Véronique Dupuis

Florent Tournus
email: florent.tournus@univ-lyon1.fr

Nils Blanc

Alexandre Tamion

Matthias Hillenkamp

Synthesis and magnetic properties of sizeselected CoPt nanoparticles

Keywords: CoPt alloy, magnetic nanoparticles, size-selected particles, magnetic anisotropy

Synthesis and magnetic properties of size-selected CoPt nanoparticles

F Tournus, N Blanc, A Tamion, M Hillenkamp,

Introduction

Magnetic nanoparticles have attracted much attention both for their fundamental interest as well as for their potential applications [START_REF] Hadjipanayis | Metallic Iron Nanoparticles for MRI Contrast Enhancement and Local Hyperthermia[END_REF][START_REF] Xu | Monodisperse magnetic nanoparticles for biomedical applications[END_REF][START_REF] Lu | Magnetic Nanoparticles: Synthesis, Protection, Functionalization, and Application[END_REF]. In particular, these nanoparticles might be used for future ultrahigh density magnetic storage devices [START_REF] Weller | High Ku materials approach to 100 Gbits/in2[END_REF].

However, below a certain size, the magnetization direction of a particle fluctuates at ambient temperature: the particle is in the superparamagnetic regime. In order to increase the nanomagnets thermal stability, great efforts have been directed toward an enhancement of the nanoparticles magnetic anisotropy [START_REF] Weller | High Ku materials approach to 100 Gbits/in2[END_REF]. One of the preferred routes is to use magnetic alloys, and in particular CoPt.

Since the proportion of surface atoms is very large (for instance, 50% of the atoms are at the surface, for a 2.5 nm particle), the properties of magnetic nanoparticles can greatly differ from the bulk ones. Hence, these properties should vary with particle size: a well-defined cluster size distribution is then needed for an accurate investigation. Moreover, in order to "decipher" the size effect, all the other parameters have to be fixed while the particle size is changed. In particular, the particles in a sample must remain far enough from each other to avoid significant magnetic interaction: this is the only to way to determine the sizedependent intrinsic magnetic properties. The mass-selected low energy cluster beam deposition technique (MS-LECBD), which is based on laser vaporization followed by ultrahigh vacuum (UHV) deposition of size selected particles, offers such a possibility.

In this paper, we report the synthesis and characterization of well-defined CoPt nanoparticles. After a description of our original synthesis technique, following a physical route, and of the samples studied, we present transmission electron microscopy (TEM) observations and superconducting quantum interference device (SQUID) magnetometry measurements on assemblies of CoPt clusters embedded in amorphous carbon.

Synthesis and structural characterization

CoPt nanoparticles are synthesized using a physical technique, as opposed to chemical synthesis of colloidal particles. We use the low energy cluster beam deposition (LECBD) technique that allows us to grow thin films of nanoparticles deposited on a substrate [START_REF] Perez | Nanostructured Materials from Clusters: Synthesis and Properties[END_REF][START_REF] Perez | Functional nanostructures from clusters[END_REF]). We will give a short description of this original technique (see Fig. 1a). Clusters are produced in a laser vaporization-gas condensation source similar to the one developed by [START_REF] Dietz | Laser production of supersonic metal cluster beams[END_REF] and [START_REF] Milani | Improved pulsed laser vaporization source for production of intense beams of neutral and ionized clusters[END_REF]. Briefly, a plasma created by the impact of a Nd:YAG (yttrium aluminum garnet) laser beam focused on a rod is thermalized by injection of a continuous flow of helium at low pressure typically 30 mbar inducing the clusters growth. Clusters are subsequently stabilized and cooled down in the supersonic expansion taking place at the exit nozzle of the source. A low-energy cluster beam is then obtained, with clusters of different sizes, mostly neutral but also ionized typically 1% of ions. These ions can be deviated with a quadrupolar electrostatic deflector (described elsewhere) acting as a mass-selection device. In this device (see Fig. 1a), charged clusters (with a charge q = e for single cations) are deviated by application of a selected potential V chosen such as qV = Ekinetic = 1/2 mv 2 , where m is the clusters' mass and v their velocity. Since previous time-of-flight experiments [START_REF] Melinon | From free clusters to cluster-assembled materials[END_REF] have revealed that the free clusters' velocity is almost independent of their mass, the energy selection corresponds to a mass selection of the ionized clusters. In addition, the cluster beam is controlled by a set of electrostatic lenses, allowing an optimization of the cluster flux and a good collimation of the beam on the substrate [START_REF] Alayan | Application of a static quadrupole deviator to the deposition of size-selected cluster ions from a laser vaporization source[END_REF]). The current corresponding to the mass-selected ionized cluster beam is then measured by a pico-amperemeter connected to a Faraday cup. This allows us to determine the flux of clusters reaching surface, before deposition on a substrate in UHV conditions: the deposition rate is then fully controlled.

The main key points of this technique are the following. The samples are produced under UHV conditions with a base static pressure of 10 -10 mbar, and around 10 -8 mbar during deposition, due to the use of helium as carrier gas. This means that, contrary to other techniques, in particular the chemical synthesis involving ligands, the clusters surface is not altered. Moreover, as shown in Fig. 1a, the samples can be protected by a capping layer in order to avoid any pollution or oxidation when they are exposed to air for subsequent characterizations [START_REF] Tournus | Magnetic Anisotropy Dispersion in CoPt Nanoparticles: An Evaluation Using the Néel Model[END_REF][START_REF] Tamion | Magnetic anisotropy of embedded Co nanoparticles: Influence of the surrounding matrix[END_REF]). In the present case, we use amorphous carbon as capping layer: it is immiscible with both Co and Pt and enables TEM observations [START_REF] Tournus | Magnetic Anisotropy Dispersion in CoPt Nanoparticles: An Evaluation Using the Néel Model[END_REF]. It is important to note that the clusters composition is determined by the one of the target used for laser vaporization. This means that the particles stoichiometry can easily be adjusted by simply changing the target. In the present case, we use an equiatomic CoPt rod, leading to nanoparticles with a composition very close to Co0.5Pt0.5. Indeed, Rutherford backscattering spectrometry (RBS) experiments indicate that the mean stoichiometry of the clusters films is Co0.56Pt0.44. Another important feature of the LECBD technique is that the clusters arrive on the substrate in a soft-landing regime, following a random deposition scheme. Consequently, as long as there is no significant diffusion on the substrate, which is the case in this study, the interparticle distance is entirely controlled by the clusters density (the surface density for two-dimensional 2D samples or the volume density for threedimensional samples where the clusters are embedded in a matrix). This allows us to adjust the strength of interparticle interactions and, by synthesizing highly diluted samples, to obtain thin films of clusters behaving as nearly isolated nanoparticles.

A remarkable feature of the MS-LECBD is the opportunity to change the particle size independently from the interparticle separation: this is not possible in the case of particles grown by atomic deposition on a surface. The efficiency of the mass selection device can be seen in Fig. 1b where cluster size distributions with and without selection are compared. The relative size dispersion is reduced by a factor of 6, down to D/Dm ~ 7-8 % where D and Dm are respectively the standard deviation and the median diameter of the Gaussian distribution that fits the incident particle size. A small shoulder can be seen in Fig. 1b, which is due to the low proportion of dimers (two particles partially coalesced) formed on the substrate, simply because of the random nature of cluster deposition. Remarkably, this proportion (~8%) is indeed in excellent agreement with the value expected just from the probability (which is fixed by the density and the cluster size) for a cluster to land on another one already lying on the surface: this means that incident clusters do not diffuse on the amorphous carbon film.

Our experimental setup can be used to produce particles with a diameter in the range 1 to 5 nm [START_REF] Tainoff | Self-Organization of Size-Selected Bare Platinum Nanoclusters: Toward Ultra-dense Catalytic Systems[END_REF]. The cluster size is easily controlled by choosing the deviation potential V, as illustrated in Fig. 2. Note that the relative size dispersion does not depend on V, and consequently on the cluster size.

However, for the largest particles a shape distribution is visible.

Magnetometry measurements

Thin films of CoPt cluster layers (0.5 Å equivalent thickness per layer ) separated by 5 nm of carbon matrix has been synthesized by the MS-LECBD technique described above. The samples' dilution (1 vol %) ensures that the interparticle magnetic interactions are negligible: the mean first-neighbor distance is around 7 nm. The clusters size distribution is either the one represented in Fig. 1b with Dm = 3.1 nm, corresponding to a 300 V deviation potential, or the similar one, centered on Dm = 3.8 nm, corresponding to a 500 V deviation potential. As expected, the as prepared CoPt particles are crystallized in the chemically disordered A1 face-centered-cubic phase [START_REF] Tournus | Magnetic Anisotropy Dispersion in CoPt Nanoparticles: An Evaluation Using the Néel Model[END_REF]. Superconducting quantum interference device (SQUID) magnetometry (Quantum Design MPMS magnetometer) is used to characterize the magnetic properties of the embedded clusters, from low-field susceptibility measurements ZFC/FC protocol, with a 50 Oe magnetic field and hysteresis loops at various temperatures. The magnetic curves obtained for the 3.1 nm particles sample are shown in Fig. 3. The remnant to saturation ratio of the magnetization at 2 K is fully consistent with the model of non-interacting and randomly oriented uniaxial macrospins (Stoner-Wohlfarth model), i.e. it is less than 0.5 [START_REF] Stoner | A mechanism of magnetic hysteresis in heterogeneous alloys[END_REF]. We also observe the expected 1/T scaling both for the susceptibility curves and the magnetization loops, as long as the temperature is high enough for the system to be in the superparamagnetic regime. Moreover, we have verified that the magnetic measurements are identical with in-plane or perpendicular applied magnetic field, which means that interparticle interactions are safely negligible.

The coercive field is reduced from 1400 to 180 Oe when the temperature goes from 2 to 10 K because some particles have become superparamagnetic: the 10 K magnetization loop has the characteristic "wasp waist" shape corresponding to the superposition of a blocked contribution and a superparamagnetic one. For higher temperatures, the system is completely superparamagnetic and the m(H) curve at room temperature can be successfully adjusted by a Langevin function using the size distribution deduced from TEM measurements. This is in agreement with previous observations on unselected CoPt clusters [START_REF] Tournus | Magnetic Anisotropy Dispersion in CoPt Nanoparticles: An Evaluation Using the Néel Model[END_REF], where the amorphous carbon matrix was shown to preserve the magnetic cluster size: Dmag = DTEM, i.e. there is no magnetically dead layer.

In order to characterize the particles magnetic anisotropy, we try to simultaneously adjust the ZFC/FC curves and the high-temperature magnetization loop (300 K) with a semi-analytical theoretical model, following the "triple-fit" procedure recently described [START_REF] Tamion | Accurate determination of the magnetic anisotropy in cluster-assembled nanostructures[END_REF]. Whereas a single anisotropy constant Keff (the anisotropy energy of a particle of volume V is then Eani = Keff V) does not allow to fit the curves [START_REF] Tournus | Dispersion of magnetic anisotropy in size-selected CoPt clusters[END_REF], we find that a Gaussian dispersion of Keff can successfully account for the three curves, while keeping the TEM particles'size distribution. A best fit provides the value of the mean anisotropy constant K0 =218 kJ/m 3 and the relative Keff dispersion wK = K/K0 = 37%, with K the standard deviation. Interestingly, the mean anisotropy constant is consistent with the value of Keff previously reported for unselected CoPt clusters. Following the theoretical considerations of [START_REF] Tournus | Magnetic Anisotropy Dispersion in CoPt Nanoparticles: An Evaluation Using the Néel Model[END_REF], we can attribute the Keff dispersion mainly to the multiplicity of atomic configurations: a huge number of chemical arrangements can indeed statistically exist in the case of chemically disordered particles of the same geometry size and shape, corresponding to different values of Eani and hence Keff.

The magnetic curves obtained for the sample of 3.8 nm diameter particles are shown in Fig. 4. As for the 3.1 nm diameter particles, the coercive field decreases when the temperature increases. According to the Stoner-Wohlfarth model, the coercive field HC at 0 K does not explicitly depend on the particle size.

It is directly linked to the anisotropy field: HC = 0.49 Hani = 0.49×2 Keff/(µ0MS), with MS the saturation magnetization of the particles (which must be independent of the size). Nevertheless, the measured HC for two distinct particle sizes could differ for two reasons: first, because of a size effect on the anisotropy constant (a Keff evolution with V); second, because in fact the measurements are not performed at 0 K. If the temperature is not strictly zero, the particle size distribution in the sample can indeed significantly change HC. In the present case, we find very similar value of HC for the two samples at 2 K. Assuming that a 2 K temperature is low enough to extrapolate this result to 0 K, this crude approach tends to show that the anisotropy constant is almost the same for the two particle sizes. Besides, compared to the sample of 3.1 nm diameter particles, the "wasp waist" shape is much less pronounced at 10 K for the 3.8 nm diameter particles. This indicates that the contribution of particles in the superparamagnetic regime is weaker: the blocking temperature should then be higher for the 3.8 nm diameter particles than for the 3.1 nm ones. This is exactly what can be seen in Fig. 4b where the ZFC curves of the two samples are compared: the susceptibility peak is situated at Tmax = 32 K for the 3.8 nm diameter particles, while we have Tmax = 17 K for the 3.1 nm diameter particles. In fact, the Tmax increase can be explained by a direct size effect: the ZFC shape is determined by the Eani distribution (which scales linearly with the particle volume) and we find that the 1.88 ratio between the two Tmax values is fully consistent with the 1.84 ratio between the two particles volume. Moreover, we can consider the entire ZFC curves (not only the ZFC peak at Tmax), and compare the normalized curves (see Fig. 4b insert). We find that the ZFC evolution with the particle size is only due to a simple scale effect: the size distribution has the same shape and the anisotropy constant (including its dispersion, as discussed above) is the same for the two diameters.

Conclusion

We have demonstrated that the MS-LECBD technique can successfully produce high quality samples made of well-defined clusters embedded in a matrix, with a controlled dilution. This original approach offers a quite unique

Fig. 1

 1 Fig. 1 Schematic view of the MS-LECBD experimental setup (a). Size histogram (deduced from TEM measurements) of size-selected CoPt particles, compared to the case of unselected particles (b)

Fig. 2

 2 Fig. 2 TEM images of size-selected CoPt clusters deposited on an amorphous carbon film and capped with an amorphous carbon layer. The deviation potential is 100 V (a), 300 V (b) and 500 V (c) corresponding respectively to a median diameter of Dm = 2.0 nm, Dm = 3.1 nm and Dm = 3.8 nm.

Fig. 3

 3 Fig. 3 Hysteresis loops at 2 K, 10 K and 300 K (a) ZFC/FC susceptibility curves (b) for 3.1 nm CoPt particles. Data points correspond to experimental measurements and the lines are either a guide to the eyes (a) or a theoretical fit (b)

Fig. 4

 4 Fig. 4 Hysteresis loops at 2 K, 6 K, 10 K, 16 K and 50 K for 3.8 nm CoPt particles (a). The coercive field evolution is given in insert. The lines are just guides to the eyes, data points corresponding to experimental measurements. Experimental ZFC susceptibility curves for 3.8 nm CoPt particles compared to the 3.1 nm particles (b). Normalized curves are shown in insert.

Acknowledgement

The authors gratefully acknowledge O. Boisron, and the Centre de Magnétométrie de Lyon (CML).

opportunity to vary independently the particle size and the interparticle separation.

In this way, model samples have been synthesized: the interparticle interactions are negligible, the particle environment is controlled (UHV deposition, followed by an amorphous carbon capping), and the particle size distribution is narrow and perfectly known. The intrinsic properties of the nanoparticles can then be determined which opens the way to an accurate size effect investigation.

Magnetic measurements on size-selected particles with a diameter around 3 nm have evidenced an anisotropy constant dispersion. Small particles with a well-defined size are needed to make this effect visible: a Keff distribution cannot be detected for unselected particles assemblies.

We have compared the magnetic measurements on two samples made of different particle sizes: 3.1 nm diameter particles and larger particles of 3.8 nm diameter, which nearly corresponds to twice the number of atoms. The results are consistent with an anisotropy constant (including its distribution) which does not evolve with the particle size. The different magnetic behaviour can be explained only by a direct size effect on the magnetization switching energy barrier. Therefore, by tailoring the particle size (i.e. simply choosing the deviation potential), some useful magnetic properties, in particular the blocking temperature, can be easily adjusted.


Guillaume Jacques

TIBETAN WA-ZUR AND LAUFER'S LAW *

Keywords: Old Tibetan, monophthongisation, Sino-Tibetan

Laufer's law, according to which proto-Tibetan *-wa monophthongized to -o in Old Tibetan, is almost universally accepted. However, Hill (2006) pointed out that this law seems to be contradicted by the existence of a genuine -wa rhyme in Old Tibetan: unless Old Tibetan -wa has a distinct origin, the sound law *-wa > -o cannot be valid. The present article proposes a simple solution to Hill's counterargument: Old Tibetan -wa comes from the fusion of two syllables.

In a recent paper, [START_REF] Hill | Tibetan vwa 'fox' and the sound change Tibeto-burman *wa > Tibetan o[END_REF] shows that the well-accepted Tibetan sound change *wa > -o is contradicted by the existence of genuine examples of -wa in Old Tibetan (henceforth OT). This sound change was first suggested by Laufer (1898/1899[1972:120]), and it is accepted by Benedict (1972:34), [START_REF] Ilya | A comparative vocabulary of five Sino-Tibetan languages[END_REF] and [START_REF] Matisoff | Handbook of Proto-Tibeto-Burman[END_REF]. Comparison with other ST languages such as Burmese shows that Tibetan -o has several distinct origins. Here are several pairs of Tibetan/Burmese cognates and their reconstruction in Peiros and Starostin (1996, henceforth P/S)'s and Matisoff (2003:167;202;224-6, henceforth M)'s reconstructions: Although P/S and M reconstruct the rhymes of these examples in a very different way, they all agree that the -o :: -wa correspondence between OT and Burmese is to be reconstructed as *-wa/-ua, and that different reconstructions have to be proposed to account for the * I wish to thank Nathan Hill and two anonymous reviewers for useful comments on an earlier version of this paper. correspondences -o :: -aw and -o :: -u. Since many ST languages have -wa or a reflex thereof in the etyma belonging to the -o :: -wa correspondence set, P/S and M's solution, a sound change *-wa > *-o took place in proto-Tibetan, is the most logical one.

However, as pointed out by [START_REF] Hill | Tibetan vwa 'fox' and the sound change Tibeto-burman *wa > Tibetan o[END_REF], in Tibetan orthography the sign wa-zur indicates a medial -w-. Although the wa-zur is spurious in some words, especially in closed syllables, where it serves as a mater lectionis, evidence from modern dialects proves that it was pronounced in OT at least in some monosyllabic open syllable nouns such as rwa 'horn', rtswa 'grass', zhwa 'hat' and vwa 'fox'. Unless we can find an alternative origin for this OT rhyme -wa, we might therefore have to revise the commonly accepted reconstruction for this ST rhyme.

A possible way to explain away the origin of the rhyme -wa in OT comes from -u / -wa doublets. As pointed out by Schiefner (1852: 343) The likeliest explanation for these doublets is to assume a fusion between two syllables. Laufer (1898:199) thought that a disyllabic form with the stress on the first or the second syllable gave rise to these two variants: rwa < *ruwá and ru < *rúwa. I would suggest a different solution: the -u forms are the original ones, and the -wa forms are derived by addition of a suffix, the common nominal -ba / -pa found in many nouns such as lci-ba 'dung', lag-pa 'hand' etc2 . The medial -w-comes in fact from the -u of the first syllable:

(2) rwa < *rua < *ru + ba zhwa < *zyua < *zyu + ba grwa < *grua < *gru + ba This fusion would have taken place before the Tibetan script was created, but after the change *-wa > -o. This explanation solves Hill's problem and saves Laufer's law.

The loss of the -b-as a result of syllabic fusion is not unknown in Tibetan. [START_REF] Hill | Alternances entre ḥ et b en tibétain ancien et dans les langues tibétaines modernes, paper presented at the XXII èmes journées de linguistique d'Asie orientale[END_REF] pointed out examples such as the doublet son / sa-bon 'seed', where the first variant is clearly a fused form of the second variant sa-bon.

The existence of nouns of the form Cu-ba in OT (such as yu-ba 'handle, stalk') could appear to be counterevidence to the hypothesis proposed in this paper (as pointed out by an anonymous reviewer). However, the explanation for the existence of forms such as these is that the -ba suffix was added after the *-u+ba > -wa fusion rule took place. Besides, it never applied to deverbal nouns such as zhu-ba 'petition' from the verb zhu 'to ask' (attested for instance in PT126:150, Hill 2009:49).

Likewise, the fact that some -wa words, such as rtswa 'grass' or shwa 'cleft lip', do not have any corresponding -u word is not a threat to our hypothesis. This simply means that the original form *rtsu and *syu has disappeared, leaving only the fused variant. Alternatively, these words could be loanwords from another language, borrowed after Laufer's law. The only problem which remains unexplained with the present theory is the -wa/-o alternation in the form vwa-dom / vo-dom 'fox-pendant worn as a badge of dishonor' [START_REF] Coblin | An Old Tibetan Variant for the Word 'Fox[END_REF]:118, Hill 2006:89), but since this example is isolated, we leave it to further research.

Table 1 :

 1 Correspondences of Tibetan -o

	Tibetan Burmese	P/S	M	Meaning
	so	swa 3	*Gʷa (s-) *-wa	tooth
	mtho	thwa 3	*Tua	*-wa	handspan
	tsho	chu 2	*chaw	*-ow	fat
	ro	raw 2 « withered »	*rɨw(H)	*-aw	corpse
	spro	pyau 2	*phrɨw	*-o	be pleased

  , several -wa words have a -u variant. Three examples are known to me: rwa / ru 'horn', grwa / gru 'angle' and zhwa / zhu 'hat'. The -u and -wa variants do not show any significant difference in meaning in OT texts, as we find examples where both variants appear in antithetic sentences:

	(1) sha.ba	rwa	mang	ste	vgyen	tam
	deer	horn	many	CONVERB fight?	or
	g.yag	ru	thunge ste	vgyen-pa
	yak	horn	short	CONVERB fight?-NMLZ
	blta-vo
	see.FUTURE-ASSERTIVE
	You can see: does the deer fight (better) 1 , having many horns, or
	does the yak fight (better), having short horns? (PT1287, 502)

The form vgyen (in fact *vgyend given the -tam allomorph of the following conjunction) is not attested in Classical Tibetan.Huang (1999:274) proposed to relate it to the verb vgyed (past bkyes) 'to dispatch, to fight a battle'. Our translation is only provisional.

It might be related, but is distinct from, the deverbal -ba suffix.


Bruno Par

Pinchard

Le chant des voyelles L'autorité des poètes selon Dante 

est destinée au dépôt

ne voyez pas ma bonté, prêtez au moins attention à ma beauté ». Et il enchaîne alors en ces termes :

Non voglio in ciò altro dire, secondo ch'è detto di sopra, se non : O uomini, che vedere non potete la sentenza di questa canzone, non la rifiutate però; ma ponete mente la sua bellezza, ch'è grande sì per construzione, la quale si pertiene a li gramatici, sì per l'ordine del sermone, che si pertiene a li rettorici, sì per lo numero de le sue parti, che si pertiene a li musici. Le quali cose in essa si possono belle vedere, per chi ben guarda 2 .

[Car, selon ce que je viens de dire, je ne veux rien dire d'autre que cela : O humains, qui ne pouvez saisir la pensée de cette chanson, ne la rejetez pas pour autant ; mais prêtez attention à sa beauté, qui est grande, tant par sa construction, qui est l'affaire des grammairiens, et par l'ordre du discours, qui est l'affaire des orateurs, que par le nombre de ses parties, qui est l'affaire des musiciens. En elles tous ces éléments sont beaux à voir, pour qui s'y rend attentif.] Cette énumération doit retenir l'attention, même si elle semble mettre de côté la référence implicite au premier vers du Cantique des cantiques. Elle comporte en effet une distinction entre la grammaire, la rhétorique et la musique digne d'attention, au moins en ce qui concerne la musique. Il est vrai qu'elle emprunte une autre voie que la théorie proprement musicale que Dante développera, dans la suite de ce second Traité, en rapportant la musique à sa place dans le quadrivium et dans la hiérarchie des étoiles dans le cosmos traditionnel.

La musique en question ici est avant tout une musique du discours. Il semble qu'on puisse attribuer ce « nombre des parties » dans le poème d'abord aux accents et aux pieds, ensuite, à ces parties proprement dites que sont les strophes avec leurs stances, et leur contribution à l'ordre général du poème. Si la grammaire et la rhétorique du poème peuvent appartenir, au même titre, à la prose et à la poésie, seule cette musique, avec ses parties, est le propre de la poésie. Ici le poète semble bien un musicien. Il le sera parce qu'il est au service des Muses. C'est ce que nous allons voir dans les autres enseignements de poétique présents dans le Convivio.

Le poète et les Muses

Alors qu'il s'en prend à l'idée de traduction, incapable de sauver la douceur d'un discours, Dante parle en effet de l'impossibilité de traduire sans la trahir une oeuvre « per legame musaico armonizzata 3 . » Cette formule introduit la notion de « lien », qui sera bientôt fondamentale et vérifie l'idée d'une musique doublement étrangère à l'exécution musicale : il 2 Conv. II, XI, 8-9. Il ne tardera pas à confesser que toute sa volonté se mit au service du vulgaire, en accentuant cette vertu du lien qui semble au coeur de la langue et qui va porter tout le poids de l'avenir du vulgaire. Voici comment il parle des liens qui l'attachent à sa langue : Anche, è stato meco d'uno medesimo studio, e ciò posso così mostrare. Ciascuna cosa studia naturalmente a la sua conservazione : onde, se lo volgare per sé studiare potesse, studierebbe a quella; e quella sarebbe, acconciare sé a più stabilitade, e più stabilitade non potrebbe avere che un legar sé con numero e con rime. E questo medesimo studio è stato mio, sì come tanto è palese che non dimanda testimonianza. Per che uno medesimo studio è stato lo suo e' l mio; per che di questa concordia l'amistà è confermata e accresciuta 8 .

[Il a été avec moi d'un même zèle et effort, et cela je peux le montrer ainsi. Chaque chose s'efforce par nature à sa conservation. Si donc le vulgaire pouvait faire effort sur soimême, il s'y efforcerait ; et cette conservation consisterait à s'efforcer à plus de stabilité, et il ne pourrait avoir plus de stabilité qu'en se liant par le nombre des syllabes et les rimes. Curieusement, quelques lignes plus haut il semblait repousser la tentation du nombre dans le mûrissement du vulgaire. Il parlait en même temps des femmes, notons-le, comme s'il n'y avait pas plus haute féminité que la langue elle-même : Ma la gran bontà del volgare di sì […] non si potea bene manifestare ne le cose rimate, per le accidentali adornezze che quivi sono connesse, cioè la rima e lo ritmo e lo numero regolato : sì come non si può bene manifestare la bellezza d'un donna, quando li adornamenti de l'azzimare e del vestimenta la fanno più ammirare che essa medesima. Onde chi vuole ben giudicar d'una donna, guardi quella quando solo sua naturale bellezza si sta con lei, da tutto accidentale adornamento discompagnata : sì come sarà questo comento, ne quale si vedrà l'agevelezza de le suo sillabe, le proprietadi de le sue costruzioni e le soavi orazioni che de lui si fanno; le quali he bene agguarderà, vedrà essere piene di dolcissima e d'amabilissima bellezza 9 .

[Cette bonté ne pourrait pas être si bien manifestée dans les oeuvres rimées à cause des beautés accidentelles qui lui sont associées, je veux dire la rime, le rythme des accents et le nombre réglé des syllabes, de même qu'on ne peut vraiment manifester la beauté d'une femme, quand les ornements du maquillage et des vêtements la font plus admirer que par elle-même. C'est pourquoi celui qui veut bien juger d'une femme regarde celle-ci quand il n'y a pour elle que sa beauté naturelle, libérée de tout ornement accidentel ; de même, ce sera le cas avec ce commentaire dans lequel on verra la fluidité de ses syllabes, l'exactitude de ses constructions et les discours persuasifs qu'on peut faire avec lui : qui les observe avec attention verra qu'ils sont pleins d'une beauté très délicate et très aimable 10 .] En cet instant, Dante semble un fondateur de la prose plus de la poésie italienne, et son oeuvre se fait plaidoyer pour le monde prosaïque de la rhétorique, plutôt que pour les inspirations sublimes du mythe poétique. Mais si la langue dans la prose apparaît dans sa belle nature, elle appartient au régime de la signification, de la persuasion et de l'oeuvre politique qui appartient évidemment à la langue, antique ou vulgaire. En revanche, quand la langue se fait non plus sens, mais lien, alors seule la poésie, avec l'oeuvre du nombre et l'ordre de la musique, est à la mesure de l'oeuvre à accomplir. Dante nous présente ici la langue comme une femme, reste à en faire une dame.

La révolution des voyelles

9 Conv. I, XIII, 6-7. 10 Conv. I, X, 12-13.

C'est précisément ce que va accomplir un texte particulièrement puissant et mystérieux du quatrième traité du Banquet auquel il convient désormais de se confronter. Au coeur du tournant politique de l'oeuvre, Dante doit s'expliquer avec la notion d'autorité, celle de l'empereur, naturellement, mais celle d'Aristote en premier lieu, qui est appelée à limiter la première. Cette digression indispensable à toute pensée de la noblesse en contexte impérial, commence par proposer deux voies : une première qui tournera court, et une autre qui sera la base des développements ultérieurs.

Et pourtant, cette première étymologie, sans suite on le voit, parcourt en quelques lignes une pensée du poétique si profonde et si essentielle qu'on doit aussitôt poser deux questions : pourquoi ici et pourquoi sans suite ? Avant de répondre à ces questions difficiles, il faut lire le texte : È dunque da sapere che "autoritade" non è altro che "atto d'autore". Questo vocabulo, cioè "autore", sans quella terza lettera C, può discendere da due principii: l'uno si è d'uno verbo molto lasciato da l'uso in gramatica, che significa tanto quanto "legare parole", cioè "avieo". E chi ben guarda lui, ne la sua prima voce apertamente vedrà che egli stesso lo dimostra, che solo di legame di parole è fatto, cioè di sole cinque vocali, che sono anima e legame d'ogni parole e composto d'esse per modo volubile, a figurare imagine di legame. Ché, cominciando da l'A, ne l'U quindi si rivolve, e viene diritto per I ne l'E, quindi si rivolve e torna ne l'O : sì che veramente imagina questa figura : A, E, I, O, U, la quale è figura di legame. E in quanto "autore" viene e discende da questo verbo, si prende solo per li poeti, che con l'arte musaica le loro parole hanno legate : e di questa significazione al presente non s'intende 11 .

[Il faut donc savoir que « l'autorité » n'est rien d'autre que « l'acte d'un auteur ». Ce vocable, « auteur », sans la troisième lettre C, peut provenir de deux origines : l'une est un verbe latin presque abandonné de l'usage grammatical, qui signifie « lier les paroles », « avieo ». Et celui qui se montre bon observateur à la première audition s'apercevra qu'il le montre luimême, puisqu'il n'est fait que de liens entre des paroles, c'est-à-dire des seules cinq voyelles, qui sont l'âme et le lien de toute parole, et composé d'elles sur un mode volubile pour figurer l'image d'un lien. Car, commençant par l'A, il se retourne de là vers le U, et va droit par le I au E, et de là se retourne et revient au O : en sorte que véritablement il permet d'imaginer cette figure : A,E,I,O,U, qui est une figure de lien. Et en tant que « auteur » vient et provient de ce verbe, on ne l'utilise que pour les poètes qui, par l'art des Muses, ont lié leurs paroles ; mais ce n'est pas de cette signification qu'on s'occupe ici.] Il est difficile d'entrer plus profondément dans le pouvoir, ou pour mieux dire, dans l'autorité du poète. Dante fait fonds sur des distinctions communes dans les glossaires médiévaux, mais c'est l'irruption du verbe avieo qui compte ici, ce verbe qui n'est que la somme des voyelles qu'il apprend à lier. Nous avions jusqu'ici rencontré le lien, voici le lien des voyelles. Avec cet entrelacs vocalique, c'est évidemment l'acte le plus intérieur de la poésie 11 Conv. IV, VI, 3-4. qui est rejoint. Il n'y a même de poésie que dans ce jeu de la voyelle, si la consonne est prononciation et la voyelle le chant de la voix. Il est clair que Dante offre ici aperçu sur sa vocation la plus haute qui rejoint les plus hautes spéculations sur le pouvoir du verbe humain, dans sa lettre comme dans son esprit. Plus tard, Pic de la Mirandole n'hésitera pas à évoquer une « alphabetaria revolutio » kabablistique et en fera une des voies magiques de l'union à Dieu [START_REF]Pic de la Mirandole[END_REF] .

Il existe donc un mot qui dit ce qu'il fait, et jamais la formule scolastique a été plus vraie : nomina sunt consequentia rerum [START_REF]Dont Dante se recommande dans la Vita nuova[END_REF] car cet avieo qui porte à lui seule tout le destin de la langue ne donne pas seulement une image fixe du fait poétique, mais une image mouvante. Il est la volubilité de la parole à l'état pur. Il est la torsion vivante qui tresse le lien du monde.

Dante peut alors déployer la formule complexe de ce mot tout en rotation. On y retrouvera le noeud de Salomon 14 , le blasonnement des lacs d'amour, les combinaisons alphabétiques des éléments selon Platon ou le « grand jeu » dialectique du Parménide, la synthèse quintuple selon Fichte ou le noeud selon Lacan,la loi de la sextine comme de la terza rima peut-être même. Qu'importe : Dante y trouve l'occasion de donner sa plus belle définition des poètes : ceux qui « coll'arte musaica le loro parole hanno legate ». Comme chez Botticelli, les Muses y dansent en rond pour relier les membres épars de l'univers. Dante pourtant ne s'attachera pas à cette percée et s'en tiendra à l'autre étymologie qui procèderait du grec « autentin ». Mais pour percer un instant l'autorité du poème, il a forgé une formule qui dit ce qu'elle fait, une formule non pas déictique, mais intégralement performative. Si c'est pour Aristote qu'il a commencé à ouvrir cette théorie du lien, et pour dire sa position de maîtrise, il a heurté le fait poétique dans cette embardée et il a accompli l'acte spéculatif le plus profond en plaçant le langage sous le signe du lien qui répète le geste le plus ancestral de l'habitation humaine sur la terre : lier avec force. Vates, selon Uguccione de Pise dans ses Derivationes [START_REF]Vieo -es -evi -vietum, idest vincire, ligare[END_REF] , vient de la même racine, vieo, nouer, tresser, lui qui tord et enroule le fil de la langue. Si le vulgaire, Dante l'a dit, fut « congiungitore delli miei generanti, che con esso parlavano 16 », celui qui a conjoint ceux qui m'ont engendré qui parlaient avec lui, ce n'est pas seulement la puissance reproductrice qui est passée par ce lien amoureux, c'est d'abord la déclinaison vocalique qui constitue le noeud du monde. Cela n'est pas une simple affirmation programmatique, c'est l'opération de Dante forgeron de la langue. C'est la gloire du souffle passant par la voyelle et retenant le nom d'Hashem dans sa lettre, comme le rappelle Schelling dans les Recherches sur la liberté humaine en 1809 en s'inspirant de la grande tradition kabbalistique : Car l'esprit éternel profère l'Unité ou le Verbe en la nature. Mais ce Verbe proféré (réal) réside uniquement dans l'unité de la lumière et de l'obscurité, voyelles et consonnes. Ces deux principes se retrouvent en toutes choses, mais sans consonance parfaite, en raison des défectuosités de ce qui a surgi du fond. C'est donc seulement en l'homme que le Verbe encore retenu et incomplet en toutes autres choses, est intégralement proféré 17 . Dante a retrouvé la langue d'Adam, cette forme de discours concréée par Dieu dans l'âme. AVIEO est le cercle de la langue primordiale. Par-delà la dispersion de Babel, le poète la prononce 18 .

La guirlande du monde

On peut supposer que Dante a renoncé à exploiter cette extraordinaire ouverture sur la synthèse poétique tout simplement parce qu'il cherche, dans ce moment du livre IV du Convivio, à construire le portrait du philosophe face à celui de l'empereur. Mais, quand il sera face à la tâche de régler les rapports entre la prose et la poésie, et marquer en quoi la poésie peut et doit régler la prose, il n'hésitera pas à revenir à ce mouvement tournant, à cette torsade des mots et des symboles, qui constitue le vrai centre « allégorique » de l'expérience poétique.

C'est en effet en ouverture du livre deuxième du traité de l'Éloquence vulgaire, qu'il va revenir sur l'oeuvre de l'avieo et pousser l'idée jusqu'à ces ultimes conséquences : Ante omnia confitemur latium vulgare illustre tam prosayce quam metrice decere proferri. Sed quia ipsum prosaycantes ab avientibus magis accipiunt et quia quod avietum est prosaycantibus permanere videtur exemplar, e non e conversoque quendam videntur prebere primatum -, primo secundum quod metricum est ipsum carminemus […] 19 .

[Avant toute chose nous professons que le vulgaire illustre italique doit aussi bien être proféré en prose que dans le discours métrique. Mais parce que ceux qui écrivent en prose le reçoivent par priorité de ceux qui écrivent par le lien des voyelles <ab avientibus>, et parce que ce qui est lié par les voyelles semble demeurer un exemple pour ceux qui écrivent en prose, et non pas le contrairece qui revient à conférer un certain primat -tout d'abord nous carderons <carminemus> ce qui est métrique.] La poétique du vulgaire vérifie un primat de la poésie sur la prose et ce primat tient à la rotation des voyelles. Car ce n'est pas seulement un primat culturel ou littéraire qui est mobilisé à cet instant, c'est un primat de volubilité. La poésie ne règne pas parce qu'elle est d'une autorité « authentin », c'est-à-dire, encore une fois, selon la traduction de Dante, « degno di fede e d'obedienza, 20 », digne de foi et d'obéissance, mais parce qu'elle est rotative et giratoire : « sì come rota ch'igualmente è mossa 21 », comme une roue qui est mue en sens égal, seront les paroles ultimes de la Comédie. Elles proviennent de la même source.

Nous ne pourrons nous étonner en conséquence quand, jouant sur les fondements étymologiques de ce lais lieur, Dante résume en ces termes son entreprise sur la langue :

Et sic, recolligentes predicta, endecasillabum videtur esse superbissimum carmen ; et hoc est quod querebamus. Nunc autem restat investigandum de constructionibus elatis et fastigiosis vocabulis ; et demum, fustibus torquibusque paratis, promissum fascem hoc est cantionem, quo modo viere quis debeat instruemus 22 . serrage, il est retour et tresse le temps autour de son axe, comme la vigne autour du thyrse 25 et le dieu dansant autour de son principe. Cette rotondité en mouvement est le rapport de Dante à la perfection, c'est-à-dire à la quadrature du cercle. Nul chant n'a, comme le mot AVIEO, mieux montré en le faisant ce qu'il disait. Ce chemin court entre la forme et le fond, entre l'énoncé et le monde, entre la volonté d'oeuvre et sa réalisation actuelle demeure un idéal incomparable pour toute pensée éprise d'une action « complète ». Dans un monde qui ne cesse de revendiquer son incomplétude et ne se croit lucide que par ses manques et ses échecs, cette oeuvre circulaire accomplie est un défi, mieux elle est un scandale. On appelle « dantologues » ceux qui s'en accommodent. 25 En Conv. III, V, 14, Dante compare la rotation du soleil autour du pôle à une meule quand le soleil est à l'équinoxe du printemps, puis à une vigne autour de son axe lors de l'élévation du soleil vers le solstice d'été.

3

  Conv. I, VII, 14. Dante ajoute que c'est la raison pour laquelle les vers d'Homère ne peuvent être traduits en grec et les vers du Psautier sont « sans douceur de musique et d'harmonie », 15. Cette douceur marque un intérêt pour le son des paroles, mais n'évoque aucune intervention musicale, que Dante nommera bientôt « modulation ». seulement illustrative, posée sur les vers comme un vêtement 7 , se retrouve désormais non seulement dans la position d'une musique « des Muses », c'est-à-dire d'une musique inspirée, mais d'une force de réalisation qui révèle comment au poème s'associe l'art et la volonté, la technique et la liberté. C'est dire comment le thème de la musique rejoint les plus hauts sommets de la spéculation dantesque. Nulle poésie sans volonté, certes, mais pas davantage de volonté sans cet exercice de liberté venant à s'introduire dans les possibilités offertes par les mots, et, nous allons le voir, par le partage entre les consonnes et les voyelles. Voilà une poétique nouvelle qui s'empare du champ de la littérature et même de l'exercice moral de l'âme, la poétique de la volonté. Elle résume assez l'oeuvre de Dante et son style.

  7. Et c'est précisément ce que j'ai fait, et cela est si évident qu'il n'y a pas besoin de témoignage. Parce qu'un même et seul zèle a été le mien et le sien ; parce que par cette concorde notre amitié a été confirmée et accrue.] Cette communauté d'âme entre le locuteur et sa langue ne peut que surprendre en nos temps où la linguistique semble la condition de toute intelligibilité de la langue, au point d'en commander tout le fondement des Sciences humaines. Chez Dante au contraire, point d'objectivisme, ni de « philosophie de l'esprit » cognitiviste, mais un pareil amour chez le locuteur et sa langue, où le parlant désire sa langue, mais la langue désire être parlée, l'un et l'autre étant doués d'un conatus qui les apparient et les conduisent à s'unir dans un même effort de nombre et de musique. Avant de lier sa langue, il faut se reconnaître lié à elle par un acte commun du parlé et du parlant, comme on dit que le sentir est l'acte commun du senti et du 7 Dante en évoque l'idée en R. XLVIII, où un poème nu, « pulcella nuda », désire être revêtu d'un manteau de musique pour être reconnu comme une vraie amoureuse, et surtout dans la Vita nuova, XII, 8, où la musique est la condition pour que la dame accepte de lire le poème. La ballade LVI revendique le droit de se présenter revêtue d'une musique qui n'a pas été créée pour elle. 8 Conv. I, XIII, 6-7. sentant. De la langue, il y a acte, et jamais l'acte n'est un procès extérieur, c'est toujours un double accomplissement unissant ce que nous appelons, d'une façon tellement plus pauvre, le sujet et l'objet. En poésie, Dante ne connaît qu'un acte pur. Il se pourrait que cet accomplissement le rapproche d'une condition divine.

  17 Ce texte semble procéder d'un propos de Hamann dans une lettre à Kant de décembre 1759 : « La nature est comme un mot hébreu qui n'est écrit qu'avec des consonnes et auquel l'entendement doit ajouter les signes diacritique », in Schelling Oeuvres métaphysiques, trad. Jean-François Courtine et Emmanuel Martineau, Paris, 1980, p. 149-150.18 Cette lecture de D.v.e., I, VII, 4-6 exigerait d'être développée. Elle revient à poser que la langue primordiale est consonantique et que chaque idiome prononce les voyelles qui y font défaut depuis la faute. 19 D.v.e., II, 1. Le rapport entre le carmen et le cardage de la laine est déjà effectué par Uguccione et Isidore de Séville ; cf. Derivationes, citées par Enrico Fenzi, op. cit. p. 138. Il permet de rapporter le « charme » au filage de laine et au tissage. Le « charme » lui-même n'échappe pas à la roue du lien.

s'agit bien de l'harmonie du vers et le lien est qualifié exactement de « musaique », ce qui signifie à la fois proprement musical et inspiré par les Muses.C'est assister à une véritable intériorisation de la musique qui mérite l'attention. C'est dans De l'éloquence vulgaire que Dante distinguera le plus nettement la « cantio », ou chanson, canzone, définie comme « fabricatio verborum armonizatorum», et la modulation qui appartient à l'ordre du son, de la tonalité, des notes, ou encore du « melos » 4 . Le poème peut alors accéder à une définition véritablement immanente, distincte de toute dépendance à l'égard de l'exécution musicale. D'où la célèbre définition de la canzone, qui touche en effet la musique, mais pour l'écarter : « Actio completa dictantis verba modulationi armonizata 5 », l'action complète de celui qui agence des mots qu'il harmonise avec une mélodie. On passe ainsi d'un accompagnement musical, plus ou moins générique et capable d'être utilisé pour divers poèmes, à une opération unique qui conduit la fabrication verbale à un accomplissement sans reste. Cette intériorisation ne peut sans doute pas se confondre avec l'idée moderne de « musicalité » du vers, mais elle repose sur le partage nombré des consonnes et des voyelles, et à leur relation avec les accents : c'est retrouver les fameuses « parties » du poème dont Dante attribue la responsabilité du « musicien ». Ce musicien n'est plus simplement l'artisan des passions, comme il le sera dans le ciel de Mars, il est le maître des « parties » du discours, et pour y parvenir, il doit se soutenir de l'inspiration des Muses. Nous ne sommes plus dans une astronomie des sciences, mais dans une mythologie des inspirations.3. Les liens du vulgaireLe Banquet n'est souvent qu'un premier essai pour les formules plus mûries des traités latins qui développeront les thèses d'abord énoncées en vulgaire. Ce sera le cas lorsque le traité de l'Eloquence vulgaire définit la poésie comme « fictio rethorica musicaque poita 6 », rien d'autre qu'une fiction rhétorique exécutée par la musique. Même si le verbe « poita » n'a pas encore livré tous ses secrets, il complète l'enseignement de l'harmonie donnée par les Muses et ne saurait se limiter à la nécessité d'une exécution « musicale » : car il n'est pas seulement question d'un ordre pythagoricien des sons et des sphères, mais manifestement d'un pouvoir de création qui joue sur la communauté linguistique entre la poésie et le faire, entre le faire et le créer, et finalement entre le créer et la musique. Cette musique, que nous aurions pu croire 4 Dante Alighieri, De Vulgari eloquentia (D.v.e), in Nuova edizione commentata delle Opere di Dante, volume III, a cura di Enrico Fenzi, Roma, 2012, II, 8, 5. 5 D.v.e, II, 8, 6. 6 D.v.e, II, IV, 2.


Christian Bassac

Bruno Mery

Christian Retoré

Towards a Type-Theoretical Account of Lexical Semantics

Keywords: Montague Semantics, Lexical Semantics, Type Theory

After a quick overview of the field of study known as "Lexical Semantics", where we advocate the need of accessing additional information besides syntax and Montaguestyle semantics at the lexical level in order to complete the full analysis of an utterance, we summarize the current formulations of a well-known theory of that field. We then propose and justify our own model of the Generative Lexicon Theory, based upon a variation of classical compositional semantics, and outline its formalization. Additionally, we discuss the theoretical place of informational, knowledge-related data supposed to exist within the lexicon as well as within discourse and other linguistic constructs.

The formalization of the structure of natural language utterances around a surface form (phenogrammatics), a deep structure (tectogrammatics) and the meaning thereof as a logical form (semantics) has developed from the original theories of Curry and Montague to form coherent, type-driven models. Most of these new theories rely upon variations of the compositional analysis of the sentence: from pheno to tectogrammatics, and then to semantics.

Our contribution to this work aims at giving such a model a means to overcome the problems posed by polysemous lexical units during the semantical analysis of the tectogrammatical form.

Building upon an assumed "deep structure", we formalize parts of Pustejovsky's Generative Lexicon Theory, linguistically motivated in [Pustejovsky, 1995], in a pre-processing of the semantics of the sentence. The mechanisms of Lexical Semantics we propose are an additional layer of classical Montague compositional semantics, and, as such, integrate smoothly within such an analysis; we proceed by converting the lexical data to modifiers of the logical form.

This treatment of Lexical Semantics furthermore induces us to think that some sort of non-evident background knowledge of the common use of words is necessary to perform a correct semantic analysis of an utterance. These "commonsense metaphysics" would therefore not be strictly confined to pragmatics, as is often assumed.

1 The need for Lexical Semantics After a brief review of common assumptions occurring in many modern theories of semantics and grammar, we will take polysemy and the creative use of words as a basis to advocate the need for lexical semantics, and place it within the analysis.

The twofold Montagovian analysis

We assume the existence of a neo-Curryan framework composed of tectogrammatics as the deep structure that yields, on the one hand, the actual written or uttered language, i.e., phenogrammatics, and on the other hand, its intended logical meaning, i.e., semantics. The process of the classical Montagovian analysis of a sentence would be to use the rules of the phenogrammar to infer the tectogrammatical structure from the sentence, by phonological and syntactic means, and then to compute the semantics of the tectogrammatical structure by a type-driven composition of lexemes. Refinements, such as intensionality or modality, might take place, but most systems use a lexicon to associate a semantic type to each word, and let the mechanism operate.

Polysemy and meaning

The association of single types (and therefore logical behaviour) to lexemes is hampered by the fact that polysemous words in natural language are the rule, not the exception. Contrastive ambiguity (the fact that the same sequence of phonemes have come to represent different and unrelated senses during the evolution of the language) led to the construction of lexicons with several possible types for every lexeme, and ad hoc mechanisms to select the correct typing in context. But those heuristics are problematic, and, as [Pustejovsky, 1995] points out, sense-enumeration lexicons do not solve the problems of logical polysemy, in which lexemes might assume many different, yet related senses in context. The need for the speaker to use preliminary, background knowledge of at least some information about every word used appears there clearly: that data enable one to distinguish between the correct and incorrect uses of the word, and to create and recognize new ones. This is not a new idea : it has been expressed in [Searle, 1979], for instance, and many ontology-based approaches of Natural Language Processing assume such a stance.

Lexical semantics: an additional layer of analysis

More specifically, when computing the semantics for a phrase like a loving smile, the speaker (and thus, any processing system) needs to be able to extract some non-trivial information from the words used: here, that a smile is typically associated to a person. In the phrase refreshing tea, not only do we need to know the properties associated to the plant, tea, but also that it might be processed to produce a brewage that can be qualified as refreshing. And in order to understand sentences such as København is a both a seaport and a cosmopolitan capital, the speaker needs to know that nouns denoting towns and cities might be employed to denote either the associated geographical or demographic data. Thus, lexical semantics information is certainly needed in order to process certain utterances correctly. More importantly, the information used here is intrinsically associated with the word used, not the context; it is not a matter of pragmatic interpretation. Ideally, therefore, it should be integrated before or during the composition of the logical form.

The Generative Lexicon and Montague semantics

After a brief review of some of the points of Pustejovsky's Generative Lexicon Theory, specifically the descriptive, ontology-grounded hierarchy of lexical types, we examine the past and current attempts to integrate portions of this theory in a compositional framework, their strength and shortcomings. We then introduce the principles that have driven our new formalization.

The Generative Lexicon Theory

The Generative Lexicon is a set of principles that allows lexical composition (the use of words in conjunction with one another) to generate a potentially unbounded number of senses for each lexical unit, from a rich but finite description of the lexemes. Various kinds of logical polysemy, such as alternations, are treated thoroughly. The Generative Lexicon can also account for the creative use of words, through the same mechanisms.

Ontological types

Those mechanisms heavily rely upon lexical types. The types associated to lexemes are based upon a hierarchy of concepts, organized in an ontology. Thus, a relation of inheritance is supposed: objects of type entity include objects of type physical and abstract, and everything is included in objects of Montagovian type e.

The construction of such an ontology is a task in itself; Pustejovsky merely supposes its existence.

Rich data structures

To each lexical type is associated a number of structures, which convey the necessary information in order for lexical composition to have the intended effects. On top of the inheritance structure needed to build the type hierarchy, there are: the argument structure, which conveys the number and types of arguments needed by a predicate, and additional data covering default and optional arguments; the event structure, which adds Davidsonstyle reification to the formalism; and the particularity of the theory, the qualia structure.

The qualia (singular: quale) can be thought of as meta-data, information associated intrinsically to the lexeme, identified as necessary, background knowledge for semantics. Pustejovsky, in accordance to Aristotle, identifies four qualia: the formal, a set of associated properties (such as color or weight); the constitutive, a set of lexemes that the item is typically in meronymic association with (commonly: made-of and part-of relations); the agentive, indicating terms that might cause the lexeme to appear or come into being; and the telic, indicating lexemes associated with the purpose, or typical behaviour of the lexeme.

In Pustejovsky's original theory, qualia merely indicate the lexical type of the items that might fill these roles.

Type coercion, type accommodation

Having detailed the data structures conveying the necessary information, the Generative Lexicon primarily uses operations over types to make use of that information. Semantical composition takes place as usual, with application occuring whenever an argument and a predicate are of compatible types. On top of that, the Generative Lexicon introduces additional mechanisms, used in case of a type clash :

-Type accommodation is used when the expected type of the argument is an ancestor (with respect to the type hierarchy) of its actual type. The application is then considered valid. (For instance, the predicate break applies to all physical objects, and thus also to artifacts, vehicles, and cars.) -Type coercion is used when the expected and actual types of the argument are neither identical, nor compatible in the hierarchy. Then, the lexical information is used in order to find a link to the expected type. A common case of type coercion is qualia exploitation: if the expected type is that of some quale, then that quale is used instead of the whole argument. Thus, supposing that the predicate to yearn for expects an argument of type event, and that the telic (purpose) of the object cigarette is the event to smoke [the cigarette], then the inference:

to yearn for a cigarette → to yearn for the smoking of a cigarette is made by means of lexical composition.

The •-type construction

Additionally, the Generative Lexicon allows for some specific lexemes to bear more than one type, corresponding to alternate aspects that the term implies: for instance, a book is both a physical object (with weight and shape), and an informational content (with an author), and would thus have P • I for type. This is called the •-type (dot-type, or complex type) construction, and words of such a lexical types are called dot objects. From the point of view of the formalism, given types A and B, the complex type incorporating both is defined as A • B, and might be interpreted either as A, B, or A • B.

This particular construction has induced many difficulties and discussions. Its original formulation, type pumping, a product with straightforward projections, has been disputed: in the same manuscript, Pustejovsky hints that the •-product is not associative, as the type journal would be society•(physical•information): factual evidence points out that meanings representative of both the publisher and physical aspects of a journal are not felicitous. Moreover, later studies have expressed doubts about the projective nature of the operation (a book consists of physical and information aspects, but the pairing of two such arbitrary items does not always result in an actual book), and even doubt whether the •-type construction is an actual product.

We therefore use the •-type construction more as the characterization of a category of phenomena to account for than as a well-established operative construction.

Additional lexical operations

Through the study of some specific constructions, several more lexical operations have been added to the Generative Lexicon. Grinding, for instance, is a destructive operation turning the reference of some words from a material (such as a plant) into a product (such as food) -e.g., fruit. Those operations cannot be handled directly by the general mechanisms expressed above, but their addition fits the formalism neatly.

Current formulations

Since Pustejovsky made his proposal, many refinements have been proposed. On the one hand, the linguistic theory has been corrected and amended; on the other hand, some formalizations and implementations have been proposed. We review some of the current formulations of the Generative Lexicon Theory, their formal assumptions and shortcomings. [Pustejovsky, 1995], as we have seen, assumes that the composition may directly take place with additional operations (accommodation, coercion, grinding. . . ) acting on type clashes. This is not entirely sufficient for whole sentences, as quantification, anaphora resolution, and variable binding, for instance, are not detailed; it also does not interface neatly with existing compositional formalisms. Moreover, the operation known as type pumping, which Pustejovsky uses to model •-types, is logically inadequate, as information that is needed in the further processing of a sentence is lost when it is applied. While formally unsatisfying, that original framework is the basis of an actual implementation in the Object-Oriented paradigm, detailed in [START_REF] Gupta | Nominal Concept Representation in Sublanguage Ontologies[END_REF] and [START_REF] Gupta | Interpreting Events Using Generative Sublanguage Ontologies[END_REF]. [Nunberg, 1993] proposes a different point of view: the consideration of meaning transfers, or shifts. In the author's perspective, the argument does not change its perceived nature when applied to a predicate that does not select for its type. Instead, the predicate changes its meaning, in order to accomodate for the argument.

Type operations : the original formulation

Transfers of Meaning

While making very accurate linguistic points, that article does not propose a formal framework in order to incorporate them. The attempts of implementation having got no further, it remains largely a theoretical issue. However, we have taken Nunberg's points into consideration for our own formulation.

Feature Logic for Dotted Types

One of the first independent formalizations for the Generative Lexicon, and its •-types specifically, has been proposed by [START_REF] Pinkal | Feature Logic for Dotted Types: A Formalism for Complex Word Meanings[END_REF]. Unfortunately, there was little follow-up and exchanges between the authors of this proposal and the persons looking for a complete formalization of the Generative Lexicon. The proposed feature logic had some promise, establishing a complete, Montague-compatible logic for compositional semantics that treated the information contained by complex types in records (a recent proposal, [Cooper, 2007], recently re-visited this prospect). Yet the logic was problematic in a fundamental way, in that any accommodation resulted in the loss of information, and thus, changes were untraceable.

Commonsense metaphysics and complex types

Well aware of the logical shortcomings of the original Generative Lexicon Theory, Pustejovsky set to describe a formally sound theory of types, together with Asher. The first effort, [START_REF] Pustejovsky | The Metaphysics of Words in Context. Objectual attitudes[END_REF], has been met with skepticism, and the system is still the object of current work -including Chapter 5 of [Asher, 2008]. The purpose of this work is to model very specific constructions using solely the interaction of types, and to provide an accurate description of difficult cases, such as different quantification and individuation conditions for the separate, yet related aspects of a single, complex item. Yet, the system remains largely unsatisfactory. The notations used are sometimes inconsistent, and the very axioms of the logic developed assume the availability of non-trivial operations on variables. The confusion of levels within the model creates a fundamentally flawed formalism.

The meeting of two theories

In [Marlet, 2007], the author attempts a straightforward gap-bridging between Computational Semantics and the Generative Lexicon. This proposal is firmly grounded and provides a solid implementation of two GL-supported operations, type coercion and selective binding, in compositional semantics. The calculus is quite complete; however, it remains a preliminary work, as many lexical operations are left unstudied, and as it presupposes the existence of working implementations of compositional semantics and of a Generative Lexicon.

A return to ontologies

Finally, [Saba, 2007] argues for a different approach altogether. While acknowledging the need for background information on the lexicon in order to process an utterance, and the pertinence of rich, ontology-based data structures akin to the Generative Lexicon to store and access this information, the author advocates that such a framework cannot be constructed ex nihilo. Instead, he proposes that the system should be used in order to learn the background lexical information automatically from corpora.

While making interesting points and presenting an approach that we partially concur with, this proposal is however too thin on known logical issues to be used as-is.

Our principles

The approach taken in this article, contrasting with the above methodologies, is to build incrementally upon a known, reliable framework: simply-typed λ -calculus à la Montague; however, we nevertheless wish to abide by the spirit of the Generative Lexicon as a linguistic theory. From our point of view, every addition, every aspect of lexical semantics integrated in that framework should be kept as simple as possible, logically sound, and linguistically motivated. More specifically, the compositional logic should keep track of changes induced by the lexicon, and be able to account for the variety of phenomena encompassed by polysemy.

These principles have led us to introduce the notion of specific morphisms in publications such as [Mery et al., 2007a] and [START_REF] Mery | A montague-based model of generative lexical semantics[END_REF]]. We model the potential semantic variations induced by lexical information using specific morphisms, represented by λ -terms, rather than canonical morphisms deduced from the typing system. This enables the framework to keep the relations between the different senses of a same word as distinct and diverse as need be, and to restrict the scope of each sense using specific constraints.

Target phenomena

In addition to the aforementioned qualia exploitation and grinding operations, we aim at modeling the co-predicative phenomena on certain kinds of words, represented and described as dot objects in [Pustejovsky, 2005]. Overall, our goals include :

-Standard behaviour: being able to account for classical composition and predication in phrases such as a small stone. -Qualia exploitation: Modeling adequately the shift of sense occurring in the use of qualia, including selective binding. Formal exploitation is seen in the phrase sunfloweryellow, agentive exploitation in a loving smile, constitutive exploitation in a powerful computer, and telic exploitation in a fair trial, an enjoyable cigarette or an easy book.

-Modeling the similar shifts of senses occurring in grinding and in the use of alternative aspects for complex objects, in phrases such as good-tasting salmon or a heavy book. -Including the different kinds of complex objects, as detailed in [Pustejovsky, 2005] :

-Words encompassing both a speech act and a proposition, such as promise.

-Words encompassing both a state and a proposition, such as belief.

-Words encompassing both an attribute and a value, such as height.

-Words encompassing both an event and some intrinsically bound content, such as seminar, appointment, concert or dinner. -Words encompassing both a physical object and an informational content, such as book, file, or cd. -Words encompassing both a process and its result, such as reference, agreement or donation. -Words encompassing both a physical object and an aperture, such as door.

-Words encompassing a variety of associated aspects, such as town, which can refer to a geographical locus, a group of people, an institution, or more. -Complex type introduction: accounting for the phenomenon which enables words with simple senses to be considered as dot objects, in phrases such as reading the subway wall. -Correct / Incorrect co-predication: distinguishing between the cases where copredication can be used, as in a heavy but interesting book, and where it may not, as in ?? delicious yet late-blooming lemongrass.

Model outline

The details of our formalization must thus indicate how the model handles type coercion and similar constructs with specific morphisms, and integrate them to classical compositional semantics. We define the structures needed, and the notion of application needed in order to allow the use of these morphisms.

Architecture of the lexicon

The lexicon is rather organised as a type theoretic grammar à la Montague, which maps a lexical entry onto a finite number of λ -terms. More specifically, each lexeme yields a pair consisting of, on the one hand, a single term that we will refer to as the main λ -term, and, on the other hand, a finite, possibly empty set of terms that we will refer to as optional terms or optional morphisms.

The main λ -term ought to be used exactly once, and is like the usual term that Montague semantics associates with a lexical item.

The optional λ -terms are added to enable some composition that, without them, would be impossible; they can be used as many times as needed, including none. Anticipating slightly, let us assume that we have to apply a main term from the lexicon τ X→Y to a another such term u Z with Z = X yielding (τ u). If one of the two entries provides an optional morphism i Z→X it becomes possible to insert this morphism at the right place, yielding (τ (i u)) : Y . Observe that a morphism j (X→Y )→(Z→Y ) would do as well, yielding (( j τ) u) : Y .

The ontology, conceived as a set of inheritance relations, is then represented as a set of morphisms written ι X→Y . If there are finitely many categories in the ontology there is a morphism ι X→Y whenever Y is an immediate superset of X. However, one could envision having such a morphism as soon as Y is a superset of X, but a more refined version would allow these morphims to be weighted, thus providing a measure of the distance of specialisation. If there are limit points, any subset of the actual inclusions which generates all of them by transitivity is fine.

Lambda calculus: types, terms, reduction

Since second-order λ -calculus is not very different from simply typed calculus, it might be convenient to use second-order types and terms, also known as polymorphic terms and types. More precisely, we use the second order propositional logic and second order λcalculus as our type system. The second order propositional quantifier (as in Girard's system F) will be denoted by Λ (Girard's original notation). The second-order λ -abstraction Λ α. T , viewed as a logical formula, would be written ∀α .T , where the ∀ quantifies over propositions or types (not first-order variables). Thus, to say that a term has Λ α. T for type means that, for any arbitrary type U, it admits T [U/α] for type (the application (Λ α. T ){U} results in T [U/α]).

From a typing system point of view, such a second-order type is a generic type, such as the ones used by (Ca)ML (yet more general, in the sense that this quantification can be nested in the right-hand side of implications or arrows). For instance, the type Λ α. α → α is inhabited by the term Λ α. λ x. x, i.e, the generic identity function, first applied to a type U and resulting in the identity λ x U . x of this type U.

Together with the ordinary, Montagovian constants e and t, we have a denumerable set P of type variables. To sum up:

-Constants e and t, as well as any type variable α in P, are types.

-Whenever T is a type and α a type variable which may but need not occur in T , Λ α. T is a type. -Whenever T 1 and T 2 are types, T 1 → T 2 is also a type.

For each type, we have a denumerable set of variables of this type.

-A variable x of type T is a term of type T .

-Whenever τ is a term of type T and f is a term of type T → U, ( f τ) is a term of type U.

-Whenever x T is a variable of type T , and τ a term of type U, λ x T . τ is a term of type T → U. -Whenever τ is a term of type Λ α. T , and U is a type, τ{U} is a term of type T [U/α].

-Whenever α is a type variable, and τ is a term of type T without any free variable involving the type variable α, Λ α.τ is a term of type Λ α.T .

The reduction is defined as follows:

-(Λ α.τ){U} reduces to τ[U/α] (remember that α and U are types).

-(λ x.τ)u reduces to τ[u/x] (usual reduction).

As with the usual simply typed λ -calculus (but with much more sophisticate arguments), this system is strongly normalising and confluent (hence every term has a unique normal form): see [Girard, 1972].

Application revisited

Application takes place as usual when types match. In the event of a type clash, however, the second order logic is used to anticipate the transformation from a yet unknown type into a type appearing in the term.

Lexical items are provided with transformation terms that model specific morphisms, to solve type clashes. There are two ways of resolving such a pattern: globally, as in (1) below, and locally (i.e., independently, in specific places), as in (2) below. The local variant is of course more general, since the global solution might be viewed as the same local type transformation applying everywhere.

Given the problematic application situation:

(λ x V . (P V →W x))τ U
The type clash might be resolved using either (1) or (2), depending on the available terms:

1. Global use of a transformation:

(λ x V . (P V →W x)) ( f U→V τ U )
Assuming that f is an optional term associated with either P or τ. The transformation is applied directly to the argument, no matter the structure of the predicate -i.e., there might be several occurrences of the variable x, and each would result in a similar type clash, should the transformation f be unavailable. For instance, a conjunction would be resolved as

(λ x V . (∧ (P V →W x) (Q V →W x)) ( f U→V τ U )
, so that each occurrence of the argument would be transformed in the same manner.

Here, the type of the argument -and, therefore, the domain type of the transformationis known. We could also write the resulting term Λ α.(λ

x α . (P α→W x)) ( f U→α τ U ){V },
in the manner of (2) below, but the second-order abstraction would be quite redundant here.

2. Local use of a transformation:

(Λ αλ f α→V .(λ x α . (P V →W ( f α→V x α )))){U} f U→V τ U
Again, assuming f is available to P or τ; this application variant actually infers the type {U} and the associated morphism f from the original formula (λ x V . (P V →W x))τ U . This construction provides "slots" for the local application of transformations.

Here, the type of the argument x is not known, and the term used to represent the predicate needs to capture it in order to infer the domain of the transformation f . Thus, the second-order abstraction is not an option in this construction.

Examples

-When there is no need to use additional lexical information, the application takes place as usual: this is standard behaviour. Here, ϕ is the type of physical objects:

small stone small (λ x ϕ . (small ϕ→ϕ x)) stone τ ϕ (small τ) ϕ -In qualia exploitation, an information such as the presence of an agentive quale of type person, associated to the lexical entry for smile, will be modeled using a term f S→P a (to be used either globally or locally, and associated to the type S of smiles), that denotes the relationship between a smile and its author. Then, that transformation term will be used to model the appropriate type coercion:

wondering, loving smile wondering, loving (λ x P . (and t→(t→t) (wondering P→t x) (loving P→t x))) smile τ S (and t→(t→t) (wondering P→t x) (loving P→t x)))( f S→P a τ S ) (and (loving ( f a τ)) (loving ( f a τ)))

-Incorrect co-predication: destructive lexical operations, such as grinding, are modeled using transformation terms that can only be used globally. Thus, there is no correct way to derive, using a transformation term such as f Fs→Fd g that models the process of turning a fish into food, the infelicitous sentence below: (??) The tuna we had yesterday was lightning fast and delicious.

-Correct co-predication: the relation between a word and its compatible aspects can be modeled using terms that might apply locally. Thus, let f T →P p and f T →L l represent the relations binding the words denoting a town to the associated people and locus, respectively; then the following co-predicative sentence is valid:

København is both a seaport and a cosmopolitan capital.

Intuitively, there should be a conjunction between predicates cospl P→t , cap T →t and port L→t , applied to the same k T with (where T stands for town, P for people, L for locus, k for København). If T = P = L = e, as in standard Montague semantics, then one would obtain (λ x e (and t→ (t→t) ((and t→(t→t)

(cospl x) (cap x)) (port x))) k.
Here, the canonical solution for building a well-typed term out of the and, the main λ -terms and the optional ones is the following:

If and is the usual constant of type t → (t → t), the and between two predicates P α→t and Q β →t with different domains α and β is:

Λ αΛ β λ P α→t λ Q β →t Λ ξ λ x ξ λ f ξ →α λ g ξ →β .(and (P ( f x))(Q (g x)))
This term first binds second-order variables to the domain types of P and Q, which are arbitrary α and β (Λ αΛ β ). The type of the argument x, also arbitrary, is then bound to ξ (Λ ξ ). In order to apply that argument to both predicates, we need to provide two separate slots for independent transformations of the argument, according to the domain type of each predicate, and the conjunction thus looks like (and (P ( f x))(Q (g x))) (both transformations are local). We straightforwardly have the necessary typing for each transformation (λ f ξ →α λ g ξ →β ), and thus the above term. Remark that, in order to obtain a well-formed, well-typed term which can be reduced to a logical formula, two suitable morphisms have to be available and substituted to the transformation slots f and g.

The conjunction is first applied to P and T and to cospl P→t and cap T →t , yielding:

( * ) Λ ξ λ x ξ λ f ξ →P λ g ξ →T (and (cospl P→t ( f x)) (cap L→t (g x)))
Likewise, applying the same conjunction to ( * ) and (port x), we obtain:

Λ ξ λ x ξ λ f ξ →P λ g ξ →T λ h ξ →L (and (and (cospl P→t ( f x)) (cap T →t (g x))) (port L→t (h x)))
This term is then applied to T , the type of the argument, k T and the morphisms. cap T →t is already of the type of the argument, so we use id T →T . The result is a term of type t:

(and t→(t→t) (and t→(t→t) (cospl (

f p k T ) P ) t ) (cap (id k T ) T ) t ) t (port ( f l k T ) L ) t ) t
4 Properties of the model, advantages and drawbacks

Relationship with classical semantics and additional power

In order to fall back on classical compositional semantics, it is sufficient to consider that the lexicon simply provides the Montagovian typing of the terms. The additional terms and second-order types would just be discarded.

From a comparison with such a classical formalism, it is clear that our model does not increase the generative power of the semantics. Indeed, if anything, the generative power is less than with Montagovian semantics, as more unfelicitous or nonsensical sentences can be filtered out.

The benefits of this approach are of expression, as the output can be fine-grained by the choice of the morphism to use: thus, the fact that we refer to the taste, in the phrase a good meal, and to the fitness for use, in the phrase a good tool, is possible in our model, and made explicit by the use of terms specific to each relation supposed, without having to rely on the pragmatics or interpretation of the sentence in context.

Keeping track

In order to cope with co-predicative sentences, the system needs to be aware of the different changes of sense applied to an item. This is one of the main logical problems of the original type coercion, and of formalizations, such as [START_REF] Pinkal | Feature Logic for Dotted Types: A Formalism for Complex Word Meanings[END_REF]] that attempt to implement it directly: if the lexical data licence it, the type is simply substituted. This means that co-predication can either be licensed in every or in no case. It also is problematic for anaphora resolution, and for any construction that uses the type-coerced term more than once. This is why our formalism provides a straightforward way of keeping track of the changes used by explicitly inserting corresponding terms in the logical form.

Predicate-induced transformations

In [START_REF] Pustejovsky | The Metaphysics of Words in Context. Objectual attitudes[END_REF], a puzzling situation (that led the authors to introduce numerous mechanisms and operations) appears in phrases such as reading the subway wall: complex type introduction. As the theory assumes that read selects for arguments objects with both physical and informational aspects aggregated in a complex type, there is no immediate and simple solution to that situation.

Our model, however, has a simple way of dealing with that problem: it is to suppose that the predicate, as well as the argument, might contribute transformation terms. Here, read conveys a term such as f A→ϕ×I a

, converting artifacts into readable objects. This consideration obviates the need for specific operations, and does not, in fact, necessitate complex types at all.

Unresolved points

We have intentionally remained vague about a certain part of our proposal, namely: when does a transformation term apply locally, and when does it apply globally?

In fact, the different ways of applying the transformation terms is the means that the system uses to license or forbid co-predications. For some cases, there are clear answers: destructive operations such as grinding may only apply globally, while accessing the multiple tropes of a single item should be able to apply locally. However, on closer inspection, there are constraints that can prevent transformations from applying locally. Some syntactic constructions might be more acceptable than others (compare a blue and open door and the blue door is open), contrastive focus also changes the felicity of some constructions (compare heavy and interesting book and heavy, yet interesting book), etc.

As we have yet to determine the precise behaviour of co-predicative constructions and are not aware of existing studies to that effect, the choice between the two modes of application is left unspecified in our system.

Information, beyond the lexicon

With our model presented and supposed sound, we examine and speculate over some points of interest that might, with further work, be part of its applications.

Multiple possibilities

A straightforward extension of the formalism is to accept that application might behave in more than one way, i.e., that there might be more than one morphism that could be selected to attain the target type. By introducing such non-determinism in the derivation process, we would keep every possibility, and get effectively several different, yet potentially all valid in context, interpretations of the same sentence. For instance, Philadelphia wants a bridge offers several interpretations (Philadelphia can stand for the mayor, city council, inhabitants as polled, or some other city representatives).

But it would be useful to integrate a limited inference system, in order to cull inconsistent choices from the interpretation set as they appear. If one says Philadelphia wants a bridge, but the mayor opposes it, then the derivation branch corresponding to mayor would have to be discarded.

Scoring Felicity

The possibility of having multiple interpretations should be moderated by the fact that some interpretations are more likely to be correct than others. Likewise, some uses of words might feel a bit forced, a bit less felicitous than others, while remaining correct. Ideally, one would need to use some felicity "score" to respond to the classical objection presented, for instance, by [Blutner, 2002]: Putsejovsky argues that want has a tendency to select the telic quale, and, thus, that want a cigarette is taken to mean want to smoke a cigarette. But to want a car, conceivably, means to want to possess a car. Rather than using Blutner's philosophy (i.e., this distinction lies entirely within the pragmatics), simply allowing the interpretation to be multiple (i.e., for want to select either the telic or the object as a possession) suffices.

But we might allow the interpretations to have different scores, based on the relative value of the object, for instance (one might conceivably want Napoleon's cigarette for a possession, and a cheap car for driving).

Integrating multiple sources of prior knowledge

Beyond the knowledge intrinsic to words in the lexicon, other sources might play an analogous role, and be treated in the same way: as means to integrate specific morphisms over lexemes. The information associated to some words might evolve in the broad context of a discourse, for instance: generic sentences acquire different meanings if used with different topics. Thus, DRT, λ -DRT or SDRT are prime candidates to become additional information sources. Likewise, cultural assumptions might infer different meanings; there are many European texts that rely upon the presence of a church in any village, for instance. Some factors induced from pragmatics, such as the circumstances of the utterance and nonverbal signs, might add some modifiers as well. It is even envisionable, in such a theory, that the two speakers in a given dialogue do not have the same background knowledge of the lexicon, culture and circumstances, which could help model misunderstandings.

Acquiring new information from corpora

The use of Lexical Semantics -or, at least, of semantics of composition grounded in an adequate ontological structure -in order to provide a framework for automated knowledge acquisition from corpora is the main point of [Saba, 2007]. Though we do not entirely agree with the overall philosophy, the approach could be put to good use in order to facilitate the improvement of an existing lexicon grounded on the above principles. The idea is simple: if a sentence is grammatically correct, but not valid from the point of view of the Generative Lexicon because the lexicon is incomplete (i.e., some specific morphisms remain yet unknown or undiscovered), then the program will consider that there must needs exist some morphisms that allow the sentence to be validated. The missing morphisms are added to the lexicon as underspecified type-conversions, and as much information as possible is gathered on their uses as they occur in the text; they can be either acknowledged and corrected, or discarded, by a human judge on a later phase.

A link with knowledge representations

In retrospect, the use of background knowledge used for the parsing of sentences goes back to [Searle, 1979], yet Pustejovsky's lexicalization of the phenomenon, and our formalization, restrict the scope of Searle's original hypothesis. It remains true that we are lead to distinguish between two aspects of world knowledge, in a theory of the language speaker's mind: the knowledge needed to process a sentence, the background, which has been the object of our model, and the knowledge obtained as a result of the processing of that sentence, the facts. We would like to speculate, at this point, that an adequate representation of this duality might successfully be combined with a many-worlds approach.

World models (incorporating both the background knowledge and resulting facts) would then be constructed for every agent and every sentence or discourse. The confrontation of this world with the agent's knowledge of its reality (that is also a world model) constructs the interpretation of the sentence.

Such a view of the interpretation of language is largely compatible with the Lexical Semantics theorized before, and should be familiar to multi-agent advocates. Indeed, it resembles some of the approaches recently developed to analyse dialogue, and it is our opinion that it would give interesting and applicable results, when further investigated.

Conclusion

While the above research goals could in time lead to many possibilities, we think that the proposed mechanisms are now sufficient to integrate many facets of the Generative Lexicon Theory, while remaining formally sound. In order to be of actual use, however, they need to be provided with a translation strategy from lexical entries to transformation terms. This would be a first step towards an actual implementation of the formalism, and its evaluation.

Acknowledgements We would like to thank the many people that commented and discussed our ideas, previous publications, addresses and drafts, including every member of the Signes group, attendants and members of the audience at ESSLLI 2007, and Nicholas Asher, for their inputs. Thanks go to Reinhard Muskens for making the NDTTG workshop possible, and for inviting us to write this article.