. It also makes DMs a useful pragmatic tool for discourse signaling and negotiation of ongoing discourse-related interaction. A final feature, which is of particular interest for the diachronic study of DMs, is that they tend to cluster with other DMs or marks of subjectivity. This is the case for all Romance lookforms, which often cluster with or without repetition; examples 1 and 2 below illustrate this point for Italian and Catalan (see also Marín and Cuenca, 2000:225-226 for various examples of clusters in Spanish and Catalan: Mira, oye; Miri, escolti'm; Sí, a veure, miri, etc.):

(1) no guarda allora guarda se se io potessi te lo te lo regalerei volentieri io "no look now look if I could I would gladly give it to you" (LIP, FB14-280A)

(2) Sí, doncs mira, este estiu he estat a... a Sicília "Yes, so look, this summer I went to… to Sicily" (CCCUB, COD, València)

These features amount to the delimitation of a specific paradigm, which can receive various denominations besides discourse markers, for instance discourse connectives (Erman and Kotsinas 1993:79), discourse organizers (Pons Bordería, 1998:215) or discourse signals (Lamiroy and Swiggers 1991:123). We will stick, for now, to the usual denomination of discourse marker.

According to this definition and to their common denomination as discourse entities, DMs arising from imperatives of perception verbs display a wide range of discourse-related functions: they are used to structure discourse, call for the addressee's attention, emphasize thematic progression and enable or facilitate turn-taking. The examples given by Brinton (2001:180) for English look-forms illustrate some of these uses; she explains that look-forms have a global meaning of the type "'pay attention', 'heed me', or 'listen (up)'".

Literature and corpora

Under the hypothesis that the evolution of English look-forms is the result of a universal linguistic trend (in the sense of Haspelmath 1997), we can assume that the functions of their equivalents in other languages are globally quite similar. In order to test this hypothesis, we studied the DM functions of Romance lookforms, mainly on the basis of the existing literature listed in the introduction. We then compared and completed the results of this preliminary study with a corpus study, using databases of Modern Spoken Romance; wherever possible, we checked our 'non-native' intuitions with native speakers. 4 We give below some details on the corpora and databases we used: first, the name and the number of words or tokens, which may indicate, not the total number of words of each database, but the size of the portions we used. Second, the number of occurrences of the main look-form for each Romance language, including lexical and DM occurrences.

For French, we used the Valibel, PFC, and Clapi corpora, which contain a total of 506 occurrences of regarde, rega'de, r'garde for approximately 1,6 million words 5 . For Spanish, we used the spoken sections of the Crea database, which contains a total of 1,373 occurrences of mira for 2,8 million words (European Spanish only, though we did include an example of South American Spanish). For Catalan, we used the on-line version of the Corpus de Català Contemporani de la Universitat de Barcelona (CCCUB) database, which contains 117 occurrences of mira for 80,000 words. For Romanian, we used the CORV and Ruxandoiu corpora, which contain 65 occurrences of uite for 100,000 words. For Italian, we used the LIP corpus, which contains 341 occurrences of guarda for 500,000 words. Finally, for Portuguese, we used the spoken section of the Corpus do Português (European and Brazilian Portuguese), which contains 609 occurrences of olha for approximately 2 million words. 6 The corpus thus constituted is more or less homogeneous in terms of text type, since most of these databases include both spontaneous face-to-face conversation and more formal types of spoken interactions such as TV shows, debates, lectures and so on. However, as can be deduced from the figures given above, the subcorpora are hardly comparable in terms of size. For this reason, although we annotated a selection of the occurrences detailed above according to formal, morpho-syntactic and semantico-pragmatic criteria, 7 we thought it wiser not to include frequencies or relative frequencies of the different uses described in Section 2 for the different Romance languages. This will have to wait for further research, on the basis of a more homogeneous corpus.

Note that Section 3 also includes corpus data, from a diachronic corpus study on two databases containing Medieval texts, the New Amsterdam Corpus for French (3 million words) and the Opera del Vocabolario Italiano for Italian (21 million words), and two diachronic databases, the Corde database for Spanish (250 million words) and the Frantext database for French (more than 250 million words).

The DM uses of Romance look-forms

We present here the main DM uses of Modern Romance look-forms. 8 Since these forms are not related, there is no specific reason to expect them to have the same uses, except as the result of a universal (cognitive) trend, as said above. Resemblances resulting from areal phenomena are not expected either, at least for Romanian. However, these forms do share many characteristics. They all present morphological variation, usually singular vs. plural and informal vs. formal, the latter actually being a form of subjunctive rather than imperative, compensating for the absence of third person imperative form. We find for instance in Spanish mira (singular informal), mire (singular formal) and mirad (plural informal), in Catalan mira (singular informal), miri (singular formal) and mirin (plural formal), in Romanian uite (singular formal) and uitaţi (plural informal), etc. Distributionally, they can all appear in sentence-initial, sentencemedial and sentence-final position. From a functional point of view, they all have variable scope, except maybe European French regarde. Finally, as we will now see, they all have similar uses, and all seem to share with English lookforms a large enough range of uses to identify them clearly as DMs.

Non-DM uses are also found for all the items under study. This is the case for lexical uses in which the imperative marks a request to look at something, as well as for more abstract uses in which the addressee is requested not to look at an object but to take something into consideration. For instance, all these markers can introduce an example. We could describe it as the result of a slight metonymic change from "look at this (concrete) and take it as a good instance of what I say" to "look at this (abstract) and take it as a good instance of what I say". Example 3 below illustrates this point for French regarde:

(3) In such contexts, Dostie (2004:112) and Rossari (2006: ex. 2) take regarde to be a DM. It is, syntactically, between clause-internal and clause-external use: on the one hand, the imperative still has a complement (here à Liège "in Liege"); on the other hand, it is not syntactically subordinated to the main verb (ont 'have'), and is hardly modifiable (regardons 'let us look' would seem quite strange). 9 At any rate, we also found clearly DM uses, for all items under study.

In those uses, which we believe to be more or less direct developments of the lexical (or propositional) meaning of look (a call for attention), these items call the addressee's attention:

-on the topic (topic shifts, subtopics, topic continuity): in these textual uses, the DM could be glossed as "talking about A, pay attention to what I have to say about B!" -on the speaker's evaluation of what is said (mark of surprise, of disapproval, of reinforcement): in these subjective or expressive uses, the DM could be glossed as "talking about A, pay attention to what I think of it!"

-on the speaker's discourse in general (turn-taking): in these intersubjective uses, the DM could be glossed as "(while you talk about A), pay attention (to what I have to say!)". Two other uses seem to us directly derived from this one, as we will see below: the introduction of reported speech, and hesitation phenomena.

This hierarchization of DM uses reflects Traugott and Dasher's (2002:170) subjectification cline, going from propositional to textual, expressive and finally intersubjective meanings.

Topic issues

In this function, the DM introduces subtopics or topic shifts, thus acting as a continuative or moving marker, "sending a signal from the speaker to the listener that the different parts of the utterance are to be connected, or rather, that the discourse is moved forward, e.g. from one event, state or mode to the next" (Erman and Kotsinas 1993:90). It is found for Spanish mira (Gallardo and Marín Jordà 2005:65, 77, Pons Bordería 1998:214, 225), Italian guarda [START_REF] Manili | Sintassi di connettivi di origine verbale[END_REF]:311, Waltereit 2002:990), Catalan mira (Marín Jordà 2005:63, Marín andCuenca 2000:233), Portuguese (see ex. 4 below) and Quebec French regarde (Dostie 2004:114) For Romanian uite, we found no example, but it seems that such uses are not completely ruled out; a suitable context would be the following:

(5) Mie nu îmi plac maşinile. Uite, motocicletele sunt mai ieftine "I don't like cars. Look, motorcycles are cheaper" (not a corpus example; A. Ştefănescu, personal communication)

Pons Bordería (1998:226) explains that this use is linked to problems of discourse planification, resulting from the speed of oral language as described by [START_REF] Chafe | Integration and Involvement in Speaking, Writing, and Oral Literature[END_REF]. According to Brinton and Traugott (2005:137), quoting [START_REF] Quirk | A comprehensive grammar of the English language[END_REF]Quirk et al. ( :1114Quirk et al. ( -1115)), it is because "these comment clauses may […] be used to claim the hearer's attention"; Waltereit (Ibid:990) provides a similar explanation.

Evaluative use

In this second type of use, the DM emphasizes the speaker's point of view. It can convey various attitudes, from surprise to disapproval, or simply put emphasis on what the speaker says. The DM is no longer clause-internal, and can therefore appear as a pro-sentence, sometimes with repetition (e.g. Italian guarda guarda "look look") or cumulation with other DMs (e.g. Spanish mira, oye "look, listen"). Such uses are found for all Romance look-forms: Italian guarda then conveys surprise, admiration [START_REF] Manili | Relazioni tra aspetti morfologici e aspetti testuali di alcuni connettivi di origine verbale[END_REF]:8, Waltereit 2002:992); it can also express disapproval, or emphasis, as in example 6 below: (6) Claudia non potrei mai guarda fare del sesso con te "Claudia I could never look have sex with you" (Lip, NA1-246B) According to Brinton (2001:181), this use of look-forms is due to the fact that they function as 'alerts' [START_REF] Stenström | An Introduction to Spoken Interaction[END_REF]) -alerts being, in Stenström's terms, "excellent interruptors" (Ibid:74).

Example 13 below illustrates the fact that it is not possible for regarde to have such a use in (European) French: 11 even in turn-initial position, regarde seems to retain a lexical meaning, since B is showing A that the S does appear.

(

Hesitation phenomenon

A similar DM use of these imperatives is as a hesitation phenomenon or a hedge. We consider this use to be derived from the turn-taking use of these For Italian guarda, Waltereit defines these uses as "a mere hesitation phenomenon", on account of its turn-medial position (2002:993-4). For Spanish mira, Pons Bordería explains that it is associated to no conversational value and that its hedging function reflects very clearly the speaker's insecurity concerning the content of his message (1998:223-4). In the above examples, we consider the look-form to be a hedge on account of its context, which indicates that the speaker is not sure of what he asserts, or does not know what to say. This is manifest in the contradiction between gostava and agora não, and in the presence of a pause (ex. 14), typical of such uses (Manili 1989:4-5); also, in the expressions non lo so, nu ştiu (ex. 15 and 16). In such contexts, the DM is used to draw the addressee's attention to the fact that the speaker does not know the answer to a given question (which could be the case in ex. 16), and sometimes seems to be used as a simple filler (Manili 1985:308).

Introducing reported speech

In this final use, the DM introduces a sequence of reported speech, usually after a verb meaning "to say". According to Waltereit (Ibid), "it is not by accident that guarda appears frequently at the beginning of quotations. Quotations are, by their very nature, introductions of a different viewpoint. They are therefore very often topic shifts". However, it could be directly derived from the clause-initial DM, used as a turn-taking or topic shifting device, and reproduced in the reported speech as a marker of spoken language. In Renzi et al.'s (1994:226) example, which we reproduce below, as well as in other cases, it is not clear, despite the quotation marks, whether the look-form introduces reported speech or is part of the reported speech itself:

(19) Mi ha detto: "Guardi, così non si va più avanti" "He told me: 'Look, we can't go on this way'"

How they come about: The evolution of look-forms in Romance

3.1 Synchronic perspective: A grammaticalization process?

From a synchronic perspective, we could describe the formation of these DMs as the result of a grammaticalization process, though the grammaticalized status of these DMs has been subject to debate. This can be explained, in our view, by two elements: on the one hand, it is only recently that DMs have been included in the grammar of languages, and it is not yet a consensual issue. In fact, DMs in general are often denied grammatical status, because, for instance, they are not obligatory [START_REF] Waltereit | Imperatives, Interruption in Conversation, and the Rise of Discourse Markers: A Study of Italian guarda[END_REF], and subject to much interpersonal [START_REF] Manili | Relazioni tra aspetti morfologici e aspetti testuali di alcuni connettivi di origine verbale[END_REF]:2), topical and regional (Dostie 2009:202) variation. However, Fraser maintains they are "part of the grammar of a language" (1988:32; see also Traugott and Dasher 2002:11).

On the other hand, as we will now see, the 'usual' grammaticalization criteria (see [START_REF] Hopper | Grammaticalization[END_REF] for a broad view on grammaticalization, Lehmann 1995 for a stricter definition) are not all met by the DMs we are interested in here, or even DMs in general. Some are met only regionally or for isolated forms, like phonological attrition and morphological bonding. Others are met in all or nearly all Romance languages, like semantic bleaching, syntactic decategorialization, syntagmatic fixation, and paradigmaticalization. Finally, others yet are not met but have recently been challenged as indicative of grammaticalization, such as scope reduction.

Phonological attrition

While the intonational status of Romance look-forms marks their parenthetical nature (at least in some cases, see Marín and Cuenca 2000:217), there is little evidence of phonological attrition, be it in Catalan (Marín Jordà 2005:57), Spanish (Pons Bordería 1998:216), Quebec French (Dostie 2004:121), European French or Portuguese. The only cases of phonological reduction appear locally, as in regional ma or mi (Marín and Cuenca 2000:230). This puts the Romance look-forms apart from the English ones, for which phonological attrition is well attested [START_REF] Brinton | From Matrix Clause to Pragmatic Marker: The History of Look-Forms[END_REF]Traugott 2005:138, Brinton 2001:193); besides, it is not a feature of Romance languages in general but of these forms in particular, as shows the existence of reduced forms for Spanish oye "hear!" to ye, yé or oy (Pons Bordería 1998:217, Marín andCuenca 2000:230-231) and Quebec French coudon, from écoute donc "do listen!" (Dostie 2004:121).

Morphology

The morphology of these forms also seems to indicate a lesser degree of grammaticalization. There is still partial agreement between the imperative forms and the addressee; this is true for all languages, which display a variety of forms: regarde, regardez (Dostie 2004:121), mira, miri, mirin (Marín Jordà 2005:53), mira, mire, mirad (Pons Bordería 1998), guarda, guardi, guardate [START_REF] Waltereit | Imperatives, Interruption in Conversation, and the Rise of Discourse Markers: A Study of Italian guarda[END_REF][START_REF] Bazzanella | Le facce del parlare. Un approccio pragmatico all'italiano parlato[END_REF], olha, olhe (and rarely olhai) in Portuguese; in Romanian, the forms uite, uita and uitaţi are specific to the DM use, in that they present no reflexive pronoun, as the two examples below illustrate. Whereas the first example is purely lexical, the second one is a DM use of uite:

(20 Even minor changes in form (singular vs. plural, formal vs. informal) can be accompanied by slight functional variations [START_REF] Renzi | Grande grammatica italiana di consultazione[END_REF]:230, Bazzanella 1994:146, 154 for guarda); this could indicate that some forms are more grammaticalized than others. There are, besides, a few signs that there is sometimes a loss of agreement, with mostly 2 nd person uses, as in Spanish (Pons Bordería 1998:216, Gallardo andMarín Jordà 2005:64, footnote 12), and formal 2 nd person in Catalan -87.5% of occurrences in the study of Marín Jordà (2005:53), with examples of discordance such as mirin, escolti'm "look.imp.2pl, listen.imp.2pl.pol (to) me" (Ibid). In Italian, there seems to be a beginning of specialization (with guardi indicating attenuation more often than guarda, see Manili 1989:7). Of course, the situation is different for English, which does not present such variations, even for lexical verbs.

)

Semantics

The meaning of look-forms is quite clearly bleached, in most uses, as noted by various studies [START_REF] Manili | Sintassi di connettivi di origine verbale[END_REF]:308, Marín Jordà 2005:49, Pons Bordería 1998:214, Waltereit and Detges 2007:78); this is also the case for English (Brinton 2001:193). Marín Jordà notes, besides, that the desemanticization of look-forms is more important than that of similar hear-forms (2005:50), which also have DM uses.

In some instances, including in some examples we gave in Section 2, the original meaning is retained, or at least some features of the original meaning [START_REF] Dostie | Analyse sémantique et traitement lexicographique[END_REF]:112, Rossari 2006: Section 6, Pons Bordería 1998:215): Brinton, for instance, writes that "It should be noted that all of the look-forms retain literal (perceptual) meaning " (2001:181). This can be explained inside the framework of grammaticalization by the phenomenon of persistence (Hopper & Traugott 2003:96).

Paradigm

In all Romance languages, these forms are part of a larger paradigm. This paradigm includes other imperative DMs which have similar semantic, morphosyntactic and discursive features (like Catalan a veure "let's see", Marín and Cuenca 2000:216), or similar functions but a different (etymological) meaning such as "listen" (like Italian senti, Spanish oye, French écoute, see [START_REF] Manili | Sintassi di connettivi di origine verbale[END_REF]:305, Pons Bordería 1998[START_REF] Rodríguez Somolinos | Un marqueur discursif du français parlé: écoute ou l'appel à la raison[END_REF] or "say", "tell me" (like French dis(-moi), Italian dimmi…). It also includes other verbal forms such as "you see": French tu vois, Romanian vezi, Italian vedi… Finally, DMs of adverbial origin can have similar functions, like alors, bon, ben "then, well" in French [START_REF] Hansen | Some common discourse particles in spoken French[END_REF].

Syntax

The syntactic features of Romance look-forms also clearly indicate that they have undergone or are undergoing a process of grammaticalization. In most instances, these forms do not accept objects or subjects, thus rejecting an analysis as centre of a verb phrase; this is true for Catalan (Marín Jordà 2005:52), Spanish (Pons Bordería 1998:216-217), and French [START_REF] Rossari | Grammaticalization and Persistence Phenomena in Two Hybrid Discourse Markers: La preuve and Regarde[END_REF]: Section 4.2), as well as Italian, Portuguese and Romanian: all rarely take overt subjects, and only tolerate postposed vocatives. For instance, Marín Jordà notes the presence, in 10.5% of the occurrences of miri in her corpus, of postposed vocatives (2005:56). In our corpora, we found no DM occurrence of the type tu guarda, etc., although such constructions do exist (Manili 1989:8). Indeed, the few occurrences of tú mira, for instance (only two in the whole CREA/spoken corpus), are not proper DM uses, like the example 22 below:

(22) yo pasé pensando que estaba solo, pero como no había luz yo pensé: bueno, estoy solo. Entonces cuando escucho una voz que tú, mira, ven acá. ¿Para qué? No, yo no te conozco. Como era en la oscuridad, bueno. "I walked on, thinking I was alone, but it was dark so I thought: OK, I'm alone. So when I hear (sic) a voice that [said] you, look, come over here. What for? No, I don't know you. Since I was in the dark, you know." (Crea, CSHC-87, Entrevista 19, Venezuela) This is quite similar to what has been observed for English (Brinton 2001:193).

There are also tense constraints, as Rossari shows for French regarde (Ibid and Section 2.2).

The fixation parameter (or syntagmatic variation) is not as problematic, in our view, as it seems that there is a clear tendency for these DMs to occupy definite positions, in particular clause-initial and clause-final. It is true that they can also appear in clause-medial position; however, in this case, they are most often clearly parenthetic, and can also be the result of "false starts" as in example 23 below:

(23) Hace poco_mira, hace poco, Jordi, me decía_ me decía Ana Belén una cosa muy graciosa… "Recently_look, recently, Jordi, Ana Belén was telling me_ was telling me something very nice" (ex. 12a in Marín and Cuenca 2000:227) Besides, in different positions, they also tend to have different pragmatic meanings, as pointed out by Lamiroy and Swiggers (1991:139). In our corpus, the main correspondences which can be observed between position and meaning in DM uses of Romance look-forms are the following. Turn-initial uses generally correspond to turn-taking and interruption. Turn-medial, clause-initial uses (such as false starts, ex. 23) are generally associated to topic-shift and subtopic introduction. Finally, turn-medial, clause-medial uses are associated to various uses: evaluative and hedge uses as well as, in specific contexts (most often after a verb of speech), the introduction of reported speech.

Other grammaticalization hallmarks

The criterion of scope reduction [START_REF] Lehmann | Thoughts on grammaticalization[END_REF]) seems more problematic. DMs do not show signs of this phenomenon, as Brinton and Traugott (2005:138) note. However, as they write, "the notion of scope reduction has been challenged in grammaticalization generally [START_REF] Tabor | Structural Scope Expansion and Grammaticalization[END_REF] and in the case of the grammaticalization of discourse markers specifically" (Ibid).

To sum up on grammaticalization, we could say, in a prototypical view of grammaticalization (as suggests Pons Bordería 1998:218), that the DM uses of Romance look-forms constitute a borderline case of grammaticalization. Similar views are defended by Marín Jordà (2005:58), Brinton and Traugott (2005:138), [START_REF] Dostie | Introduction[END_REF] and Traugott (2007:151); and, for other DMs, by Rodríguez Somolinos (2003:73, 81); Lamiroy and Swiggers (1991:121) speak of "functional 'displacement'" with a "diachronic 'emptying'" of their meaning.

A brief history of imperative DMs

The evolution of English look-forms, as reconstructed on the basis of written corpora by [START_REF] Brinton | From Matrix Clause to Pragmatic Marker: The History of Look-Forms[END_REF], seems to confirm the grammaticalization hypothesis. She explains (there and in Brinton and Traugott 2005:138) that these forms start out as free matrix clauses in Middle English, later develop pragmatic uses, in which the imperative "gives a pragmatic instruction to the hearer to 'be careful'", and finally what we take to be proper DM uses in Modern English, in which the imperative "conveys the speaker attitude of impatience" (Ibid). These imperatives thus evolve from free clauses to adjunct uses and finally extrasentential uses.

In this evolution, the importance of the frequent initial and parenthetic use of DMs has been pointed out by several studies (see [START_REF] Fraser | Pragmatic markers[END_REF], in particular studies of imperatives of perception verbs, like Brinton (2001:178, 183), Marín Jordà (2005:51, 54); indeed, this seems to be an important feature of their evolution (Traugott 2007a:151). Is this true for Romance imperative DMs as well?

History of DMs: the case of Romance

On the basis of the literature and the observation of synchronic, spoken corpora, we proposed in Section 2 a similar cline of grammaticalization and (inter)subjectification for the development of Romance look-forms, hypothesizing that their evolution went from propositional to textual, expressive and finally intersubjective uses.

In order to check this hypothesis, we conducted a limited diachronic corpus study, analysing occurrences of Spanish mira, Italian guarda and French regarde in Medieval texts. This was done with the following databases: NCA, Frantext, Corde and OVI. Of course, our results are only indicative of these items' evolution, rather than proof: the fact that DMs are spoken elements par excellence makes it hard to use written texts to study their development. We did, however, observe an evolution which closely resembles at least the first steps of our 'cline'. The evolution of Romance look-forms, as we (tentatively) reconstructed it on the basis of written corpora, thus also seems to confirm the grammaticalization hypothesis. Two other arguments can be called upon here. The first one is that a feature often associated (though not consensually) with grammaticalization is (inter)subjectification. The subjective and intersubjective uses we saw in Section 2 could therefore constitute an argument for the grammaticalization hypothesis, if we accept the claim that the two do go hand in hand. The second one is that we can show, as Himmelmann suggests (2004:33), that "semantic-pragmatic context expansion is accompanied by syntactic context and host-class expansion". This is certainly true for our DMs, which start out with a semanticpragmatic context expansion from contexts in which the speaker calls the addressee's attention on something to contexts in which he simultaneously organizes discourse (while still calling the addressee's attention); this expansion goes hand in hand with the diversification of syntactic contexts (clause-internal uses to clause-initial, clause-medial and clause-final, extrasentential uses) and host-class expansion from look at an object to look at this (object/event) to look at this (object/event/discourse).

Discussion: What about French?

Our corpus is not homogeneous enough in terms of size for us to draw conclusions on the specificities of each marker: We established, rather, the possibility for each marker to have the different functions we illustrated in Section 2. We have shown, from this point of view, that French regarde has a much more limited range of uses, and lacks in particular a series of DM uses related to modalization and turn-taking. Other uses seem present only regionally (i.e. for Quebec French) or in certain contexts, constituting a mark of intersubjectivity rather than intersubjectivation (see Traugott 2007bTraugott :298-9, 2010)). 13 These elements indicate a lesser degree of grammaticalization for French regarde, with respect to its Romance counterparts. This seems to go against recent observations that French is more grammaticalized than all other Romance languages, in most if not all areas of language: from articles to quantifiers and auxiliaries (see for instance [START_REF] Carlier | From Preposition to Article. The Grammaticalization of the French Partitive[END_REF][START_REF] De Mulder | La linguistique diachronique: grammaticalisation et sémantique du prototype[END_REF][START_REF] Herslund | Lingue endocentriche e lingue esocentriche: aspetti storici del lessico[END_REF], Marchello-Nizia 2006:53, 111-112, 139). This apparent contradiction could be explained in one of three ways. First, it could simply constitute a counterexample to the general evolutive trend of Romance languages. Second, it might mean that this trend suffers partial exceptions, with elements which started to grammaticalize earlier in French (see for instance the existence of voici and voilà in Old and Middle French, Oppermann 2006) but stopped on the way and were replaced by yet other elements. Finally, it could also constitute not a counter-example but another proof that there is such a trend. This hypothesis is more convincing yet if we take into account Dostie's sketch of the history of regarde: she suggests (Dostie 2004:117 sqq.) that regarde did not acquire discourse uses in Quebec French, but already had them before the 16 th century, and were thus imported with French into the 'New World'. This would mean that the discourse uses of regarde later decreased in European French, as has been shown for other DMs (Dostie 2009:204,207), owing to a continued renewal of the paradigm of DMs in this variety of French. 14 The question is: what elements are used in Modern European French for the modalization and turn-taking functions displayed by guarda, mira and the like? We would have liked to provide here a definitive answer to this question, but will have to restrain ourselves, for now, to propose a few possible lines of inquiry. The most obvious answer would be tu vois, which can in some contexts alternate with regarde [START_REF] Bolly | Frequency Effects on the Evolution of Discourse Markers in Spoken vs[END_REF]; however, it is also far from having the range of uses of Romance look-forms. Other DMs which should be taken into consideration here are the elements bon, ben, beh, 15 eh bien and alors, which Hansen (1996:115, 18, 124, 140) describes as introducing topic changes and/or marking refutation. Rodríguez Somolinos (2003:74, 78) and Dostie (1998:89, 92) show that écoute "listen!" may be used to express disapproval. As for turn-taking devices, we analysed the Valibel corpus, and found that three paradigms are very frequent as first elements of a turn: oui "yes" and the like (ouais, mouais, etc.: approximately 3000 occurrences); hm and the like (euh, oh, ah, etc.: approximately 5000 occurrences) and finally ben and bon "well, good" (approximately 800 occurrences). Their relative frequency at the beginning of turns is 8 (for ben and oui) to 17 (for hm) times higher than it is inside a turn. This is not true of other grammatical elements, such as the definite article (half as frequent in turn-initial position) or common nouns (français "French", ten times less frequent in turn-initial position). Further research could show whether such elements are used by French speakers as equivalents of the other Romance look-forms, and whether this has ever been the case -providing we find a suitable corpus.

  ) (A) que quand je dois taper trois fois normalement j'ai S (B) ouais (A) et ici ça le fait pas (B) ben si (A) non |-écoute <(B)> regarde -| le S donc |-normalement <(B)> oui oui -| je fais / un deux trois quatre hein (B) ouais / voilà |-tu as un S"(A) that when I have-to hit three times [on the key] normally I get an S (B) yeah (A) and this-time it doesn't work (B) yes it does (A) no |-listen <(B)> look -| the S now |-normally <(B)> yes yes -| I do / one two three four huh (B) yeah / there |-you have an S" (Valibel, famES1r)

  People don't trust me enough, that's all! Look…! My idea is far from being silly"In European French, these uses are rather infrequent and probably not yet conventionalized, but example 10 below seems to illustrate the possibility of partially integrated instances. Here, regarde is not really part of the main sentence (here tu es déjà en deuxième), and it is in initial (thus peripheral)

	"(A) but there's only one from from abroad from Ucraine. so…
	(B) oh sure we cannot send [it]
	(A) look
	+ (B) just like that to…
	(B) Brussels to that guy
	(A) mister C*** sent [it] to Vienna yesterday"
	position, just like dis (lit. "say, tell me") which clearly functions as a DM in this (Ruxandoiu, dialog 'pe stradă')
	excerpt.
	(10) (A) c'est c'est combien d'années toi que tu es parti là quatre ans ou |-
	c'est <B> ouais -| ah oui quatre ans / regarde un peu dis tu es déjà en
	deuxième / ça ça passe vite quand même
	"(A) it's it's how-many years you that you have-been gone there four
	years or |-it's <B> yes -| oh yes four years / look now say you're
	already in second grade / it [time] it goes by don't you think"
	(Valibel, famES1r)
	eh\
	(A) [no s'ha acabat_
	(A) la sopa\]
	(B) [mira\	do a
	massage as I can with [my] fingers (B) digue-li que xx] s'acabi la sopeta com tu\
	(D) but Look this way you do it MUCH better "(A) auntie doesn't behave eh
	(A) well SUre (that) I do it better" (A) [she didn't finish
	(Ruxandoiu, dialog 'aparatul de masaj') (A) her soup]
	(B) [look (8) B: e ALtu. (B) tell her to xx] finish her soup like you" C: da↓ uite ĂSta este care trebuie. "(B) it's ANOther one (CCCUB, COC, Conversa 4)
	(C) yes look THIs one is the one we need" (12) A: da' nu e decît una din# din străinătate din ucraina.# aşa că:
	(Ruxandoiu, Ibid) B: da chiar↓ noi nu putem să trimi[tem#

Spanish and Catalan mira have similar uses, in which mira functions as a false solicitation for the addressee's attention, according to Pons

Bordería (1998:221- 223

and personal communication; see also

Marín and Cuenca 2000:217, ex. iv, footnote 5 and Ibid:233, Marín Jordà 2005:61, 66

). Portuguese olha and Romanian uite also have such uses, as shown in examples 7 and 8 below for Romanian: (7) A: da' eu zic↓ faceţi şi voi↓ că n:u vă strică. eu eu fac masaj aşa cum pot↑ cu degetele↓ D: da' Uite↓ cu ăsta faci cu MULT mai bine. A: păi SIgur că fac mai bine. "(A) but I say do it too because it won't do you any harm. I Quebec French regarde can be used for emphasis, as in Dostie's (2004:117) example 9 below: (9) On ne me fait pas assez confiance, c'est tout! Regarde…! C'est loin d'être bête ma suggestion "However, it is part of a (lower-status) syntagm, regarde un peu (lit. "look a bit"). Regarde un peu, along with regarde donc and other similar constructions, has clearly not yet reached the lexicalized state of English look-a-here or lookit, but might be said to have reached the preceding stage of 'fixed formula', along with other constructions such as regarde donc "do look, please look" 10 (Brinton 2001:190, table

I

).

2.3 Turn-taking / Interruption

This use is attested for most Romance look-forms, but not for (at least European) French regarde. It is found for Italian guarda

[START_REF] Manili | Sintassi di connettivi di origine verbale[END_REF]:305-6, Waltereit 2002:991, 995)

, for Spanish mira (Pons Bordería 1998:214, Gallardo and Marín Jordà 2005:67, Marín and Cuenca 2000:219, 231), for Catalan mira (Marín and Cuenca 2000:232), Romanian uite and Portuguese olha. Examples 11 and 12 below illustrate this phenomenon for Catalan and Romanian: (11) (A) la tieta no se porta bé A: [uite + B: pur şi simplu aşa la: B: /brucsel/↓ la ăştia. A: a trimis domnu c*** ieri la viena (…)

  DMs, with a pragmatic meaning shift from "look what I have to say" to "look, I have something to say (even if I don't yet know exactly what)". We found such instances in our corpora for Spanish, Portuguese, Catalan, Italian and Romanian, : (uite↓) nu ştiu. trebuia să plecăm amîndoi."(A) I missed the six o'clock train (B) WHAT train (A) look I don't know. We had to leave, both-of-us" (Ruxandoiu, dialog 'povestirea unui vis')

	illustrated by examples 14 to 16:
	(14) E eu! Eu também bem gostava... Olha, agora não, mas nalgum tempo…
	"Me too! I liked [that] too… Look, now I don't [anymore], but there
	was a time…"
	(Corpus do Português, 19Or:Pt:Cordial, OUT08)
	(15) non lo so guarda ieri ieri ho avuto una difficoltà a parlare questo sì
	"I don't know look yesterday yesterday I had trouble talking that's
	true"
	(LIP corpus, R A 8 220 E)

(16) A: (…) n-am prins trenul de la şase.

B: CE tren.

A

  The initial use is, of course, lexical; we do not need to illustrate this use. The first step of the evolution is the development of metaphorical uses, still intrasentential, illustrated by examples 24 and 25 below:(24) ¿Non bastan tus propios males e particulares penas, que con las glorias ajenas sientas tormentos mortales? mira que todos yguales en este mundo venimos, e assí mesmo morimos, mas bivimos desiguales. "Are your own aches and pains not enough, that you must endure mortal torment through others' glories? look that we all arrive as equals to this world, and perish in the same way, but our lives are not equal" (Corde, Cancionero castellano, 15 th c., 283)

	devoured by the same vice"
	(Ovi, Tesoro di Brunetto Latini volgarizzato, 1300, L. 7 cap. 13)
	Non-literal reduplicated uses appear later:
	(29) ¿Y asimismo, que hasta agora siempre has estado dudoso de la
	alcanzar y tenías sofrimiento; agora que te certifico el fin de tu penar,
	¿quieres poner fin a tu vida? mira, mira, que está Celestina de tu parte,
	y que aunque todo te faltase lo que en un enamorado se requiere, te
	vendería por el más acabado galán del mundo (…)
	"And still, although until now you have always doubted your success
	and suffered; now that I assure you the end of your pains has come, you
	want to put an end to your life? Look, look, that Celestina is on your
	side, and that even if you lacked all that is required in a lover, she
	would claim you to be the most perfect gentleman on earth"
	(Corde, Fernando de La Celestina Rojas, Tragicomedia de Calisto y
	Melibea, 1499-1502, 234)
	Finally, extrasentential uses only arise very late, in the 19 th century for Spanish
	mira:
	(25) regarde chu ki est presens et chu ki est a uenir.
	"look at what is present and what is to come"
	(NCA, Gloses wallonnes, 1290, 201)
	The second step, illustrated in the examples 26 and 27 below, is the use of look-
	forms with a meaning close to English "beware!".
	(26) car regarde a ton afaire si te retien de mal a faire dont tu mes t'ame en
	grant dolor
	"do take care of yourself and beware not to do any wrong by which you
	might put your soul in great pains"
	(NCA, Verite, 1450, l.1181)
	(27) E llamaron al portero del castillo e dixeron: -Cata aquí presos que
	traemos al rey Artur; e liévagelos e mira que no pierdas ninguno
	dellos, ca te dezimos, cierto, que tu señor nunca tan grand plazer uvo
	ni vio como éste.
	"And they called the guard at the door of the castle and told him: -See
	here the prisoners we bring to the King Arthur; and take them to him
	and look [to it] that you do not lose any of them, because we tell you,
	for sure, that your lord never had or saw anything so pleasant." (Corde, El baladro del sabio Merlín con sus profecías, 15 th c., Fol. 60
	R°)
	(28) Se tu voli biasimare o riprendere altrui, guarda che tu non sia
	magagnato di quello vizio medesimo
	"If you want to blame or criticize others, look [to it] that you not be

(30)

No, mujer, no me altero... pero a lo menos que oiga el que yo la propongo, que le conozca y le trate, y después... mira, Bernardo a la hora esta debe haber llegado ya de Barcelona; habrá consagrado los primeros instantes a sus parientes; pero de un momento a otro le tendremos aquí, y es preciso recibirle como a quien viene a ser mi yerno "No, woman, I am not angry… but hear at least what I have to offer you, get to know him, and after that… look, Bernardo by now must have arrived already from Barcelona; he will have devoted his first hours to his parents; but any minute we will have him here, and we have to honor him like one who will become my son-in-law"

(Corde, Mariano José de Larra, No más mostrador, 1831, 18)

Author's address

Benjamin Fagard Laboratoire Lattice, CNRS 1 rue Maurice Arnoux F-92120 Montrouge France benjamin.fagard@ens.fr Notes 1 This is, actually, a true example. All examples are given with a personal translation; here, as in all other translations, we try to follow the structure of the original language, and modify it only to obtain acceptable English translations; for DMs and other idiomatic elements, however, we did take a few liberties. Corpus examples are presented with their original annotations. 2 Here and in the rest of our paper, we will (for the sake of simplicity) use the term "Romance" as referring to the Romance languages we took into account in our study; of course, what we say is not necessarily true for Sardinian, Galician, Rhaeto-romance and other Romance languages or dialects. Further research will, hopefully, fill the gaps. 3 This has been noted for French vs. Italian by [START_REF] Rossari | Grammaticalization and Persistence Phenomena in Two Hybrid Discourse Markers: La preuve and Regarde[END_REF] and [START_REF] Waltereit | Imperatives, Interruption in Conversation, and the Rise of Discourse Markers: A Study of Italian guarda[END_REF]Waltereit ( :1008, footnote 6, footnote 6). 4 For Italian, Spanish, Catalan, Portuguese and French; for Romanian, we relied on native speakers' judgments and benefited in addition from the advice of two colleagues, Alexandru Mardale and Ariadna Ştefănescu, which we here thank. We also would like to thank Salvador Pons Bordería, Sophie Prévost, Fabio Zinelli, Anna Mauri Graells, Laure Sarda and Paola Pietrandrea for their advice, as well as the anonymous reviewers for their very helpful comments. 5 We also used the CFPQ corpus for Quebec French, with 136 occurrences of regarde for 160,000 words (by our count). 6 As we did not, unfortunately, find the exact size or constitution of this corpus, this is only a rough approximation. 7 We coded mainly meaning, pragmatic inferences, integrated vs. non-integrated use (presence of a complement, of a complementizer, etc.), internal vs. peripheral position, form and context (presence of (other) DMs), for all Catalan, French and Romanian occurrences, and for a selection of Portuguese, Spanish and Italian occurrences of look-forms. For these three languages, we arbitrarily extracted 150 occurrences from the respective subcorpora. 8 For obvious reasons of space, we cannot illustrate all uses for all languages… We tried, as far as possible, to give examples for those cases that are not illustrated in the literature. 9 I would like to thank one of the anonymous reviewers for pointing this out to me. 10 With relative frequencies which remain however very low, even with the slight increase in the 19 th century for regarde donc (1,6 occurrences for 1 million words, ten times as much as in the 16 th century, in the same database). 11 One anonymous reviewer suggested that uses similar to that in (11) could be found in Quebec French. This would indicate that regarde can appear in turn-initial position in this variety of French, and may therefore have a turn-taking use: Fagard Benjamin (A) Elle n'a même pas fini sa soupe (B) Regarde! dis-lui de la finir si tu veux bien (A) She hasn't even eaten up her soup (B) Look! Tell-her to finish it, please. 12 This use seems to be quite frequent in the CFPQ corpus, in exactly the same contexts: j'ai dit regarde prends le temps de te faire soigner pis tout ça "I said look take the time to get this taken care of and all that" (Subcorpus 6, section 12, p. 87, l. 1). 13 Meaning that the intersubjective reading results only from the context of use: "unless a formmeaning pair has come to code intersubjectivity, we are not seeing intersubjectification (-ation being the important item here)"; such items might be said to have "pragmatically" but not "semantically" intersubjectified, "because they do not code semantic intersubjectivity" [START_REF] Traugott | Inter)subjectivity and (inter)subjectification: a reassessment[END_REF], sections 2 and 4). 14 As one reviewer kindly pointed out, suggesting that this decrease of regarde's DM uses might be linked to a competition with the DM uses of écoute "listen". 15 Considered by the author to be "a free variant" of ben (Ibid:146).


Baptiste Gaillard
email: baptiste.gaillard@fr.thalesgroup.com

Sylvie Guillemin-Lanne
email: sylvie.guillemin-lanne@temis.com

Guillaume Jacquet
email: guillaume.jacquet@xrce.xerox.com

Claude Martineau

Aurélie Migeotte
email: aurelie.migeotte@arisem.com

Combining NER Systems via a UIMA-based platform

In this paper, we present a tool aiming at merging named entity annotations provided by different named entity recognition systems. This tool is based on UIMA platform and contains a merging module which uses information about the compatibility of various annotations and can point out conflicts, and thus yields annotations that are more reliable than those of any single annotator. This work has been performed as part of the Infom@gic project

Introduction

In this paper, we present a tool aiming at merging named entity annotations provided by different Named Entity Recognition systems (henceforth NER systems). It take as input a set of text (simple text, xml or html) and give as output a set of annotated text in a UIMA format. It contains an algorithm for merging the different annotations which uses information about the compatibility of various annotations and can point out conflicts, and thus yields annotations that are more reliable than those of any single annotator. This work has been performed as part of the Infom@gic project, whose goal is the integration and validation of knowledge engineering and information analysis applications, and which is supported by the pole of competitiveness Cap Digital "Image, MultiMédia et Vie Numérique". We first describe UIMA, which provides archi-tecture to coordinate information from different modules. Then, we present the needed input of our software. Then, we present an algorithm for merging the different annotations. We conclude by describing the software output and a preliminary evaluation of the results we obtained.

Connected works

In many scientific domains, it is well known that combining different methods or systems allows a result improvement comparing to results obtained by each system. For instance, the Adaboost Algorithm [START_REF] Schwenk | Using boosting to improve a hybrid Hmm/Neural Network speech recognizer[END_REF] consists in training a set of similar systems as a workflow where each system is trained to correct errors from the previous system. In the NER domain, [START_REF] Borthwick | Exploiting diverse knowledge sources via maximum entropy in named entity recognition[END_REF] and [START_REF] Kozareva | Combining Data-Driven Systems for Improving Named Entity Systems[END_REF] merged some NER system using majority vote method. In each case, the merged system obtains better precision results than any system alone. Our tool aims at helping NER community to improve their results by merging existing systems. Our specificity is to propose a common platform where we can aggregate any NER system and where the merging module is already integrated. Moreover, inside the Infom@gic project, we developed this tool as an input for search engine or information extraction systems. Consequently, our tool deals with xml and html input format. Comparing to [START_REF] Borthwick | Exploiting diverse knowledge sources via maximum entropy in named entity recognition[END_REF]) and [START_REF] Kozareva | Combining Data-Driven Systems for Improving Named Entity Systems[END_REF], our last algorithm specificity is to deals with annotation overlapping cases.

UIMA (Unstructured Information Management

Architecture) is an architecture for managing, organizing and coordinating unstructured information [START_REF] Ferrucci | UIMA: an architectural approach to unstructured information processing in the corporate research environment[END_REF]. It originated at IBM and is now an open source project at the Apache Foundation (http://incubator.apache.org/uima/). This architecture has been developed specifically for the management of NLP tools: Ferrucci and Lally propose an example of rapid integration of a syntactic parser and a NER system. Its goal is to increase scientific progress with a fast combination of unstructured information management technologies. In our tool, we used UIMA as a common platform for all the used NER systems and for developing our merging module.

Software input and output

Our software takes as input a set of text (simple text, xml or html), integrate them in the workflow of a set of existing NER systems, merge their output and finally yield a UIMA CAS object (Common Analysis System object readable as an xml file) containing a unique set of annotations without redundancy, resolving some named entity boundary or identification conflicts. Each NER system can be implemented directly using the UIMA libraries or using another language and then encapsulate it in the UIMA platform (this is the usual case). In this case, the only added work for an existing NER system is to establish a correspondence table between its own annotations and the UIMA platform annotations. Figure 1 describes the UIMA interface to construct the NER systems workflow, to define the used merging module and to choose the input and output format.

Algorithm for merging annotations

This merging process combines annotations from different NER systems in order to obtain a system that benefits from the unique characteristics of each annotator. This merging process is not trivial: First of all, all annotators must agree on a common type hierarchy of annotations. Secondly, the merging process must deals with redundant annotations. It corresponds to six different cases which are covered by our algorithm. Thirdly, it must deal with conflicting annotations. The algorithm has been developed by the four partners of Experiment 1:

Experiments and results

Our tool has been tested on two experiments. Experiment 1 (Brun et al, 2009): software input is a set of web sites and the merged NER systems are four NER systems based on symbolic approaches implemented by four different partners (Arisem, IGM, Temis and Xerox). After an agreement on a common hierarchy of annotation types, each partner encapsulated its own NER system in a common platform. This experiment is done on French texts.

  Table below present a summary of the obtained results: Experiment 2 (Ah-Pine and Jacquet, 2008): The input is a hybrid case combining a new statistical approach implemented in the UIMA formalism with different existing systems: Stanford, Gate and Xerox NER systems. This experiment is done on English texts. Table below present a summary of the obtained results:

		P	R	F2
	Annot. 1	67.53	60.85 64.02
	Annot. 2	61.85	44.36 51.67
	Annot. 3	73.24	49.38 58.99
	Annot. 4	75.23	66.35 70.51
	Fusion	80.10	65.11 71.83


Javier M Sastre Martínez
email: sastre@univ-mlv.fr

Computer Tools for the Management of Lexicon-Grammar Databases

Keywords: Table de lexique-grammaire, base de données, interface graphique, XML Lexicon-grammar table, database, graphical interface, XML

Le lexique grammaire est une méthode systématique d'analyse et de représentation des structures de phrase élémentaire d'une langue naturelle ; son produit: des grandes collections de dictionnaires syntaxiques électroniques ou tables de lexiquegrammaire (LGTs). Du travail collaboratif à très long terme est nécessaire pour achever la description d'une langue. Cependant, les outils informatiques de gestion de LGTs actuels ne remplissent les besoins suivants : intégration automatique de données multisource, control de cohérence de données et de versions, filtrage et tri, formats d'échange, gestion couplée des données et de la documentation, interfaces graphiques (GUIs) dédiées et gestion d'utilisateurs et contrôle d'accès. Dans cet article nous proposons une solution basée sur PostgreSQL et/ou MySQL (systèmes de gestion de bases de données libres), Swing (une librairie pour la programmation de GUIs en Java), JDBC (API pour la connectivité de Java aux bases de données), et StAX (API pour l'analyse et la création des documents en XML).

Introduction

Lexicon grammar is a model of syntax focused on the elementary sentences of a natural language [START_REF] Gross | Lexicon Grammar. Concise Encyclopedia of Syntactic Theories[END_REF]. Its major principle is that the unit of meaning is the sentence, but the word or the words composing the predicative element (PE) of a sentence constraint its structure. Natural language grammars are too irregular to be described by a set of general rules [START_REF] Gross | The Construction of Local Grammars. Finite State Language Processing[END_REF]. Rather than that, the lexicon grammar approach consists in enumerating the sentence structures for each use of a sentence PE. In order to compact and split the list into components easy to handle, the structures are classified by similarity into lexicon-grammar tables (Leclère, 2002) or LGTs. Each table is associated to a common sentence structure; table columns are associated to variants or differential properties of the common structure; table rows illustrate the possible structures of a specific sentence PE. Two kinds of columns are used: boolean and text. The former indicate the acceptability or unacceptability of a structure property; e.g.: N1 =: Qu Psubj meaning that the direct object may be a clause in subjunctive mood introduced by the conjunction que (e.g.: Max aime que Marie lui fasse des câlins ≈ Max likes that Marie gives him cuddles 1 ). The latter, to point out the use of a specific word within the sentence (e.g.: the preposition introducing a verb argument; in tomber amoureux de quelqu'un, only the preposition de can introduce the object complement quelqu'un as well as in the English version to fall in love with somebody only the preposition with can introduce the object complement somebody).

LGTs can be automatically transformed into finite state automata (FSTs) in order to perform parsing [START_REF] Roche | Une représentation par automate fini des textes et des propriétés transformationnelles des verbes[END_REF][START_REF] Constant | Converting Linguistic Systems of Relational Matrices into Finite State Transducers[END_REF]. Each table is associated to a set of parameterized FSTs 2 , which recognize every variant of the common sentence structure. By instantiating the parameters by the values contained in each row we obtain the set of FSTs recognizing each particular structure. Other ongoing projects intend to use LGTs with other parsing frameworks [START_REF] Garden | Maurice Gross' Grammar Lexicon and Natural Language Processing[END_REF].

Summarizing, the representation of syntactic structures by means of LGTs benefits from three important properties:

1. Simplicity: each cell contains a single unit of information, namely the acceptability or unacceptability of a property or the potential use of a word, and information units are grouped into tables which can be easily viewed or printed.

2. Exhaustiveness: a large coverage of a natural language can be achieved by the incremental construction of LGTs, yet many irregularity instances can be taken into account.

3. Potential exploitability for automatic parsing: it is possible to automatically transform the tables into FSTs for corpus parsing given a set of parameterized FSTs.

1 Literal translations.

2 Parameterized FSTs are built manually and tested against corpus.

Computer Tools for the Management of Lexicon-Grammar Databases

State of the art in computer tools for the management of lexicon grammar databases

LGTs are presently created and maintained using common spreadsheet software, mainly Microsoft (MS) Excel but also OpenOffice. A web interface is used for public 2. These tools do not support network shared objects; every LGT is locally developed and registered as a file in the author's computer. In order to share a LGT through the network the correspondent file is copied into a public web folder, where its access is limited to read-only by means of a web interface (Figure 2). The integration of different data sources must be manually done by locating the last version files, mixing the modifications done by different authors and recollecting them within a public web folder. As the number of files, different file versions and different file copies increases, the integration of the global database is complicated.

3.

LGTs can reach a size of a thousand rows and forty columns, resulting in fortythousand information units within a single by a short code, which tries to reflect the nature of the referenced object. However, codes may not always be easily interpreted without the aid of documentation; for example, the code Nnr (non-restricted noun) indicates if the sentence may accept any subject independently of its semantic nature (e.g: human or not human) or syntactic structure, namely a completive or an infinitival clause [START_REF] Gross | Méthodes en syntaxe : régime des constructions complétives[END_REF]. Direct access to documentation fragments would be useful not only for the interpretation of existent data but also to facilitate the creation of new documentation. Current tools provide direct access to documentation about tables but not about finer-grained objects like columns. Row documentation is limited to an extra field within the table containing a general sentence example (Figure 1). Examples for each cell could be added by increasing the number of example columns, but the resultant tables would be too big to be easily handled without selective data access support.

6. There is no inherent data access control or user management. Private files are simply not distributed. If a file or a data subset of a file is to be shared, a new file containing the required data is created and placed within a public web folder. This complicates data maintenance because of the increasing number of copies to keep up to date. LGT involves the identification of a sentence structure class and its possible variants which are represented by property codes. Some properties are extensively reused whilst others need to be created for dealing with new scenarios. Due to the absence of a data coherence control and the increasing number of properties, it happens that different codes are used to represent the same property in different tables. This may not be problem for the human reader, but it is a serious obstacle to automatic management.

Computer tools proposal

We propose a computer tool solution based in a Java web/local client interface from which the user will be able to manage shared lexicon-grammar databases contained in a PostgreSQL or a MySQL database server. Clients use JDBC to communicate with the database server.

Each part is explained in detail in the following subsections.

Java web/local applications

A very convenient feature of Java [START_REF] Eckel | Thinking in Java[END_REF] is the possibility of embedding Java applications within web pages (Java applets). Applets can be downloaded from the web and directly executed on several platforms just by opening their embedding web pages. An important drawback is the potential danger of executing malicious code, since we may not have any control over the software origin. That is the reason why applets are executed, by default, in a restricted resource access environment called "sandbox" [START_REF] Gong | Java TM 2 Platform Security Architecture[END_REF]). However, it is possible to digitally sign our software packages in order to provide a mean of ensuring their authenticity. Once the software packages are signed and deployed on a public web server, it is up to the user to trust or not the software web distributor in order to grant the same resource access as local applications. By adding some little source code to our typical Java applications and signing the correspondent software packages it is possible to use the same software package for local use as well as for web direct execution. This permits the user to directly execute our application through the web, thus avoiding the software installation, or to download the package and execute it locally in order to avoid network transfer overhead. Both scenarios have been taken into account for our LGT computer tools, the former for facilitating the diffusion of LGTs and providing an easy and fast way to access them, the latter for users who constantly work with them. Instead of having to develop two separate tools, we have developed a single one able to deal with both scenarios.

The Swing graphical interface

Swing [START_REF] Loy | Java Swing[END_REF] provides a complete framework for the development of graphical interfaces in Java. Amongst others, it gives a good support for the implementation of tabular data graphical interfaces. One important requirement was to be able to horizontally scroll a set of columns whilst keeping static the other ones. Since the LGTs may be larger than the computer screen, scrolling is necessary for viewing all the data. However the column or columns containing the PE must remain in view so that we can know at anytime which PE each row corresponds to. The column containing the example sentence may be required to remain as well. In Figure 3 we can see a LGT split into four column groups: properties affecting the sentence subject, the PE, complement properties and the examples.

Another important requirement was to handle

LGTs for any language. This is quite problematic due to the existence of different character coding tables for different language alphabets. The appropriate character coding table must be selected in order to correctly draw the correspondent characters, but it may be also necessary to mix different alphabets within the same table representation (e.g.: to compare tables of different languages). The unique homogeneous solution is the use of Unicode, a universal character coding system. Java natively supports Unicode and Java Swing can render Unicode symbols without further complication (Figure 4).

The lexicon-grammar database

LGTs can be easily inserted into database systems [START_REF] Ullman | Principles of Database Systems[END_REF] due to their similarity with respect to relational tables. Nowadays there exist reliable and fully functional open source implementations of database management systems (DBMS), mainly PostgreSQL (PostgreSQL, 2005) and MySQL [START_REF] Mysql Ab | MySQL 5.1 Reference Manual[END_REF]. These systems receive and process requests from client programs formulated in SQL (Structured Query Language) not only for data creation, access and modification but also for statistical analysis. An immediate application of LGT statistical analysis is the study of candidate LGT subclasses (decomposition of LGTs into sets of rows sharing similar value patterns).

Both PostgreSQL and MySQL do correctly manage concurrent database access thanks to the use of ACID transactions [START_REF] Häder | Principles of Transaction-Oriented Database Recovery[END_REF]. Both provide a graphical interface for the management of generic databases, users, and access rights;

LGTs are created within a database server from which network access is possible depending on the set permissions. Both provide data backup mechanisms. Both allow computer programs written in Java or C++, amongst other languages, direct database access for automatic data processing.

LGT properties are managed by maintaining within the database server a table of every existent property and its documentation. During the creation of new LGTs, current properties can be easily consulted in order to avoid the assignation of multiple codes to the same property. If a new property is to be created, it is added to the property table with its correspondent documentation. This mechanism provides a fast and direct access to property characteristics, both useful for the creation and the consultation of LGTs. A table containing the code and documentation of each LGT is also maintained.

Communicating with the database through JDBC

The JDBC API provides a universal mechanism to database access for Java clients [START_REF] Fisher | JDBC TM Database Access[END_REF]. The same Java program may access different database systems by loading the correspondent JDBC driver. Basically, a JDBC driver makes it possible to connect to a data source, send SQL statements and process the results. Since both PostgreSQL and MySQL provide such a driver, our LGT management system can rely on both systems without having to change a single line of source code. Since it is based on SQL, very few commands are needed in order to perform complex operations on LGTs. For making things even easier, it is even not necessary to have a perfect knowledge of SQL: the graphical interfaces included with PostgreSQL and MySQL show the SQL statement correspondent to each one of the requests we compose with mouse clicks and key presses.

XML data exchange interface

XML [START_REF] Skonnard | Essential XML Quick Reference: A Programmer's Reference to XML, XPath, XSLT, XML Schema, SOAP and More[END_REF] constitutes a convenient way for the representation of data to be exchanged amongst computer applications. XML, Unicode and Java technologies converge into a set of multiple free tools for the generation, analysis and validation of XML documents, each one following a different approach:

1. Document Object Model (DOM) is a platform independent interface that exposes XML documents as a tree structure. It loads the whole XML document in memory and then provides an easy way to access specific parts. Random access to different document parts is enabled with a memory cost proportional to the document size 2. XML Schema [START_REF] Vlist | XML-Schéma[END_REF] is a XML-based language for the definition of XML formats. JAXB [START_REF] Amstrong | The Java tm Web Services Tutorial[END_REF] is a metacompiler that automatically generates Java code for the analysis, validation and generation of XML documents following a specific XML Schema description. This is a Java specific solution similar to DOM: a Java object tree is created in memory representing the whole document.

3.

The XMLEncoder [START_REF] Philip | Using XML Encoder[END_REF] provides a way to XML automatic serialization of Java Beans [START_REF] Desoto | Using the Beans Development Kit 1.0: A Tutorial[END_REF]. Java Beans are Java classes that follow some naming conventions. Using the Java reflection mechanism [START_REF] Green | Reflection API Tutorial[END_REF], XMLEncoder can find out which data must be registered for the object serialization by inspecting the object structure. XML documents generated this way are intended to be decoded by the XMLDecoder, which in turn recreates the original Java object. This is the easiest but most Java specific solution to XML serialization: we are not able to choose the XML format; it is automatically generated for the serialization and recreation of Java objects by Java applications.

4.

Document streaming consist in serially parsing XML documents. Random access to specific parts is not allowed but the resource requirements are often smaller, mainly if we work with big data objects. Parsed elements may be pushed or pulled from the parser towards the application. In the first case, the application passively receives and deals with the events generated by the parser. In the second case, the application actively requests the XML parsers for data fragments. Examples of push and pull parsers for Java are, respectively, SAX [START_REF] Brownell | SAX2[END_REF] and StAX [START_REF] Amstrong | The Java tm Web Services Tutorial[END_REF]. SAX provides document parsing only, StAX both parsing and generation.

Since we do not require random document access, StAX represents the most suitable solution because it is the minimal resource consumer, the source code required for pull parsing models is usually simpler than for push parsing models, it can be used not only for reading but also for writing XML documents and it is not restricted to the use of Java technologies (other computer applications developed with other computer languages, like C++, may interact with XML-serialized LGTs).

The XML-LGT format

LGTs are represented by <lgt> tags, e.g.: <lgt name="38L" version="1.0" docUri=" http://

Conclusion

Lexicon grammar is a promising methodology for the collection of syntactic information which can be later used for automatic parsing. As the work in this field has advanced, the current used computer tools have begun to show their limitations. In order to ensure the progress of lexicon-grammar based research, we have proceeded to study the new requirements, to analyze the current existent free tools which could best fit them, and to develop a LGT management system based on them. The use of a centralized database serves as a nexus between linguistic data compilation from human experts and its exploitation by computer programs. Future work will consist in the study of optimal algorithms for the conversion of LGTs into FSTs and their implementation for lexicon-grammar based parsing.

Figure 1 :

 1 Figure 1: Classic representation of a LGT fragment (LGT 1) under MS. Excel

Figure 3 :

 3 Figure 3 : Fragment of LGT 38L, highlighted line correspondent to verb balancer

table .

 .

	Under these conditions, filtering of
	columns and rows becomes a need rather than an asset. Selective data access is limited
	to the search within a single table of text sequences potentially contained in a single
	cell. The web interface allows direct access to the table or tables containing a
	specified PE.
	4. Problems of software and data portability: MS Excel is meant to be run only on MS
	Windows's platforms 3 and uses, by default, a proprietary file format 4 . MS. Excel

allows for exporting into Unicode

[START_REF] Becker | The Unicode Standard Version 4.0. The Unicode Consortium[END_REF]

plain text files with some extra manual effort, but a more appropriate solution would be the default use of an XMLbased exchange format

[START_REF] Sastre | XML-Based Representation Formats of Local-Grammars for the NLP[END_REF]

. 5. Just for distributional verbs there are already sixty LGTs available, which jointly contain a set of 428 different properties. Each table and each property is represented 3 MS. Windows's applications may work on other platforms thanks to Windows emulators or Windows software compatibility layers (e.g.: Wine); however such scenarios may be unacceptable due to the potential emulation errors and the added complexity to software utilisation. 4 There exist tools able to load MS. Excel files (e.g.: OpenOffice), but errors due to format misinterpretation may happen. Those tools are usually not able to modify MS. Excel files, thus access is restricted to readonly.

  •••/38L.html">. The attributes name, version and docUri indicate, respectively, the table name, format version and the URI where to locate the tabledocumentation. <lgt> tags may contain a set of <column> tags, one per property column, followed by a set of <row> tags, one per table row. <column> tags describe the properties of a column by the following attribute set: type indicates the property type ("boolean" or "text"), isPrimaryKey indicates whether a column contains the row identifiers (the sentence PEs) and acceptsNulls whether a column may contain null values (usually non-primary key columns). <row> tags contain a set of <value> text tags, one per column. Empty content is used to represent null values (e.g.: <value/>). "true" and "false" strings indicate true and false values for boolean type columns (e.g.: <value>true</value>). For text type columns, the correspondent text is the content of the <value> tag (e.g.: <value>aimer</value>). This representation format is appropriate for loading tables within a database by a document streaming parser, since the information is accessed in the optimal order required by a database to create new tables: table name, column properties and row values.

Acknowledgements

We would like to thank Pr. E. Laporte for his continuous help. This work has been partially supported by CNRS, the French Ministry of Industry and the Institut de linguistique française.


Arnaud Le Ny
email: arnaud.leny@math.u-psud.fr

Range of a Transient 2d-Random Walk

Keywords: Random walks on randomly oriented lattices, range, law of large numbers. MSC 2000 Classification: 60K37, 60G50, 60F05

come

Range of a Transient 2d-Random Walk

Preliminaries

We focus on a particular type of random walk in a random environment (RWRE), where the environment is inherited from orientations of the lattice on which the walker evolves, providing thus two independent sources of randomness: The horizontal orientations of the lattice and this of the walk performed on it afterwards, once the realization of the orientation has been fixed. We introduce first an horizontally oriented square lattice L ǫ . The orientations ǫ = (ǫ y ) y∈Z are families of i.i.d. Rademacher random variables taking values in the product probability space (E, E, ρ) = {-1, +1}, P({-1, +1}, 1 2 δ -1 + 1 2 δ +1 ⊗Z . A given horizontal level y is then oriented to the right when ǫ y = +1, to the left when ǫ y = -1, and induces an horizontally oriented version of Z 2 for every realization of the random field ǫ:

Definition 1.1 (Horizontally Oriented Lattice L ǫ ) Let ǫ = (ǫ y ) y∈Z ∈ {±1} Z . The oriented lattice L ǫ = (V, A ǫ ) is the (random) directed graph with (deterministic) vertex set V = Z 2 and (random) edge set A ǫ defined by the condition that for u = (u

1 , u 2 ), v = (v 1 , v 2 ) ∈ Z 2 , (u, v) ∈ A ǫ ⇐⇒ v 1 = u 1 and v 2 = u 2 ± 1, or v 2 = u 2 and v 1 = u 1 + ǫ u 2 .
One performs then a simple random walk (SRW) M = (M n ) n∈N on L ǫ . For a given ǫ, it is a Z 2 -valued Markov chain defined on a probability space Ω 0 , B 0 , P (ǫ) , starting at the origin (0, 0), whose (ǫ-dependent) transition probabilities are defined for all (u, v) ∈ V × V by

P (ǫ) [M n+1 = v|M n = u] = 1 3 if (u, v) ∈ A ǫ , 0 otherwise. 1
An interesting feature is that this SRW has been proven to be transient for almost every orientation ǫ [START_REF] Campanino | Random walks on randomly oriented lattices[END_REF]. This almost sure approach is referred as the quenched case and we focus here on a more collective annealed approach: We consider the law of the process under the joint measure P := ρ ⊗ P (ǫ) . Thus, we study the behavior of the SRW as a discrete-time process on (Ω, B, P) := E × Ω 0 , E ⊗ B 0 , ρ ⊗ P (ǫ) .

with its annealed law P formally defined as P = E P (ǫ) dρ(ǫ). We write E (or E (ǫ) or E ρ ) for the expectation under P (or P (ǫ) or ρ). Due to the non-local character of the orientations, the main drawback of this annealed model is that the walk is not Markovian anymore. Nevertheless Proposition 1.1 Under the annealed law P, the process M is reversible. Indeed, consider a trajectory ω = (ω 0 , . . . , ω n ) and change ǫ into -ǫ : It has the law of the reverse trajectory ω * = (ω n , . . . , ω 0 ) and one concludes using the symmetry of the law ρ of ǫ.

Under this annealed law, a non-standard functional limit theorem has been proven in [START_REF] Guillotin-Plantard | Functional Limit Theorem for a Random Walk with Dependent Marginals[END_REF], while we shall start our study of the range of the random walk thanks to the following estimation of the probability of return to the origin due to Castell et al. [START_REF] Castell | A Local Limit Theorem for Random Walks in Random Sceneries and Random Walks on Randomly Oriented Lattices[END_REF]:

Theorem 1.1 (Local Limit Theorem [3]) There exists a constant C > 0 such that u cp (n) := P[M n = (0, 0)] = C • n -5/4 + •(n -5/4 ) as n → ∞. (1.1)
The main tool is to embed the two-dimensional random walk into a vertical SRW and an horizontal random walk in random scenery [START_REF] Kesten | A Limit Theorem Related to a New Class of Self Similar Processes[END_REF]. The fluctuations of the latter being of order of n3/4 , this explains why combined with the vertical SRW -whose fluctuations are of order of n1/2 -it requires a proper normalization of the order of n 5/4 , see also [START_REF] Campanino | Random walks on randomly oriented lattices[END_REF][START_REF] Guillotin-Plantard | Transient Random Walks in Dimension Two[END_REF][START_REF] Guillotin-Plantard | Functional Limit Theorem for a Random Walk with Dependent Marginals[END_REF]. This strong estimate (1.1) implies the convergence of the annealed Green function

U cp := ∞ n=0 P[M n = (0, 0)] < ∞ (1.2)
which in turns implies this of the quenched Green function for ρ-a.e. orientation ǫ :

0 < U (ǫ) cp := ∞ n=0 P (ǫ) [M n = (0, 0)] < ∞, with U cp = E ρ U (ǫ) cp > 0. (1.3)
This also implies 1 by Borel-Cantelli the transience of the SRW on L ǫ for ρ-a.e. orientation ǫ. Thus, the usual dichotomy on Z d (Pólya, 1923) between low dimensions (recurrence for d = 1, 2) and higher dimensions (transience for d ≥ 3) is broken by the extra-randomness of the orientations 2 . In order to precise the characteristics of this two-dimensional transient random walk, we focus in this paper on the asymptotic behavior of its range R n , defined to be the number of distinct sites visited by the walker during the first n steps:

R n = Card M 0 , M 1 , . . . , M n-1 .
It has been first studied for SRW on Z d by Dvoretsky and Erdös ( [START_REF] Dvoretzky | Some Problems on Random Walks in Space[END_REF], 1951) who provided estimates of its expectation together with (weak and strong) laws of large numbers under different forms for dimensions d = 2, 3, 4, . . . 3 .

Results

Theorem 2.1 The expectation of the range grows linearly :

For ρ-a.e.(ǫ),

E (ǫ) [R n ] = n • γ (ǫ) cp + • n with γ (ǫ) cp = (U (ǫ) cp ) -1 ∈ ]0, 1] (2.1) E[R n ] = n • γ cp + • n with γ cp = E ρ 1 U (ǫ) cp ∈ ]0, 1]. (2.2)
The rates of growth γ cp and γ

(ǫ)
cp are well-defined as the probability of escape 4 in next section. We emphasize that γ cp is not given by the inverse of the annealed Green function U cp , which coincides with the expectation of the quenched Green function U (ǫ) cp . It indeed coincides with the expectation of the inverse of the quenched Green function and when the orientations ǫ are truly random, these two quantities are not necessarily equal 5 .

One gets thus a linear growth of the expectations of the range similar to the behavior in the space described in [START_REF] Dvoretzky | Some Problems on Random Walks in Space[END_REF], where a rate γ 3 > 0 is defined similarly, but on a 2-dimensional manifold instead of a 3-dimensional one. The walker visits thus a strictly positive fraction of n sites, on the contrary to the standard planar SRW, for whom the walker typically visits a fraction π log n of n sites, that goes to zero as n goes to infinity, see [START_REF] Bass | Moderate Deviations for the Range of Planar Random Walks[END_REF][START_REF] Dvoretzky | Some Problems on Random Walks in Space[END_REF][START_REF] Jain | The Range of Recurrent Random Walk in the Plane[END_REF][START_REF] Gall | Propriétés d'intersection des marches aléatoires. I. Convergence vers le temps local d'intersection[END_REF]. This can be explained by the larger fluctuations, that make the walker escaping from the ball of radius √ n, and visiting on the way less points already visited. In dimension two, the estimate (2.20) of [START_REF] Dvoretzky | Some Problems on Random Walks in Space[END_REF]

yields lim n E[Rn] n
= 0 but also the convergence in probability. Here, we also get :

Theorem 2.2 [Weak Law of Large Numbers (WLLN)] : R n n P -→ n γ cp = E ρ 1 U (ǫ) cp > 0. (2.3)

Linear growth of the expected range

To prove Theorem 2.1, we follow the road of the original study of [START_REF] Dvoretzky | Some Problems on Random Walks in Space[END_REF], generalized afterwards by Spitzer [START_REF] Spitzer | Principle of Random Walks[END_REF], and write this range as a sum of (dependent) random variables R n = n-1 k=0 1 A k where A k is the event that the walker discovers a new site at the k th step i.e.

A 0 = Ω, A k := {M k = M j , ∀j = 0, . . . , k -1}.
We also introduce the probability of escape at time k to be γ cp (k) := P(A k ). As in [START_REF] Dvoretzky | Some Problems on Random Walks in Space[END_REF][START_REF] Spitzer | Principle of Random Walks[END_REF], but with a different manner, we prove that it in fact coincides with the probability that the walk does not come back to its origin during the first k steps.

Lemma 3.1 Denote, for k ≥ 1, B k := {M l = (0, 0), ∀l = 1, . . . , k}. Then γ cp (k) = P B k .
Proof. On the contrary to the SRW on Z d , we cannot write M n as a sum of i.i.d. random variables, but in fact the result can be deduced from the reversibility of the walk. Write 4 They are related to the notion of capacity of a set reduced to a single point, see [START_REF] Spitzer | Principle of Random Walks[END_REF]. The notation γcp stems for Campanino and Pétritis who first introduced this peculiar random walk in [START_REF] Campanino | Random walks on randomly oriented lattices[END_REF]. 5 This phenomenon occurs rather often in disordered systems or for random walks in random environment.

P(A k ) = x∈Z 2 P(A k ∩ {M k = x}) = x∈Z 2 E ρ P (ǫ) (A k ∩ {M k = x})
and use that for a fixed ǫ, it corresponds to any trajectory in A k starting from the origin a unique reversed trajectory in B k , of equal length and equal weight, that is at the origin at k:

P(A k ∩ {M k = x}) = P ∩ k-1 j=0 {M k = M j } ∩ {M k = x} = m j =m k ∈Z 2 ,j<k E ρ P (ǫ) (M 0 , . . . , M j , . . . , M k ) = (0, . . . , m j , . . . x) = m l =m k ∈Z 2 ,l<k E ρ P (-ǫ) (M 0 , . . . , M l , . . . M k ) = (x, . . . , m l , . . . , 0) = m l =m k ∈Z 2 ,l<k E ρ P (-ǫ) (M 0 , . . . , M l , . . . M k ) = (0, . . . , m l , . . . , -x) = P(B k ∩ {M k = -x})
where we use in the last lines the translation-invariance of ρ. Integrating out over all the possible final points, one gets

P(A k ) = x∈Z 2 P(B k ∩ {M k = -x}) = P(B k ).
Hence, the escape probability at time k coincides with the probability of no return to the origin until time k. These events B k are, on the contrary to the A k 's, decreasing events (B k+1 ⊂ B k ), in such a way that we get a decreasing sequence

1 = γ cp (1) ≥ • • • ≥ γ cp (k) ≥ γ cp (k + 1) ≥ • • • ≥ 0.
Together with the transience of the walk, this proves that the so-called probability of escape γ cp exists and is strictly positive: 0 < γ cp := lim k γ cp (k) ≤ γ cp (k) for all k ≥ 0. We use now the LLT (1.1) to get an estimation the growth of the average range,

E R n = n-1 k=0 P[A k ] = n-1 k=0 γ cp (k). (3.1)
Like in [START_REF] Dvoretzky | Some Problems on Random Walks in Space[END_REF], we partition the paths according to the last return to the origin occurring (strictly) before some given time n. The origin can only be reached at even times, so we consider m = (n -1)/2 for n even (and m = n/2 -1 for n odd) to write, for a given orientation ǫ,

m k=0 P (ǫ) M 2k = (0, 0), M j = (0, 0), ∀j, 2k < j ≤ n -1 = 1 (3.2)
where, by the Markov property of the quenched measure, the summands of (3.2) are

P (ǫ) M 2k = (0, 0) • P (ǫ) M j = (0, 0), ∀j = 2k + 1, . . . , n -1 | M 2k = (0, 0) .
Introduce now the following characteristics for the quenched law, for a given orientation ǫ:

u (ǫ) cp (k) := P (ǫ) [M k = (0, 0)] and γ (ǫ) cp (k) := P (ǫ) [B k ] = P (ǫ) [M j = (0, 0), ∀j, 1 < j ≤ n].
For ρ-a.e. ǫ, the quenched escape probability γ

(ǫ) cp := lim k γ (ǫ)
cp (k) > 0 exists and by symmetry, the probability of discovering a new point at time k is also

P (ǫ) [A k ] = γ (-ǫ) cp (k) = γ (ǫ) cp (k).
The techniques developed by [START_REF] Dvoretzky | Some Problems on Random Walks in Space[END_REF] relies on the LLT, here valid in the annealed set-up, yielding the existence of a strictly positive and finite annealed Green function (1.2) and, for ρ-a.e(ǫ), of a quenched Green function (1.3) in such a way that

U cp = E ρ [U (ǫ) cp ].
The renewal structure inherited from the Markov property is enough to get

P (ǫ) M j = (0, 0), ∀j = 2k + 1, . . . , n -1 | M 2k = (0, 0) = γ (ǫ) cp (n -2k)
so that (3.2) becomes here, for ρ-almost every orientation ǫ and for all n ∈ N m k=0

u (ǫ) cp (2k).γ (ǫ) cp (n -2k) = 1 (3.3)
with m = (n -1)/2 for n odd and m = n/2 -1 for n even. This implies the following

Lemma 3.2 1. For ρ-a.e ǫ, γ (ǫ)
cp .U

(ǫ) cp = 1 and γ cp = E ρ 1 U (ǫ) cp > 0.
2. For all n ∈ N, there exists

B(n) = •(1) such that 0 < γ cp ≤ γ cp (n) ≤ γ cp + B(n).
(3.4)

Proof. Let ǫ such that (1.3) is true, fix 1 < l < m and split the lhs of (3.3) to write it

l k=0 u (ǫ) cp (2k).γ (ǫ) cp (n -2k) + m k=l+1 u (ǫ) cp (2k).γ (ǫ) cp (n -2k) = 1.
Use the monotonicity of γ (ǫ) cp (k) to get a lower bound of the first term of the lhs:

l k=0 u (ǫ) cp (2k).γ (ǫ) cp (n -2k) ≤ γ (ǫ) cp (n -2l) • l k=0 u (ǫ) cp (k)
and the fact that these escape probabilities are indeed probabilities for the second term:

m k=l+1 u (ǫ) cp (2k).γ (ǫ) cp (n -2k) ≤ m k=l+1 u (ǫ) cp (2k)
to eventually get the lower bound γ

(ǫ) cp (n -2l). l k=0 u (ǫ) cp (2k) ≥ 1 -m k=l+1 u (ǫ)
cp (2k). Consider now l -→ ∞ such that n -2l -→ ∞ as n goes to infinity, to get that for ρ-a.e. ǫ γ (ǫ) cp .U (ǫ) cp ≥ 1 or, the quenched Green function being strictly positive, γ

(ǫ) cp ≥ 1 U (ǫ) cp
, ρ-a.s. By monotonicity one gets in particular for all n ∈ N and for ρ-a.e. ǫ

γ (ǫ) cp (n) ≥ 1 U (ǫ) cp . (3.5)
To get the lower bound, we proceed like in [START_REF] Dvoretzky | Some Problems on Random Walks in Space[END_REF] with a weaker result 6 and substract

1 U (ǫ) cp m k=0 u (ǫ)
cp (2k) to both sides of (3.3) to get first that for ρ-a.e. orientation ǫ,

u ǫ cp (0) • γ (ǫ) cp (n) - 1
U (ǫ) cp + m k=1 u (ǫ) cp (2k). γ (ǫ) cp (n -2k) - 1 U (ǫ) cp = 1 - 1 U (ǫ) cp m k=0 u (ǫ) cp (2k) so that u (ǫ) cp (0) • γ (ǫ) cp (n) - 1 U (ǫ) cp ≤ 1 - 1 U (ǫ) cp m k=0 u (ǫ) cp (2k).
Using (3.5) and u , and

γ cp = E ρ 1 U cp .
Eventually, we also get that ρ-a.s., for all n ∈ N

0 < γ (ǫ) cp ≤ γ (ǫ) cp (n) ≤ γ (ǫ) cp + B (ǫ) (n)
where

B (ǫ) (n) = 1 -1 U (ǫ) cp m k=0 u (ǫ) cp (2k) = U (ǫ) cp -m k=0 u (ǫ) cp (2k) U (ǫ) cp
goes ρ-a.s. to 0. Taking the expectations w.r.t. ρ, this yields the annealed result (3.4) where, by dominated convergence,

B(n) = E ρ U (ǫ) cp -m k=0 u (ǫ) cp (2k) U (ǫ) cp = E ρ 1 U (ǫ) cp . ∞ k=m+1 u (ǫ) cp (2k) -→ n 0.
This provides an estimation of the expected range using (3.1) to get

n • γ cp ≤ E[R n ] ≤ n • γ cp + G(n)
where by Cesaro's theorem,

G(n) = n-1 k=0 B(k) = n-1 k=0 E ρ 1 U (ǫ) cp . ∞ l=m(k)+1 u (ǫ) cp (2l) = • n .
One can proceeds similarly in the quenched case and eventually gets Theorem 2.1.

Weak Law of large numbers

Theorem 2.1 provides thus a linear growth of the expectation of the range

E[R n ] n -→ n γ cp = E ρ 1 U (ǫ) cp > 0
similar to the spatial behavior described in [START_REF] Dvoretzky | Some Problems on Random Walks in Space[END_REF] where the limit γ 3 > 0 is defined similarly. This walker goes further than the usual planar one, visiting much more sites but less often.

For the standard SRW on the standard (unoriented) version of Z 2 , the estimate (2.20) of [4]

E[R n ] = n • π log n + O n log log n log 2 n yields lim n E[Rn] n
= 0 while Spitzer [START_REF] Spitzer | Principle of Random Walks[END_REF] also proved that Rn n P -→ n 0. To investigate this weak LLN 7 , we need to estimate the variance of R n , defined to be

V cp (n) := σ 2 (R n ) = E R n -E[R n ] 2 = E[R 2 n ] -E[R n ] 2 (4.1)
7 Established for all d ≥ 2 in [START_REF] Dvoretzky | Some Problems on Random Walks in Space[END_REF], who also derive strong LLN.

which is also the ρ-expectation of the quenched variance, defined for a given orientation ǫ by

V (ǫ) cp (n) := E (ǫ) R n -E[R n ] 2 = E (ǫ) [R 2 n ] -E (ǫ) [R n ] 2 . (4.2)
Introduce for all j < k the events A j,k defined as

A 0,k = A k , A j,k = M k = M l , ∀l = j, . . . , k -1}.
Re-write now (4.1) and (4.2) as follows

V cp (n) = E R 2 n -E R n 2 = E n-1 j=0 1 A j 2 -E n-1 j=0 1 A j 2 = n-1 j,k=0 P A j ∩ A k -P A j .P A k V (ǫ) cp (n) = n-1 j,k=0 P (ǫ) A j ∩ A k -P (ǫ) A j .P (ǫ) A k .
Following carefully again the road of [START_REF] Dvoretzky | Some Problems on Random Walks in Space[END_REF] or [START_REF] Spitzer | Principle of Random Walks[END_REF], we establish now the following bound, not optimal8 but sufficient to get afterwards a weak law of large numbers:

Proposition 4.1 The variance of the range of the SRW on the oriented lattices satisfies

V cp (n) = • n 2 . ( 4.3)
Proof. The main ingredient is a sub-additivity of the summands of the variance, that we cannot get using the standard methods of [START_REF] Dvoretzky | Some Problems on Random Walks in Space[END_REF][START_REF] Spitzer | Principle of Random Walks[END_REF]. Hence, we first work on the quenched law:

Lemma 4.1 For all 0 ≤ j < k, for all ǫ, P (ǫ) A j ∩ A k ≤ P (ǫ) A j .P (ǫ) A j,k . (4.4)

Proof. Use that the quenched law P (ǫ) is Markov for any orientation ǫ to get for 0 ≤ j < k ǫ) {M k = M l , ∀j ≤ l < k} = P (ǫ) A j .P (ǫ) A j,k .

P (ǫ) [A j ∩ A k ] = P (ǫ) {M j = M i , ∀i < j} ∩ {M k = M l , ∀l < k} ≤ P (ǫ) {M j = M i , ∀i < j} ∩ {M k = M l , ∀j ≤ l < k} = P (ǫ) [A j ].P (
Remark 4.1 Inequality (4.4) relies on the Markovian character of the quenched law, not true in the annealed case. Indeed, taking the expectation under ρ in both sides yields

P A j ∩ A k ≤ E ρ P (ǫ) A j .P (ǫ) A j,k
and it is an open question whether the product structure of ρ allows to get

E ρ P (ǫ) A j .P (ǫ) A j,k ≤ E ρ P (ǫ) A j • E ρ P (ǫ) A j,k .
One would get, by translation-invariance of ρ, the standard inequality [START_REF] Dvoretzky | Some Problems on Random Walks in Space[END_REF][START_REF] Spitzer | Principle of Random Walks[END_REF] because

E ρ P (ǫ) A j,k = E ρ P (ǫ) A k-j = P A k-j . (4.5)
Using now the estimate (4.4) and the expression (3.1), we can estimate (4.2)

V (ǫ) cp (n) = 2 n-1 j=0 n-1 k=j+1 P (ǫ) A j ∩ A k -P (ǫ) A j .P (ǫ) A k + n-1 j=0 P (ǫ) A j -P (ǫ) A j 2 ≤ 2 n-1 j=0 P (ǫ) A j • n-1 k=j+1 P (ǫ) A j,k -P (ǫ) A k + n-1 j=0 P (ǫ) A j so that 1 n 2 V (ǫ) cp (n) ≤ 2 n n-1 j=0 P (ǫ) A j • n-1 k=j+1 1 n P (ǫ) A j,k -P (ǫ) A k + E (ǫ) R n n 2 = G n (ǫ)+ E (ǫ) R n n 2 .
The last term of the rhs goes ρ-a.s. to zero by (2.1) while we write

G n (ǫ) = 2γ cp • E ρ 1 n n-1 j=0 n-1 k=j+1 1 n P (ǫ) A j,k -P (ǫ) A k + 2D n (ǫ) = 2(F n (ǫ) + D n (ǫ))
in such a way that we control the annealed variance by

1 n 2 V cp (n) ≤ 2E ρ [F n ] + 2E ρ [D n ].
To deal with the second term, remark that, for given j and k, A j,k = A k ∪ Ãj,k where the events Ãj,k consists of the trajectories visiting at k a point not visited since j but who has been visited before. In particular, since

A j,k ⊂ A 0,k = A k , 0 ≤ 1 n n-1 k=j+1 P (ǫ) A j,k -P (ǫ) A k = 1 n n-1 k=j+1 P (ǫ) Ãj,k ≤ 1 so that 0 ≤ E ρ [D n ] ≤ E ρ 1 n n-1 j=0 P (ǫ) A j -γ cp = E ρ 1 n n-1 j=0 P (ǫ) A j -γ cp = E[R n ] n -γ cp
that goes to zero by (2.2). To deal with F n , we write

E ρ [F n ] ≤ γ cp • n-1 j=0 1 n n-1 k=j+1 P A j,k -P A k ≤ n-1 j=0 1 n γ cp • max j=0,...k-1 n-1 k=j+1 P A k-j -P A k
where to get the last inequality we have used (4.5) for the annealed measure 9 . Now, we can work exactly like in the standard case treated in [START_REF] Dvoretzky | Some Problems on Random Walks in Space[END_REF][START_REF] Spitzer | Principle of Random Walks[END_REF]: The balance between the number of possible points to discover and the number of points already visited reaches its maximum for j = n 2 so that, using (2.2), we get (4.3) because

0 ≤ E ρ [F n ] ≤ γ cp • 1 n • E R n-[n/2] + R [n/2] -R n ≤ γ cp • 1 2 γ cp + 1 2 γ cp -γ cp + •(1) = •(1).
Using Markov's inequality one gets Theorem 2.3, because for all δ > 0

P R n n -γ cp > δ ≤ 1 n 2 δ 2 .E |R n -n.γ cp | ≤ 1 n 2 δ 2 .V cp (n) + 1 δ 2 . γ cp -E R n n 2
and the WLLN in the annealed set-up, by (4.3) and (3.4). As a by-product, one recovers also in the quenched WLLN for ρ-a.e. orientation.

Conclusions and perspectives

Further investigations, in the spirit of Jain et al. [START_REF] Jain | The Range of Transient random walk[END_REF][START_REF] Jain | Further Limit Theorems for the Range of Random Walk[END_REF], would require a quenched local limit theorem or at least more accurate asymptotic of the variance of the range, using e.g. a less crude inequality than (4.4), and in this transient case the relationship between the range and the number of points that are never revisited. We suspect that in fact the variance is of order n 3/2 = n √ n, and that this should lead to an unconventional CLT:

R n -nγ cp n √ n L =⇒ N (0, 1)
like in the three-dimensional case (where the normalization is √ n ln n), while in the twodimensional case the limiting law is the so-called self-intersection local times [START_REF] Gall | Propriétés d'intersection des marches aléatoires. I. Convergence vers le temps local d'intersection[END_REF].

Aknowledegments : I am grateful to Jean-Baptiste Bardet (Rouen), Frank den Hollander (Leiden) and Bruno Schapira (Orsay) for their interest and their advices.

1 U

 1 = 1, let n (and m) going to infinity to get for ρ-a.e. ǫ γ(ǫ) cp ≤

Although the transience under in this quenched law has been proven before, using slightly weaker estimations, but following similar techniques in the vein of Fourier's analysis, see[START_REF] Campanino | Random walks on randomly oriented lattices[END_REF][START_REF] Guillotin-Plantard | Transient Random Walks in Dimension Two[END_REF].

[START_REF] Campanino | Random walks on randomly oriented lattices[END_REF] While it is also proved in[START_REF] Campanino | Random walks on randomly oriented lattices[END_REF] that deterministic alternate horizontal orientations do not break this

recurrence. 3 Later on, Jain et al. ([9, 10], 1970's) established a Central Limit Theorem (CLT), see Section 5.

because we do not know whether the quenched local limit theorem is valid or not.

Investigations around a quenched LLT should lead to Vcp(n) = O n 3/2 , see Section 5.

This step is not true in the quenched case so we cannot get the same bound, at least in this way.