Adrien Leman
email: adrien.leman@orange-ftgroup.com

Julien Faure
email: julien.faure@orange-ftgroup.com

Etienne Parizet
email: etienne.parizet@insa-lyon.fr

A non-intrusive signal-based model for speech quality evaluation using automatic classification of background noises

Keywords: speech quality, background noise classification, non-intrusive model, model based on signal

. These experiments show that background noise can be more or less tolerated by listeners, depending on the sources of noise that can be identified. Using a classification method, the background noises can be classified into four groups. For each one of the four groups, a relation between loudness of the noise and speech quality is proposed.

Introduction

Previous subjective experiments [START_REF] Leman | Influence of informational content of background noise on speech quality evaluation for VoIP application[END_REF] have shown the influence of loudness of background noise on perceived speech quality. An interesting point to note is that their relation depends on meaning associated with the sources of the background noise. For example, if the listener identifies the noise as coming from a source in the vicinity of the talker, some tolerance was noticed for the voice quality assessment. This can be seen in figure 1, for noises coming from: a city environment, inside of a restaurant, and a television. The evaluation of speech quality is higher for these noise sources than for others which do not have informational content. This result was confirmed in two experiments: the first combined different kinds of noises with three different levels of loudness (cf. figure 1), and the second also involved various voice codecs and IP degradations. This effect of background-noise-type influencing evaluation of speech quality is not taken into account in existent models, such as ITU-T PESQ/P.862 [START_REF] Iut-T | P.862 Perceptual Evaluation of Speech Quality Assessment of Narrowband Telephone Networks and Speech Codecs[END_REF] and ITU-T G.107/E model [START_REF] Iut-T ; | The E-model, a computational model for use in transmission planning[END_REF]. The present paper proposes an original model of speech quality perception for situations in which there are different kinds of noises present in the speech signals. First, models relating loudness and type of the background noise to speech quality will be presented. Then, a classification scheme allowing to separation of the four groups of background noises will be described. This model will be tested using stimuli from the first experiment [START_REF] Leman | Influence of informational content of background noise on speech quality evaluation for VoIP application[END_REF] and the results will be compared to the existing PESQ model [START_REF] Iut-T | P.862 Perceptual Evaluation of Speech Quality Assessment of Narrowband Telephone Networks and Speech Codecs[END_REF].

Presentation of the proposed model

Subjective experiments [START_REF] Leman | Influence of informational content of background noise on speech quality evaluation for VoIP application[END_REF] lead us to separate background noise into four classes according to the level of tolerance of noise in the assessment of speech quality:

• Class 1 Intelligible noise. This group includes noise from music or some other speech. This class of background noise is characterized by high tolerance of noise by subjects concerning the speech quality perception, in comparison with a random noise with same loudness.

• Class 2

Environmental noise. This noise has informational content and has given information about the location of the talker, such as city noise, restaurant noise... This class is characterised by light tolerance of noise by subjects concerning the speech quality perception.

• Class 3

Breath noise. This noise is stationary and does not contain informational content. Examples are random pink noise, stationary wind noise or stationary speech noise.

• Class 4

Crackling noise. This noise does not contain informational content and is stationary, such as electric noise. This class is characterised by a significant decrease in speech quality perception, as assessed by subjects, in comparison to random noise with the same loudness. For each of the four classes of noise, a relation between loudness of the noise and estimated speech quality with MOS-LQSN score has been determined (figure 2) from the 152 stimuli used in the first experiment [START_REF] Leman | Influence of informational content of background noise on speech quality evaluation for VoIP application[END_REF]. The classes are empirically labelled for each of the 152 sounds. The optimum relation between loudness of the noise and MOS-LQSN is characterized by a logarithmic regression. Four steps are necessary in applying the speech quality model. First, voice activity detection (VAD) is used to detect the presence of background noise in the audio signal. This technique is described in [START_REF] Itu-T | P.56 Mesure objective du niveau vocal actif[END_REF]. Second, the overall loudness of the background noise is computed using Zwicker's model [START_REF] Zwicker | Psychoacoustics: Facts and Models: Springer[END_REF]. Third, the class of background noise is calculated from signal analysis. Finally, a logarithmic relation is applied according to the class of background noise in order to obtain the MOS Score. The next part of the paper describes the way this classification model is constructed.

Classification of background noises

Methodology

First of all, a set of 632 stimuli was selected, composed of various types of background noises from two experiments explained in [START_REF] Leman | Influence of informational content of background noise on speech quality evaluation for VoIP application[END_REF], and from a public sound database. Eight indicators were then computed on the 632 background noises of this set; some of them are well-known objective measures for the discrimination between different kinds of sound [START_REF] Didiot | Segmentation parole/musique pour la transcription automatique de la parole continue[END_REF] or recognition of real-life sound and speech [START_REF] Istrate | Détection et classification des sons : application aux sons de la vie courante et à la parole[END_REF].

The signal correlation: This is the correlation between the signal and its one sample shifted version (Bravais-Pearson coefficient) 2. The zero-crossing rate (ZCR) of noise 3. The variation of acoustic power of noise 4. The spectral centroid of noise 5. The spectral roughness of noise 6. The spectral flux of noise 7. The spectral rolloff point of noise 8. The harmonic coefficient

The classes are empirically labelled according to the tolerance level in the assessment of speech quality, which was obtained after listening of each sound. The classification tree algorithm [START_REF] Breiman | Classification and regression trees[END_REF] was then used to obtain a full decision tree. The entry parameters to the classification tree algorithm were made up of the 8x632 indicators and the class label of each of the 632 sounds. Post-analysis produced an optimum decision tree using only necessary indicators presented above, and keeping a low classification error.

Stimuli

The set of 632 stimuli was a combination of 344 stimuli used in experiments 1 and 2 (see [START_REF] Leman | Influence of informational content of background noise on speech quality evaluation for VoIP application[END_REF] for detail) and of 288 other stimuli issued from a public sound database. These 288 new stimuli were composed of 48 new sounds, such as circuit noise, wind noise, car noise, vacuum cleaner noise, hairdryer noise, babble noise, natural noise or music noise, presented with six conditions of degradation. To simulate noise for narrow band transmission, each noise signal was sampled at 8 KHz and filtered with a band pass IRS filter (300 -3400 Hz), then encoded and decoded either with G.711 or G.729. To simulate noise for wideband transmission, each sound was sampled to 16 KHz and filtered with a band pass filter using ITU-T P.341 (50 -7000 Hz), then encoded and decoded with G.722. The three coding conditions were presented at two loudness levels (N=63 and 47 dB SPL in the case of random pink noise). Each noise signal was eight seconds long.

Determination of the different classes

Each used background noise for each degradation was attributed to one of the four classes (by the first author) because some that are, perfectly recognisable without degradation may no longer be as such with the insertion of degradation (encoding-decoding / packet loss). Thus, a better source recognition is observed when noise is encoded and decoded with a wideband codec (G.722) than with a narrowband codec (G.711 or G.729).

Presentation of the classification model

This section presents the results of the tree classification method explained in section 3.1. In a construction step, 500 stimuli out of 632 were randomly chosen to compute model parameters. The last 132 stimuli were used to validate the model. The optimum decision tree is presented in figure 3. It shows that only two indicators were necessary to classify the different kinds of noises into four classes. The first is a temporal indicator named "the variation of acoustic power". The second is a spectral indicator named "spectral flux" according to [START_REF] Didiot | Segmentation parole/musique pour la transcription automatique de la parole continue[END_REF].

The temporal indicator represents the time variation of the power of the noise signal. It is defined as the standard deviation of power of all frames of the signal. Power is computed for every frame, each consisting of 512 samples, with an overlap between successive frames of 256 samples (50%), corresponding to a time period of 64 ms per frame, with an overlap of 32 ms with a sample rate of 8 KHz. The acoustics power for frame i, P i is given by: ) 1 log( . 10

1 2 ∑ = = N n n i x N P . ( 1
)
Where n=1…N represents the samples on frame i with N=512, and x n is the amplitude of sample n. When the background noise is longer than one frame, the value IND_TMP of temporal indicator is calculated as the standard deviation of acoustic power P of all frames.

For the noises used, this indicator increases as the noise becomes more and more non-stationary.

The spectral indicator is designated by "IND_FRQ", and is calculated from the power spectral density (PSD) of the background noise. This indicator is determined per frame using 256 samples, corresponding to a time period of 32 ms with a sample rate of 8 KHz. Unlike the temporal indicator, there is no overlap between successive frames. The spectral flux SF represents how quickly the power spectrum of a signal is changing. SF for frame i, SF i is given by:

∑ ∑ ∑ - = - - k k k k k k k i a i a i a i a i SF 2 2 ) ( ) 1 ( ) ( ). 1 ( 1 .
(

Where a k represents the PSD value of the frequency components k of the frame i or i-1. IND_FRQ is defined as the mean of SF coefficient for all frames. Firstly, the proposed tree separates background noise into two categories related to the stationarity of the noise. If the variation of acoustic power is less than IND_TMP=1.03485, then the background noise is considered as stationary, otherwise it is considered as non-stationary. Secondly, these two main categories can be subdivided using the spectral flux indicator. In the first case of stationary noise, if the value of spectral flux is lower than 0.145, the noise belongs to the class "crackling" otherwise it belongs to the class "breath". In the case of non-stationary noise, if the value of spectral flux is lower than 0.280, the noise belongs to the class "environment" otherwise it belongs to the class "intelligible". The predictive potential of the tree can be assessed by calculating the number of background noises that are correctly classified. This proposed tree presents a global percentage of correct classifications of 87.3 %. More precisely, the percentage of correctly classified for each class is as follows:

• 100% for the class "crackling"

• 96.4% for the class "breath"

• 79.2% for the class "environment"

• 95.9% for the class "intelligible" It appears that "environment" class obtains a proportion of correctly classified noises lower than the other classes. It is caused by the similarity of certain noises that can be classified into two classes, for example, wind noise or hair drier sounds which are between environment and breath noises.

Validation of the classification model

The 132 stimuli not taken into account during the learning phase were used to verify the robustness of the classification model. The percentage of correctly classified background noises was 91.47%. Table 1 presents the percentages of the correctly classified noises for three combinations of stimuli: all 632 stimuli, the 500 stimuli used during the learning phase of the model of classification, and the 132 stimuli used in the validation phase.

Advantages and applications

The advantage of the proposed classification model is mainly the low number of indicators used to classify several kinds of background noises into four classes. This model can also be used in real time, for example in telephony applications with an implementation directly at the end of the transmission close to the listener. Moreover, the proposed model of classification is valid with different conditions of degradations like packet loss, or different wideband and narrow band codecs. The classification model of background noises can be used in many applications. For example, according to the classification result a noise cancellation tool can be used or not. If the noise is judged to be helpful, noise cancellation is not performed, as opposed to situations when the noise is considered to be disturbing. The classification model can also be used to identify the type of noise present in speech, helping to find the origin of the degradation, thus enabling improvement of the quality of service. Furthermore, the classification model can be used with existing speech quality models like G.107 [START_REF] Iut-T ; | The E-model, a computational model for use in transmission planning[END_REF] or PESQ [START_REF] Iut-T | P.862 Perceptual Evaluation of Speech Quality Assessment of Narrowband Telephone Networks and Speech Codecs[END_REF], to take into account the different kinds of noises present in speech, in order to improve the performance of existing model.

Speech quality model using classification model vs PESQ model

Finally, the overall speech quality model based on loudness and on classification, as presented in section 2, was evaluated in two steps.

• Firstly, the model was applied using a perceptual loudness determined by subjective experiment described in [START_REF] Leman | Influence of informational content of background noise on speech quality evaluation for VoIP application[END_REF] in order to evaluate the performance of the proposed model with potential errors due only to classification algorithm. • Secondly, the model was applied using an estimation of loudness provided by the Zwicker's overall loudness model [START_REF] Zwicker | Psychoacoustics: Facts and Models: Springer[END_REF] in order to evaluate the performance of the model in its application (without subjective experiment needs). The 152 stimuli of experiment 1 described in [START_REF] Leman | Influence of informational content of background noise on speech quality evaluation for VoIP application[END_REF] were used to compare objectives scores with scores from subjective experiment. PESQ model obtained a correlation of R=0.91 (p<0.001)(see [START_REF] Leman | Influence of informational content of background noise on speech quality evaluation for VoIP application[END_REF]). The PESQ evaluation performance was taken as reference score and was compared with performance of the proposed speech quality model.

Speech quality model using perceived loudness

In this step, the speech quality model was evaluated with a classification model and subjective loudness.

Speech quality model using calculated Zwicker's loudness model

In this step, the speech quality model was evaluated with a classification model and Zwicker's loudness model.

Figure 5: Comparison of MOS scores between subjective experiment and the speech quality model using classification model and Zwicker's loudness model

The labels represent the background noise classes, as defined section 2. When Zwicker's loudness model is used, the correlation coefficient was R=0.93, (p<0.001). This model is not as effective as using subjective loudness, but it is still more accurate than the reference PESQ model (r = 0.91). In the future, Moore's loudness model will be tested to compare the accuracy of the two loudness models.

Conclusions

The present article demonstrates that the different types of background noises present in speech signal should be taken into account in speech quality models. The developed nonintrusive model achieves a very good performance in comparison with existing intrusive models like PESQ model. It uses only two indicators issued from signal analysis and the calculated loudness. In this sense, it could be employed in real time to evaluate speech quality on a telephony network. An interesting point to note is that the proposed speech quality model, using classification, as well as giving a MOS score, allows identifying the type of noise present in speech. This can be helpful in supervision of tasks in communication networks, thus improving the quality of service.

Figure 1 :

 1 Figure 1: Differences of speech quality for the six kinds of noises for three loudness levels (the flat line represents the situation without background noise)

Figure 2 :

 2 Figure 2: relation between noise level and speech quality for the four classes of background noises.

Figure 3 :

 3 Figure 3: Decision tree classification of the four classes of noises.

Figure 4 :

 4 Figure 4: Comparison of MOS between subjective experiment and speech quality model using classification model The labels represent the background noise classes from 1 to 4, obtain by the classification model, as defined in section 2. The performance of both methods of regression functions and classification model is measured by the correlation coefficient between the MOS scores issues from the subjective experiment and the scores estimated by the model. The correlation score was R=O.98, (p<0.001).

Table 1 .

 1 Percentage of correctly classified background noises for three subsets of the stimuli corpus.

	Number of	Percentage
	stimuli	correctly
	considered	classified
	632 (total)	87.28 %
	500 (learning)	86.20 %
	132 (test)	91.47 %


Susanne Salmon-Alt
email: susanne.alt@loria.fr

Bertrand Gaiffe
email: bertrand.gaiffe@loria.fr

Laurent Romary
email: laurent.romary@loria.fr

Questioning Indefinites in Dialogues

The standard analysis of indefinites (e.g. Russell or more recently in the Discourse Representation Theory) views them as introducing a new discourse referent that is considered as independent from both the textual and extra-textual context. Still it can be observed that in many situations such as dialogue there are cases where sequences of indefinites are explicitly referring to the same entity, when for instance its properties have to be refined. On the basis of a corpus study of task-oriented dialogue transcriptions, we show that indefinites can only be coreferential if the events that bear them as arguments are coreferential as well. We thus identify the basic cues that may lead to the automatic determination of such situations (e.g. adverbials, sub-categorising statements etc.) and apply them to analyze our corpus examples. We also show that the configuration of dialogue acts (re-statements, question-answer pairs) directly influence the subsequent use of indefinite following an initial statement.

Standard Analysis of Indefinites

The standard analysis of indefinite noun phrases is based on Russell, viewing them as introducing a quantifier. In traditional first order logic, existential and universal quantification states a relation between the denotations of two predicates, and is opposed to designation which consists in naming individuals by constants. For a sentence like (1), the standard translation for a is the following :

(1) A man is walking : ∃x man(x) ∧ walking(x)

The advantage of this analysis is to isolate noun phrases which do not refer to a particular individual, and to give a rather good approximation for linguistic observations like those well known as "quantifier scope ambiguities". But an important limitation of this view is that it is unable to give a correct account of phenomena like cross-sentential anaphora and "donkey sentences" [START_REF] Kamp | A Theory of Truth and Semantic Representation[END_REF].

This limitation was one of the criteria 1 for considering that indefinites in a restricted sense -a N, Ns, two Ns -are not to be treated as quantifiers like at least one N, every N, exactly two Ns. It leads to a separate treatment of quantified NPs and indefinites in the DRT framework [START_REF] Kamp | From Discourse to Logic[END_REF]. Whereras quantified NPs introduce a tripartite structure, where the quantifier expresses a particular relation between a restrictor and a scope, indefinite NPs introduce just a new variable for an individual. In the following, we concentrate on such indefinites.

The fact that indefinites introduce a new variable is intended to reflect the idea that they are used to introduce new discourse referents, whereas definite descriptions, demonstratives and pronouns are used to refer to already known entities. Such a correlation between linguistic 1 Other criteria and a more detailed overview can be found in [START_REF] Corblin | La condition de nouveauté comme défaut[END_REF].

forms and assumed familiarity or cognitive status has been proposed in particular by Prince's Taxonomy (1981) and refined by the Givenness Hierarchy [START_REF] Gundel | Givenness, Implicature and the form of referring expressions in discourse[END_REF]. For both, the use of indefinite descriptions is optimally associated to "brand new" entities [START_REF] Prince | Toward a taxonomy of given-new information[END_REF], for which the hearer can only access a representation of the type described by N [START_REF] Gundel | Givenness, Implicature and the form of referring expressions in discourse[END_REF]. But following Gundel et al., a cognitive status of the Givenness Hierarchy entails all lower statuses, and a particular form can be often replaced by forms which require a lower status. Since the status "type-identifiable" is entailed by all other statuses, all other statuses meet necessary conditions for use of the indefinite article. Nevertheless, as shown in data from different languages, it is not the case. Therefore, [START_REF] Gundel | Givenness, Implicature and the form of referring expressions in discourse[END_REF] invoke supplementary conversational implicatures, stating that the use of an indefinite noun phrase implicates that the referent is not uniquely identifiable, and hence not familiar.

Related to this cognitive aspect of the use of indefinites -non familiarity -is a linguistic one, which is context independance. From a linguistic point of view, [START_REF] Corblin | Indéfini, Défini et Démonstratif[END_REF] opposes the category of indefinites to the categories of definites and demonstratives on the basis of their relations to the context. He considers the category of indefinites as a typically context independent category, taking this feature as a consequence of the basic referential operations associated with the interpretation of indefinites : enumeration and extraction. This means, that a sentence of the type "n N X" (Two dogs bark) an always be interpreted as an extraction of n individual values from the the class of N, based on information given by X. It follows from this principle that each possible extraction is strictly independent from all the others, since the conditions for an extraction are fully defined by a given class N, a number n and predicative information X. This view on the functioning of indefinites excludes any connection to the context or to previous extractions.

The condition of non familiarity and the interpretation principle of context independance justify the standard view on indefinites, which is a non coreferential one. Indeed, coreference -defined as referentiel identity for two or more linguistic forms [START_REF] Milner | Ordres et raisons de langue[END_REF] -links usually a first expression introducing a new referent to subsequent mentions of this referent (see example 2) : (4a) A et tu prends une deuxième barre take a second line (4b) A une petite a small one (2) A man is walking. The man is followed by a dog.

(5a) A et tu vas prendre une ligne verticale and you have to take a vertical line Since the referent has already been isolated via the first mention making it uniquely identifiable, the conditions of non familiarity and context independance do not hold for subsequent mentions. Therefore, the use of a second indefinite intended to refer to the same referent is not suitable (see example 3) :

(5b) B une grande ? a big one ? (5c) A une grande oui a big one, yes (6a) A donc au bord de cette route, il y a deux (3) A man is walking. A man is followed by a dog. maisons so beside this road, there are two houses (6b) A donc une maison qui se trouve à gauche Not only does this not correspond to the cognitive status of the referent, but it would also suggest a context independent interpretation : In (3), the second indefinite simply operates a second extraction of an individual from the class MEN, but since nothing forces nor prevents the identity of the two mentioned individuals, the discourse is somehow odd. de cette route et une autre à droite one house on the left of this road and another one on the right (7a) A et tu vas prendre un rond and you have to take a circle The standard analysis of indefinites -seeing them as introducing new discourse referents which are non familiar and context independant -seems to fit well in the general picture. Still, it does not account entirely for the data we observed.

(7b) B un grand ou un petit ?

a big one or a small one ? (7c) A un petit a small one (8a) A alors, il va falloir que tu fasses un toit

The Data

now you have to make a roof (8b) A il faut que tu mettes un grand triangle Our data stems from a french corpus of task oriented dialogues2 , involving two persons, A and B, in a task of figure manipulation. Following the instructions given by a A, B has to reconstruct simple pictures(Figure 1a). The pictures are composed of geometrical figures, available from a virtually illimited stack of objects of various shapes (Figure 1b).

you have to put a big triangle

In (4), ( 5) and ( 7), there are respectively two, three and four indefinites specifying the same referent, i.e. the figure to be manipulated. In (6b), the two indefinite noun phrases une maison qui se trouve à gauche de cette route and une autre à droite do not introduce new referents, but rather refer to the same entities as deux maisons in (6a). Finally, in (8), un toit and un grand triangle stand for the same object, even if they project probably different points of view on this entity.

In each of these cases, introducing two different discourse referents for the indefinite noun phrases cannot be the correct reading, since the indefinite descriptions are clearly understood as referring to the same object. What we need therefore is first a mechanism which blocks the introduction of new referents for indefinites under certain conditions, and second, a clearer idea about what can be the very nature of these conditions.

Cues for Coreferential Indefinites "Condition of newness" as a default

A proposition concerning the first point -blocking the introduction of new discourse referents for indefinites under special conditions -has been elaborated by [START_REF] Corblin | La condition de nouveauté comme défaut[END_REF]. He proposes to consider the "condition of newness" underlying the analysis of indefinites within the DRT framework as a default condition. From a logical point of view, he first shows that the introduction of two different discourse referents for two indefinite descriptions does not have any consequences on the model Analysing the dialogues, we found several cases where sequences of indefinites are explicitly referring to the same entity : theoretic interpretation of a DRS. Indeed, defining embedding as a function from the universe of the DRS into the universe of the model does not exclude the possibility of mapping two different discourse referents onto the same individual in the model, since this relation is not an injective one. This means that the standard version of DRT [START_REF] Kamp | From Discourse to Logic[END_REF] does not predict any difference between a coreferential and a non coreferential use of indefinites.

In order to strengthen the intuition that it is much more natural to use two indefinites for two different individuals, but without excluding definitly a coreferential use, Corblin proposes to extend the standard version of the theory regarding to two points : First, the embedding function is redefined as an injective function. Second, the rule for indefinites is redefined as a defeasible rule, stating that an indefinite is interpreted as introducing a new discourse referent, as long as there are no explicit indications against this.

The problem is now to give a more detailed, and ideally formalized description of the conditions under which this rule has to be overwritten. [START_REF] Corblin | Indéfini, Défini et Démonstratif[END_REF][START_REF] Corblin | La condition de nouveauté comme défaut[END_REF][START_REF] Corblin | Les formes de reprise dans le discours[END_REF] mentions only some informal cues, like enumeration of properties ( 9), previous announcements (10) and identity statements (11).

(9) Tu as trompé Marie. Tu as déçu une femme qui t'adorait.

(10) Here is a story about Mary. One day, a woman crossed the road… (11) Pierre was looking for Mary. A woman crossed the road. It was Mary.

The last type of examples seems to play a central role in suspending the default interpretation of indefinites by stipulating explicitly -through the use of the verb to bethe identity of the mentioned entities. It can be related to another -may be the best known -case of coreference between indefinites, which is an attributive use 3 , like in (12). ( 12) My teacher is a woman.

In these cases, the indefinite is not used in order to isolate, via the specific reference calculus for indefinites, a referent, but rather to define a property of a referent identified independently, based on discourse features.

Discourse features, and more specifically rhetorical structure (Mann and Thompson, 1986) or discourse relations [START_REF] Asher | Reference to Abstract Objects in Discourse[END_REF] can also be seen as indicators to take into account the interpretation of ( 9) and ( 10). This brings us to the next section, which relates recent work bringing together a particular kind of discourse structure and coreference between indefinites.

Event Coreference and Indefinites

In a recent paper on event coreference and discourse relations within the framework of SDRT [START_REF] Asher | Reference to Abstract Objects in Discourse[END_REF], [START_REF] Gaiffe | Coréférence événementielle et relations de discours[END_REF] give evidence for the need of a 3 We do not use "attributive" in the sense of [START_REF] Donnellan | Reference and Definite Descriptions[END_REF].

new discourse relation Particularisation. The arguments are based on the observation of discourses like ( 13) and ( 14) :

(13) Ted damaged a garment. He stained a shirt. ( 14) Guy experienced a lovely evening last night.

He had a fantastic meal.

(14) is a classical example of Elaboration, since the event introduced in the second sentence (S2) is a part of the event introduces in the first sentence (S1). Example (13), however, cannot be analysed like this. Indeed, the event introduced in S2 is not a part of the event introduced in S1 : the events are the same. In other words, ( 13) is a particular case of event coreference, where the second sentence contains more specific information about the event than the first one [START_REF] Danlos | Event Coreference between two sentences[END_REF]. For this kind of discourse configuration, a new discourse relation Particularisation has been proposed. The introduction of this new relation is justified in particular by the fact that event coreference implies necessarily a coreferential relation between the arguments of the same thematic role. This is for example the case for the indefinites a garment and a shirt in (13).

Therefore, the discourse relation Particularisation can be useful regarding our goal -establishing formal criteria overwriting the default rule for the introduction of a new referent for an indefinite. Indeed, since Particularisation → event coreference → argument identity, Particularisation can be seen as one of the criteria we are looking for. Applied to (13), it means, that the Particularisation relation between the first and the second event cancels the introduction of a new discourse referent for the indefinite a shirt by setting it identical to another one.

The problem we have to solve then is to establish a Particularisation relation between two discourse segments π1 and π2, corresponding to S1 and S2. Following [START_REF] Gaiffe | Coréférence événementielle et relations de discours[END_REF], this can be done based on a set of linguistic constraints C part . If π1 and π2 have to be related by a discourse relation τ, and S1 and S2 met the constraints C part , then the Particularisation relation is inferred by default (>) :

(τ, π1, π2) ∧ C part > Particularisation (π1, π2)
The elements of C part are the following : (a) Cue phrases : S1 and S2 are not related by a cue phrase, excepted such cue phrases as more precisely or in fact. (b) Semantic relations between the constituents of S1 and S2 : In order to concentrate on what will be useful in the following, we limit ourselves to cases where the predicates of S1 and S2 are identical 4 . In this case, the conditions for a particularizing event coreference between S1 and S2 are given below (Arg n r stands for an argument of the predicate of sentence n, with the thematic role r, with n ∋ {1,2,..} and r ∋ {agent, patient,…}) :

particularizing_event_coreference (S1,S2) if Predicate 1 =Predicate 2 ∧ for each Arg 2 r : Arg 2 r = SPEC (Arg 1 r ) ∨ Arg 2 r = IDENT(Arg 1 r
) and some other element in S2 brings new information SPEC stands for a relation of semantic specification and includes hyponomy (a garment vs. a shirt) and identification (a tree vs. a tree near the house). IDENT stands for a semantic relation of identity and includes pronominal anaphora (a tree vs. it) and semantic identity (same expression, synonymy,…). Roughly speaking, these conditions state that, if the predicates of two sentences are identical, either the arguments in S2 have to give more information than the arguments in S1, or, if the the arguments do not give new information, another element in S2 (for example, a temporal adverbial like yesterday) has to do it.

Bringing them together…

Our main goal is to account for coreferential indefinites, such as presented in section 2. Therefore, we were looking for a mechanism integrating coreferential indefinites into a DRT-like semantic framework, and for linguistic cues triggering this mechanism. A suitable mechanism has been proposed by [START_REF] Corblin | La condition de nouveauté comme défaut[END_REF] -see section 3.1. [START_REF] Gaiffe | Coréférence événementielle et relations de discours[END_REF] consider the Particularisation relation within an SDRT-like framework as a cue for coreference between indefinites -see section 3.2

The main steps for dealing with indefinites can thus be defined as follows : If an indefinite occurs in a sentence S i giving raise to an S-DRS π i , then

-the indefinite introduces a new discourse referent x into π i -if π i has to be linked to a previous S-DRS π i-1 by a relation τ and the conditions for a particularizing discourse C part are met, then a Particularisation relation is inferred by default :

(τ,π i-1 , π i ) ∧ C part > Particularisation (π i-1 ,π i ) -Particularisation(π i-1 ,π i )
implies event coreference between S1 and S2, and event coreference implies the identity of the arguments -therefore, x has to be marked as identical with another discourse referent of π i-1 Applying this to the toy example (15) yields to :

4.

4.1.

Application to the data

In this section, we try to apply the machinery presented in 3. This example contains two indefinites, une deuxième barre and une petite, specifying the same object. Therefore, the discourse referent introduced for une petite has to be merged with the referent for une deuxième barre.

One possibility to justify this is to establish a Particularisation relation between the discourse segments for (4a) and (4b). Nevertheless, the problem is more complicated than for the toy examples : The first difference concerns the illocutionary force of the discourse segments. Up to now, Particularisation has been used for statements, whereas (4a) and (4b) are orders. The second difference concerns the syntactical completeness of the utterances. Since we are interested in the modelling of spoken discourse, we have to deal with additional phenomena such as VP-and noun head ellipses, like in (4b).

Our representation of the speech acts and propositional contents follows [START_REF] Grisvard | An Event Based Dialogue Model and its Implementation in MultiDial2[END_REF] Indeed, at a first time, all we know about the propositional content from the ellipsis is the introduction of a small entity. However, (4b) being an order, the eventuality under its scope must be a future event which the hearer as an agent [START_REF] Grisvard | An Event Based Dialogue Model and its Implementation in MultiDial2[END_REF]. From the dialogue context, and taking into account discourse coherence constraints such as Common Theme Maximization [START_REF] Asher | Discourse Parallelism, Scope, and Ellipsis[END_REF], we infer supplementary information about π 2 : the category of e' and of s, and the fact that s has to be an argument of the event. Intergrating this information into π 2 leads to : The agent is the same in (4a) and (4b). The category of the predicates are compatible. The patients of (4a) and (4b) are compatible too : they are of the same category, as required in [START_REF] Gaiffe | Coréférence événementielle et relations de discours[END_REF]. Since nothing has been detailed concerning the modifiers, we consider here that it is sufficient to have modifiers which are not mutually exclusive 5 . Since small do not exclude 4.2. 5 In further work, this hypothesis needs to be refined in order to take into account more fine-grained linguistic observations : [START_REF] Corblin | Indéfini, Défini et Démonstratif[END_REF], for example, points out that the use of different types of modifiers can be seen as an indicator for a non coreferential interpretation, even for second, C part holds and we can infer Particularisation (π 1 ,π 2 ). From that follows that the events in π 1 and π 2 are the same and therefore, s in π 2 has to be identical with l in π 1 : π 2 : ∃s∃e' small(s) ∧ EVENT(e', B) ∧ e' > now ∧ category(EVENT) = take ∧ category(s) = line ∧ e = e' ∧ s = l

In comparison to previous examples, the Particularisation relation holds here between the propositional content of two orders, and not between two statements.

Example type B (5a) A et tu vas prendre une ligne verticale

and you have to take a vertical line (5b) B une grande ? a big one ? (5c) A une grande oui a big one, yes

The dialogue in example (5) contains three indefinites specifying a same referent : une ligne verticale (5a), une grande (5b) and une grande (5c). Here, the problem is a little bit more complex than in (4) : Not only have we to insert a discourse relation justifying the identity between indefinites, but we have also to deal with typically dialogical aspects, such as questions and answers.

The first step is the introduction of a representation for (5a) : tell_to(A, B, π 1 ) with : π 1 ∃l∃e line(l) ∧ vertical(l) ∧ take(e,B,l) ∧ e > now Treating (5b) consists then in resolving the ellipsis, like in (4). Additionally, (5b) is a question, and we consider it as a form of yes-no question (which can be paraphrased as Should I take a big vertical line ?). Therefore, it introduces a proposition for which the truth has to be validated in the continuation of the dialogue : ask_if(B, A, π 2 ) with :

π 2 ∃b∃e' line(b) ∧ vertical(b) ∧ big(b) ∧ take (e',B,b) ∧ e' > now
definite descriptions, such as in : Cette rose rouge me gêne. Je vais jeter la rose fânée. We think, however, that this assumption is a little bit too strong. It is also possible that the conditions in dialogues with an immediatly accessible perceptual environment are not exactly the same as in discourse, where the objects can be identified only based on discursive information.

-ellipse comme en (4) … ? pas très clair… π 2 can be attached to π 1 by a discourse relation NotEnoughInformation [START_REF] Asher | Varieties of Discourse Structure in Dialogue[END_REF]. ( 5c) has an illocutionary force of say_that.

-relation QAP entre CP ou entre AdL ?

Example type C

say_that(A, B, π 3 ) (6a) A donc au bord de cette route, il y a deux π 3 , introduced for the propositional content of (5c), is a response to (5b). Therefore, the relation between π 2 and π 3 is QuestionAnswerPair [START_REF] Asher | Questions in Dialogue[END_REF]. maisons so beside this road, there are two houses (6b) A donc une maison qui se trouve à gauche Since the ask_if act can be merged with the say_that act into a global say_that act, where π 3 confirms the truth of π 2 , it yields to a new representation with a new S-DRS π 2' . de cette route et une autre à droite one house on the left of this road and another one on the right In example ( 6), deux maisons introduces a new complex discourse referent with a cardinality constraint. The indefinites une maison qui se trouve à gauche and une autre à droite introduce new discourse referents too, but the new referents have to be related to the complex one, since they refer to parts of it. say_that(A, B, π 2' )

π 2' ∃b∃e' line(b) ∧ vertical(b) ∧ big(b) ∧ take(e',B,b) ∧ e' > now
This new DRS may be attached to π 1. The conditions C part holds : there are no discourse cues linking the utterances, and the semantic relations are the following :

π1 ∃h∃r∃s house(h) ∧ card(h) = 2 ∧ road(r) ∧ state(s) ∧ beside(s, h, r) (6b
) can be interpreted as : say_that(A, B, π 2 ) The agent and the predicate are the same in (5a) and (5b). The patient in (5b) is more specific, since grande ligne verticale implies ligne verticale. Therefore, C part holds, and we can infer Particularisation (π 1 ,π 2' ). The final discourse structure of ( 5) is given in Figure 2. At this stage, nothing says that y and z are part of m. Postulating Particularisation(π 1 ,π 2 ) would lead to this result. However, as defined in Gaiffe and Danlos (1999), this relation holds between events and not between states. Therefore, we have to adapt it to coreference between states. Let us say that the conditions on discourse cues remain inchanged, and the conditions on the semantic relations concern the arguments and the predicate of the state.

The relation could be justified since there are no discourse cues, and with regard to the following reasoning : Figure 2. Discourse Structure for (5)

From Particularisation (π 1 ,π 2' ) follows, that the events in π 1 and π 2' are the same and so do the particpants : on_the_left_of(s, x, y) > beside(s, x, y) on_the_right_of(s, x, y) > beside(s, x, y)

π 2' ∃b∃e' line(b) ∧ vertical(b) ∧ big(b) ∧
take(e',B,b) ∧ e' > now ∧ e' = e ∧ b = l ∧ e > now meaning that the states being on the left and being on the right are more specific than the state being beside and, therefore, include it. The identity of the argument y, road, is guaranted, since it is used deictically in (6a) and (6b). The agents of state s, s' and s'' are semantically compatible. Now, what happens here is a Particularisation relation holding between, on the one In this example, the Particularisation relation has been extended in a manner to hold between the propositional content of an order (tell_to) and a statement (say_that). problèmes : hand, the sum of the states s' and s'' (π2), and, and the other hand, the state s (π1). Therefore, the sum of the agents of s' and s'' has to be identical to the agent of s. From this, it follows that the two indefinites in (6b) introduce referents which are parts of the referent introduced in (6a).

It is worth to mention that the Particularisation relation holds indeed between s and the sum -and not only one part -of s' and s''. In fact, a discourse composed only of s and s' would be awkward :

(16) There are two houses beside the road. One house stands on the left of this road.

An explanation for this is the fact that Particularisation cannot hold between the two sentences, since the cardinalities of the arguments are incompatible. But this example seems also to indicate that the Elaboration relation needs to be redefined more precisely : In fact, such as defined in [START_REF] Asher | Temporal Interpretation, Discourse Relations and Common Sense Entailement[END_REF], nothing prevents from the establishment of such a relation between the states in ( 16). That means that the awkwardness of this example cannot be predicted with the current state of the definition of this discourse relation.

Example type D (7a) A et tu vas prendre un rond

and you have to take a circle (7b) B un grand ou un petit ?

a big one or a small one ? (7c) A un petit a small one This example differs from (5) in one point : the question in (7b) is not a yes-no-question, but a whquestion about the kind of object to be manipulated. The specification of this object is realized through the use of four indefinites. Establishing a Particularisation relation between (7a) and a complex segment composed of (7b) and (7c) would be one possibility to treat these indefinites adequatly.

As in (5), the first utterance is an order of the form : tell_to(A, B, π 1 ) with : The agent and the predicate are the same for π 1 and π 2'' .

π 1 ∃c∃t circle(c) ∧ take(t
The patient in π 2'' is more specific, since petit cercle implies cercle. Therefore, C part holds, and we can infer Particularisation (π 1 ,π 2' ).

From Particularisation (π 1 ,π 2'' ) follows, that the events in π 1 and π 2'' are the same and so do the particpants : π 2'' ∃s∃e small(s) ∧ take(e, B, s) ∧ circle(s) ∧ e > now ∧ e = t ∧ s = c

Example type E

(8a) A alors, il va falloir que tu fasses un toit now you have to make a roof (8b) A il faut que tu mettes un grand triangle you have to put a big triangle

For this example, it seems impossible to establish the coreference of the indefinites un toit and un grand triangle on the basis of linguistic indicators for event coreference. We do not have cue phrases, nor semantic relations linking the arguments or the predicate. Indeed, even if mettre un grand triangle can be seen as specifying the action of faire un toit in this particular context of the task, establishing this relation needs to take into account extralinguistic knowledge. [START_REF] Danlos | Event Coreference between two sentences[END_REF] proposed therefore to extend the notion of hyperonomy between lexical items so as to cover extralinguistic hyperonomy between clauses. This type of extended hyperonomy is not only close to the notion of inference, but it depends also on the application specific context. One possibility to treat example (8) would be to use an inference rule, such as : R1 : putting a triangle > moving geometrical figures modelling the fact that putting a triangle is a particular form of moving geometrical figures. In addition, we need an application specific rule, stating that in this context, making pictures (such as a roof) consists in moving geometrical figures : R2 : moving geometrical figures > make a roof Based on this knowledge, it is possible to infer that putting a triangle is a specification of making a roof, and therefore, (8a) and (8b) refer to the same event. Since event coreference implies the identity of the arguments, a roof and a triangle have to refer to the same entity.

Summary and Discussion

The standard analysis of indefinites sees them as context independent and therefore non coreferential. However, we presented corpus examples, containing sequences of indefinites explicitly referring to the same entity. The problem was then to account for such cases in an DRT or SDRT-like framework.

This paper presents an attempt to do this, based on recent work on a new discourse relation -Particularisation. This relation has one specificity : it implies the identity of the participants involved in the related events. It can therefore be considered as one possibility to take into account coreferential readings of indefinites.

However, the Particularisation relation has been defined for discourse and not for spoken dialogues. Adapting it to our dialogue examples demands in particular to deal with NP-and VP-ellipses and with a variety of speech acts -questions, answers and orderswhich are different from statements. The first problem can be (partially) solved by taking into account the second one : Indeed, it has been shown that different speech acts impose different constraints their propositional content [START_REF] Grisvard | An Event Based Dialogue Model and its Implementation in MultiDial2[END_REF]. Based on this observation and on work about common theme maximazation [START_REF] Asher | Discourse Parallelism, Scope, and Ellipsis[END_REF], is it possible to infer missing information. In order to deal with the second problem -the variety of speech acts -it is first necessary to combine them into more complex discourse segments (for example, a question and an anwser into a statement). Secondly, we have to admit that Particularisation can hold not only between statements, but also between orders, between an order and a statement, and between a statement and the sum of several statements.

The mechanism we present here may seem quite complicated, if compared to the mechanisms for identity postulation for anaphora or identity assertion for to be constructions in DRT. Nevertheless, we think that there are necessary since a coreferential reading of indefinites does not function in exactly the same way as anaphora resolution or identity assertion.

Concerning anaphora resolution in DRT, the principle consists in introducing a new discourse referent and to choose a suitable antecedent from those which are accessible in the discourse universe. The difference with the coreferential reading of indefinites is the choice of the antecedent : whereas the only choice constraints for antecedents of anaphora are pragmatic ones (excepted gender, number and semantic restrictions), there is no choice at all for coreferential indefinites involved in a Particularisation relation : the identity is mandatory for the arguments of the same thematical role.

The main difference with identity assertions such as in Fred is a linguist is the following : for coreferential indefinites in particularizing discourses, the identity is not asserted, but stipulated. Kamp and Reyle (1993 : 258) point out that this is not a trivial point, even if the truthconditional interpretations for stipulated and asserted identity are the same. Stipulated identity (represented by a condition x = y) represents the fact that a certain NP is being used as a means for picking up a certain discourse referent introduced by independent means. Asserted identity (represented by a condition x is y) represents the fact that the interpreter understands the identity statement of x and y, but it does not mean that he or she thinks necessarily that this statement is true. If needed, such a condition, in which no conflation has taken place, can in some way be marked as "dubious", in order to reflect the interpreter's epistemic state more accurately.

Finally, given the unusual mechanisms involved in coreferential readings of indefinites, it seems worth to ask why speakers use indefinites in such a way. The response tho this question lies in the specific interpretation principle for indefinites : As opposed to definites, demonstratives and pronouns, indefinites do not presuppose an external mechanism in order to identify a particular individual : they don't designate. The only thing they do is to provide information about properties of individuals satisfying the description. To put it in other words, an indefinite description "a N" presupposes a domain of entities of type N, but cannot be used to identify a particular individual of this domain. In many cases, this domain is context dependent, either given by discourse information or by perceptual information, as it is the case for our dialogues : here, the interpretation domains for the indefinites are provided by the virtual stacks of geometrical figures (Figure 1b). To give an example, an expression like a triangle presupposes the existence of a set of triangles. Such a domain of triangles is indeed available, given by the virtual stacks of big and small triangles, represented explicitly in (Figure 3). The utterance Take a triangle means then that the hearer has to choose one of the triangles of this domain. Now imagine that the speaker would like to precise the size of the triangle which has to be manipulated. Since there are always more than one possible referents in the perceptual domain, he has to use an indefinite description Take a small triangle. A definite description Take the small triangle would be inappropriate, simply because the structure of the perceptual domain don't allow the hearer to identify uniquely a particular triangle.

What we would like to stress here is the important role of the contextual structure for the use of different types of referring expressions. Concerning the use of coreferential indefinites, we assume the following : Since an indefinite description is not used to uniquely identify a referent, but to identify a contextual domain, the specific role of a sequence of coreferential indefinites is to state a relation between two or more domains. In case of Particularisation between two utterances, this relation is a domain restriction, like in our corpus examples.

Figure

  Figure 1a. Example of a picture to construct

Figure 1b .

 1b Figure 1b. Available geometrical figures

( 15 )(

 15 Ted damaged a garment. He damaged a shirt. S1 : Ted damaged a garment. π 1 ∃g∃e garment(g) ∧ damaged(e,Ted,g) S2 : He damaged a shirt. π 2 ∃s∃e' shirt(s) ∧ damaged(e,h,s) ∧ h = ? (τ,π 1 , π 2 ) ∧ C part , since : (a) no cue phrases linking S1 to S2 π 1 , π 2 ) ∧ C part > Particularisation (π 1 ,π 2 ) Particularisation(π 1 ,π 2 ) → event coreference → argument identity π 2 ∃s∃e' shirt(s) ∧ damaged(e,h,s) ∧ e'=e ∧ s=g ∧ h = Ted Following this reasoning, the coreferential relation between the indefinites a garment and a shirt is established, based on the Particularisation relation between the two sentences of (15).

  3. to our corpus examples. Since the criterion of Particularisation has been introduced for examples taken from written discourse, we have to adapt it in several ways to oral dialogues. Nevertheless, we try to keep the same backbone of the reasoning, based on a comparison of the predicates and arguments in order to obtain a coreferential reading for the indefinites occuring in our corpus examples Example type A (4a) A et tu prends une deuxième barre take a second line (4b) A une petite a small one

  . An utterance is represented as IF ( S, H, PC) with IF = Illocutionary Force {tell_to, say_that, ask_if, ask_wh-}, S = Speaker, H = Hearer and PC = Propositional Content. The propositional content is equivalent to an S-DRS. Representing the first utterance of (4) in this form leads to : tell_to(A, B, π 1 ) with π 1 : ∃l∃e second(l) ∧ line(l) ∧ take(e, B, l) ∧ e > now Introducing a representation for (4b) gives raise to : tell_to(A, B, π 2 ) with π 2 : ∃s∃e' small(s) ∧ EVENT(e', B) ∧ e' > now

π 2 :

 2 ∃s∃e' small(s) ∧ EVENT(e', B) ∧ e' > now ∧ category(EVENT) = take ∧ category(s) = line The next step is linking π 1 and π 2 by a discourse relation. Therefore, the conditions C part for a particularizing discourse have to be tested. There is no discourse cue between (4a) and (4b), and the semantic relations are the following :

  (6a) leads to a first representation of the speech act as : say_that(A, B, π 1

  with :π2 ∃y∃z∃r'∃s'∃s'' house (y) ∧ house(z) ∧ state(s') ∧ state(s'') ∧ road(r') ∧ on_the_left_of(s',y, r') ∧ on_the_right_of(s'',z , r') ∧ r' = ?

Figure 3 .

 3 Figure 3. Interpretation domain for a triangle

  ∃s∃e small(s) ∧ take(e, B, s) ∧ circle(s) ∧ e > now This new DRS may be attached to π 1. The conditions C part holds : there are no discourse cues linking the utterances, and the semantic relations are the following :

	π 2 λNP. [NP] [λx. ∃e take(e, B, x) ∧ circle(x) ∧ (big(x) ∨ small(x)) ∧ e > now]
	(7c) is a response to (7b), providing the NP which has
	to be applied to π 2 .
	say_that(A,B, π 3 )
	with
	π 3 λP. ∃s small(s) ∧P(s)
	Applying this to π 2 yields to : π 2'' λP. ∃s small(s) ∧P(s) [λx. ∃e take(e, B, x) ∧ circle(x) ∧ (big(x) ∨ small(x) ∧ e > now]
	π 2'' ∃s small(s) ∧ ∃e take(e, B, s) ∧ circle(s) ∧ (big(s) ∨ small(s) ∧ e > now
	π 2'' Tu	Arg 1 agent
	vas prendre un cercle. Tu	Pred 1 patient Arg 1 Arg 2 agent = IDENT (Arg 1 agent )
	va prendre un petit cercle	Pred 2 = Pred 1 Arg 2 agent = SPEC (Arg 1 agent )
	,B,c) ∧ t > now
	(7b), as a wh-question, is a propositional function
	(paraphrased as Which circle should I take ?), taking a
	NP as an argument :
	ask_wh(B, A, π 2 )
	with
	π 2 λNP.[NP][TAKE]
	[TAKE] = λx. ∃e take(e, B, x) ∧ circle(x) ∧ (big(x) ∨ small(x)) ∧ e > now

The corpus has been collected by N.[START_REF] Ozkan | Vers un modèle dynamique du dialogue : analyse de dialogues finalisés dans une perspective communicationnelle[END_REF].

The full list of conditions can be found in[START_REF] Danlos | Event Coreference between two sentences[END_REF].