Fadel Chamssedine

Daniel Claves
email: daniel.claves@univ-bpclermont.fr

Selective substitution of fluorine atoms grafted to the surface of carbon nanotubes and application to an oxyfluorination strategy

Different modes of fluorine chemisorption on the surface of single wall carbon nanotubes (SWCNTs) are shown to result in varied tendencies of the F atoms to behave as leaving groups, in the presence of a nucleophilic reagent. Fluorine species in weak interaction with the carbon matrix can be readily displaced and therefore, exhibit enhanced exchange properties, while those more strongly bound to the sidewall resist substitution. Such a tunable reactivity of the F atoms in a fluorotube has been used to selectively replace some of them by hydroxyl functional groups. The scheme illustrated here represents a first step toward a quantitative functionalisation process of the SWCNT surface by heteroelements.

Introduction

The C-F single bond is listed among the most thermochemically favourable combinations, conferring this moiety a relative chemical stability. It is thus common knowledge that perfluorocarbons are prototypes of chemically inert compounds. However, it has been widely illustrated that the C-F bond strength becomes notably weakened when fluorine is associated with a fullerenic carbon network. This arises essentially from reduction of the carbon and fluorine orbital overlap upon curvature of the pristine carbon framework. From the physicochemical properties standpoint, the "imperfect" C-F covalence realised in curved fluorocarbon lattices does not go without important consequences, related to easy bond cleavage. For instance, fluorine gas is rapidly given off from of a sample of fluorinated single wall carbon nanotubes (F-SWCNTs) upon simple prolonged annealing under an inert atmosphere [START_REF] Zhao | Thermal recovery behavior of fluorinated singlewalled carbon nanotubes[END_REF][START_REF] Pehrsson | Thermal fluorination and annealing of single-wall carbon nanotubes[END_REF][START_REF] Gu | Cutting single-wall carbon nanotubes through fluorination[END_REF]. The defluorination of such entities can also simply occur upon gentle chemical reduction [START_REF] Mickelson | Fluorination of single-wall carbon nanotubes[END_REF]. The overall weakening of the C-F interaction makes the former macromolecular clusters sensitive to nucleophilic attack as well, whereas it is widely acknowledged that the fluorine atom is otherwise a very bad leaving group. Originally initiated in the framework of the study of the chemical reactivity of fluorofullerenes [START_REF] Taylor | The chemistry of fullerenes[END_REF], investigations on this latter aspect have since been intensively extended to fluorine atoms grafted to the surface of a carbon nanotube and have shown the ability of the latter to be readily displaced. The research group from Rice University had thus initially reported the attachment of alkyl chains [START_REF] Boul | Reversible sidewall functionalization of buckytubes[END_REF][START_REF] Saini | Covalent sidewall functionalization of single wall carbon nanotubes[END_REF] and various oxygen or nitrogen-based functional groups [START_REF] Khabashesku | Fluorination of single-wall carbon nanotubes and subsequent derivatization reactions[END_REF] to the sidewall of a carbon nanotube by starting from a fluorinated precursor.

Beside this overall C-F bond weakening phenomenon, pioneering studies [START_REF] Zhao | Thermal recovery behavior of fluorinated singlewalled carbon nanotubes[END_REF][START_REF] Pehrsson | Thermal fluorination and annealing of single-wall carbon nanotubes[END_REF][START_REF] Gu | Cutting single-wall carbon nanotubes through fluorination[END_REF][START_REF] Mickelson | Fluorination of single-wall carbon nanotubes[END_REF][START_REF] Lee | Surface properties of fluorinated single-walled carbon nanotubes[END_REF] dedicated to F-SWCNTs also commonly reported that two distinct types of C-F bonds must be distinguished and can seemingly even coexist [START_REF] Gu | Cutting single-wall carbon nanotubes through fluorination[END_REF][START_REF] Lee | Surface properties of fluorinated single-walled carbon nanotubes[END_REF] within a sample, depending on the synthesis temperature and precursor SWCNTs used. Similar conclusions, regarding a either uniform or binary nature of the C-F chemical bond, were reached in the course of more recent studies on fluorotubes synthesised by CF4 or SF6 plasma treatment [START_REF] Plank | Fluorination of carbon nanotubes in CF4 plasma[END_REF][START_REF] Plank | Functionalisation of carbon nanotubes for molecular electronics[END_REF][START_REF] Khare | The fluorination of single wall carbon nanotubes using microwave plasma[END_REF][START_REF] Valentini | Sidewall functionalization of single-walled carbon nanotubes through CF4 plasma treatment and subsequent reaction with aliphatic amines[END_REF]. Our own contribution to the subject [START_REF] Chamssedine | Three different modes of fluorine chemisorption on the surface of single wall carbon nanotubes[END_REF] has recently distinguished a third mode of fluorine chemisorption in fluorotubes.

Compiling the two preceding aspects, we have tried in this paper to examine the consequences of a varied C-F bonding scheme on the substitutional properties of fluorotubes. Indeed, a selective reactivity of each C-F bonding mode can be expected, the weakest ones conferring fluorine atoms an enhanced leaving group character and, as a corollary, a greater exchanging power. We have then shown, from the oxyfluorination case, how such differentiated nucleofugal properties can turn out to be a fruitful tool for the subsequent derivatisation of SWCNTs, paving the way toward quantitative methods of synthesis of a hetero-functionalised one-dimensional material.

Results

In the following, we present a wet chemistry method to modify the surface of SWCNTs via the coaddition of both fluorinated and oxygenated hetero-functions. The staged pattern developed starts from a sample of fluorotubes, further treated with nitric acid, a common procedure known to yield oxygenated functional groups at the surface of graphitised carbonaceous materials [START_REF] Gardner | Surface characterization of carbon fibers using angle-resolved XPS and ISS[END_REF][START_REF] Lakshminarayanan | Nitric acid oxidation of vapor grown carbon nanofibers[END_REF][START_REF] Ago | Work Functions and surface functional groups of multiwall carbon nanotubes[END_REF][START_REF] Okpalugo | High resolution XPS characterization of chemical functionalised MWCNTs and SWCNTs[END_REF]. The fluorinated precursor and the final oxyfluoro-compound have then been characterised by x-ray photoelectron spectroscopy (XPS), which allows to establish both the nominal composition and the nature of the functions created for each sample. The successive C1s spectra and elemental contents obtained are presented in figure 1 and table 1, respectively.

Experimental

A batch of purified SWCNTs, grown from chemical vapour deposition (CVD), was used in the present study. Transmission electron microscopy (TEM) observations showed that the majority of the tubes have diameters between 1 and 2 nm and form bundles. Fluorination was carried out under pure molecular fluorine (2h, 300°C), within a tubular Monel reactor initially purged with nitrogen until the synthesis temperature was reached. The gas flow was maintained during cooling of the samples. Subsequent oxygenation was performed by reflux in 11 M nitric acid, for 10h at 100 °C, under continuous stirring. The oxyfluorinated compound thus obtained was then filtered, washed with distilled water until complete neutralisation of the filtrate, and dried under vacuum at 60 °C for one night.

Anhydrous KBr pellets were used for Fourier transform infrared spectroscopy (FTIR) analysis. Nominal compositions were obtained from XPS analysis, using relative sensitivity factors for fluorine and oxygen, with respect to carbon, adjusted from standards. Charge compensation was ensured via an electron flood gun.

Characterisation of the precursor fluorotubes

We first proceeded to the fluorination, at 300°C and for two hours, of a CVD-grown batch of SWCNTs, as described in the experimental part. We had previously shown [START_REF] Chamssedine | Three different modes of fluorine chemisorption on the surface of single wall carbon nanotubes[END_REF] that in such conditions, the chemisorption of fluorine at the surface of such SWCNTs can be classified into three different categories of C-F bonds, differing by their robustness, i.e. by the ease with which fluorine can be released from the carbon substrate.

The C1s XPS spectrum (fig. 1) corresponding to the fluorinated tubes comprises a first feature centred at 284.5 eV, similar to the one present in the C1s spectra of the raw tubes, and therefore related to bare graphitic carbon atoms. It is experimentally well established that the C1s core level energy undergoes substantial primary and secondary shifts in the presence of a strong electron-withdrawing element.

Accordingly, the existence of carbon atoms not directly linked to a fluorine atom but having fluorinated nearest neighbours splits the first "graphitic" signal into a second component lying at a higher binding energy, as shown earlier in the case of graphite fluoride (C2F)n [START_REF] Kita | Chemical composition and crystal structure of graphite fluoride[END_REF] b The contribution of carbonyl and carboxyl groups to the corresponding XPS signal can be safely neglected according to the IR data analysis.

BE (eV) c) F+O-SWCNTs b) F-SWCNTs a) SWCNTs CF 3 CF 2 C-F C-O-C C-OH+C-CF C-CO CF 3 CF 2 C-F C-CF
carbon fibres [START_REF] Tressaud | On the nature of C---F bonds in various fluorinated carbon materials: XPS and TEM investigations[END_REF], or fluorofullerenes [START_REF] Claves | Structural, bonding and electrochemical properties of perfluorinated fullerene C70[END_REF], and here present at 286.1 eV. To further proceed with the analysis of the spectrum, one may recall that the C1s signal related to carbon atoms attached to one fluorine atom usually appears in the 287-289 eV region [START_REF] Kita | Chemical composition and crystal structure of graphite fluoride[END_REF][START_REF] Tressaud | On the nature of C---F bonds in various fluorinated carbon materials: XPS and TEM investigations[END_REF][START_REF] Claves | Structural, bonding and electrochemical properties of perfluorinated fullerene C70[END_REF][START_REF] Matsuo | Synthesis and spectroscopic study of fluorinated fullerene C60[END_REF]. A corresponding feature is observed here, with a large width reflecting multiple contributions that therefore confirms the presence of several C-F bonding modes in the fluorotubes sample. The latter signal has been treated as a unique envelope, adjusted in width and position. Finally, weak shoulders at 291.1 and 292.8 eV have been attributed to some >CF2 and -CF3 groups appearing on edges or at local defect sites. The fluorine content (table 1) calculated from the relative intensities thus assigned corresponds to CF0.61, not in contradiction with the nominal composition CF0.52 determined from the XPS F1s/C1s area ratio, taking into account the respective elemental sensitivity factors. 5 and 2 % of atomic oxygen with respect to carbon have also been detected in the pristine carbon material and after its fluorination, respectively. At last, one may note that though a similar peak assignment was already made in earlier XPS studies of F-SWCNTs C-F bonding modes in the sample, but resolution of signal overlap at the F1s level remains limited owing to the restricted energy splitting range and larger peak width characterising the latter (even the minor >CF2 and -CF3 groups present appear as part of the line foot and can not be distinguished).

At last, the IR spectral data presented in figure 3 display large unresolved bands covering the 1000-1250 cm -1 zone, unambiguously revealing that the strength of the C-F bonds formed covers a significant amplitude interval. In contrast, IR spectra of conventional fluorocarbons always exhibit narrow bands over a usual 1100-1250 cm -1 wave number range. The continuous variation in bond energy here established is consistent with the conclusions drawn from the XPS analysis regarding the presence of different chemisorption modes of fluorine within the present fluorotubes.

Characterisation of the final oxyfluorotubes

The precursor fluorinated sample obtained has then been further treated with nitric acid (see experimental section). Once the whole functionalisation process was completed, subsequent TEM observations showed individualised tubular entities (Fig. 4). Though some fragmentation could be evidenced, it seems that F-SWCNTs offer much better resistance to destruction than raw tubes, probably because the hydrophobic CF groups present on their outer surface initially make them slowly wet by the aqueous medium, so that it takes time before the well-known etching effect of nitric acid on tubes can manifest.

The elemental stoichiometry of the sample issued from the complete chemical treatment, as determined by XPS, was CO0.47F0.29, giving evidence of a mixed final functionalisation state and of a significant increase in the global addition level. No other element has been revealed by the survey spectrum. The shift toward higher binding energies of the peak arising from the non-directly "addended" carbon atoms is noticeable on the C1s spectrum displayed on figure 1. This drastic change finds its origin in the fact that bare carbon atoms now systematically have at least one immediate carbon neighbour attached to a strongly electronegative element (F or O), in compliance with the increase of the global addition rate. This leads to a general core level secondary shift and to the extinction of the previously observed purely "graphite-like" photoemission line. The remaining part of the spectrum can be deconvoluted with the help of five additional components at higher energies, assigned to carbon atoms bonded either to oxygen under the form of ether and hydroxyl groups or to fluorine, according to standard chemical shift tables [START_REF] Moulder | Handbook of x-ray photoelectron spectroscopy[END_REF]. The attributions thus performed are listed in table 1 and are consistent with published data dealing with the identification, by means of core level photoelectron spectroscopy, of oxygenated functional groups grafted to the surface of carbon fibres [START_REF] Gardner | Surface characterization of carbon fibers using angle-resolved XPS and ISS[END_REF][START_REF] Lakshminarayanan | Nitric acid oxidation of vapor grown carbon nanofibers[END_REF] or carbon nanotubes [START_REF] Ago | Work Functions and surface functional groups of multiwall carbon nanotubes[END_REF][START_REF] Okpalugo | High resolution XPS characterization of chemical functionalised MWCNTs and SWCNTs[END_REF] The corresponding IR spectrum is shown in figure 3. The distinct absorption bands can be easily identified and fully confirm the conclusions drawn from the XPS study, regarding the nature of the functions created. One may therefore successively identify the signature of hydroxyl groups (3100-3600 cm -1 ), covalent C-F moities (1205 cm -1 ) and C-O (alcohol and ether) bonds (1090 cm -1 ). Another noticeable fact is that only very few carbonyl functions from ketones and carboxylic acids are present.

Discussion

O/F substitution

The experimental statement of the decrease in the elemental F/C ratio and concomitant increase in the O/C one, after acid treatment, is noteworthy. A straightforward interpretation would be that some fluorine atoms are consumed during the grafting of the oxygenated functionalities to the carbon lattice, implying therefore a fluorine-mediated reaction mechanism. Such an assumption is supported by the fact that the oxygen-containing functional groups here obtained are clearly different from those formed via the direct action of nitric acid on a non-fluorinated carbon network. Numerous studies [START_REF] Gardner | Surface characterization of carbon fibers using angle-resolved XPS and ISS[END_REF][START_REF] Lakshminarayanan | Nitric acid oxidation of vapor grown carbon nanofibers[END_REF][START_REF] Ago | Work Functions and surface functional groups of multiwall carbon nanotubes[END_REF][START_REF] Okpalugo | High resolution XPS characterization of chemical functionalised MWCNTs and SWCNTs[END_REF] have indeed shown that the functionalisation by nitric acid of carbon fibres or nanotubes results in the formation of >C=O terminations in significant amounts, whereas these are almost absent here. Further support is gained through the high oxygenation level here obtained, which is quite well above the around 10% rate usually resulting from the previous process.

In the second place, one may have a closer look at the nature of the subsisting C-F groups in the oxyfluorinated product. The F1s spectrum of the latter remains characteristic of fluorine atoms attached to carbon, as shown by a corresponding broad hump centred around 689.7 eV (figure 2). However, this apparent average position is upshifted by +2.1 eV, with respect to its value before acid treatment, and is therefore indicative of stronger C-F interactions. One may also note a similar shift in the same direction (see table 1 and figure 1), though of lower amplitude, between the positions of the respective C-F signals on the C1s spectra of the CFx and COyFz products, confirming the stronger nature of the residual carbonfluorine bonds after oxygen fixation. This can only be explained by the vanishing of the weakest C-F bonds initially present in the precursor material, while the strongest ones have been preserved.

Confronting the two former aspects, a tantalising conclusion is that a selective displacement of fluorine by oxygen can take place. Recent work by Plank et al. [START_REF] Plank | Electronic properties of n-type carbon nanotubes prepared by CF4 plasma fluorination and amino functionalization[END_REF] has also supported such an hypothesis, following reaction of plasma-prepared F-SWCNTs with 1,2-diaminoethane. However, the extremely low residual fluorine contents obtained after amino-functionalisation reflected a very poor variation in reactivity between the different C-F bond types that the authors identified in their precursor fluorotube samples. Owing to the lower nucleophilicity of the O atom with respect to that of the N atom, selectivity is greatly enhanced in the present study and the evolution in the nucleofugal properties of fluorine atoms grafted to a SWCNT is then given here a solid quantitative basis.

Primary and secondary mechanisms

Though a formal and detailed mechanistic approach of the O/F exchange process lies beyond the scope of this work, one may invoke a path similar to the one initially inferred to account for the nucleophilic substitution of fluorofullerenes [START_REF] Taylor | Nucleophilic substitution of fluorinated C60[END_REF], and whose relevance has since been confirmed [START_REF] Taylor | Why fluorinate fullerenes?[END_REF], to presently explain the formation of the -OH groups. The fluorine departure may then take place through the SN2' mechanism, since a tubular topology prevents the occurrence of a direct backside attack. As conjectured earlier [START_REF] Taylor | Why fluorinate fullerenes?[END_REF][START_REF] Taylor | Fluorinated Fullerenes[END_REF] in the homologous case of the hydroxylated derivatives of fluorofullerenes, a secondary reaction between hydroxyl and fluorine linked to contiguous carbons can also result in cyclisation. Therefore, it is likely that at least part of the C-O-C functions identified in our oxyfluorinated SWCNT samples exists under the form of epoxides, which can not be distinguished from alkoxides in the light of the spectroscopic techniques employed in this work.

Yet, it should be noted that according to the former substitution pattern anticipated, an exact balance between the levels of oxygen and fluorine should result, a condition which is not verified in the present case, since the final number of oxygen atoms significantly exceeds that of the missing fluorine species.

This unbalance highly likely results from an independent side-reaction involving the direct oxidation by nitric acid of the carbon-carbon  bonds [START_REF] Gardner | Surface characterization of carbon fibers using angle-resolved XPS and ISS[END_REF][START_REF] Lakshminarayanan | Nitric acid oxidation of vapor grown carbon nanofibers[END_REF][START_REF] Ago | Work Functions and surface functional groups of multiwall carbon nanotubes[END_REF][START_REF] Okpalugo | High resolution XPS characterization of chemical functionalised MWCNTs and SWCNTs[END_REF] which subsist in the precursor fluorotubes. This secondary reaction should therefore be at the origin of the creation of further -OH and C-O-C functions and of the very few >C=O ones detected by IR. It can be hold responsible for the fragmentation observed at the level of the oxyfluorinated carbon frame, meaning marked edge effects on the final O/C stoichiometry determined.

Summary and conclusion

Partial fluorination is an efficient way to stimulate the subsequent fixation of organic terminations at the surface of SWCNTs. In order to emphasise the consequences, from a reactivity standpoint, of the existence of carbon-fluorine interactions of different strength within the overall C-F bonding scheme of an F-SWCNT, we have illustrated the opportunity of a selective O/F exchange. The related mechanism involves the substitution of fluorine by oxygen and the selectivity encountered lies on the enhanced nucleofugacity of those fluorine atoms involved in the weakest C-F bonds present at the surface of a fluorotube. In the short term, one may imagine that the relative proportions of each C-F bond type may be modulated according to the preparation conditions of the initial CFx precursor, and that so may be the displacement of fluorine by oxygen and the consequent final O/F/C stoichiometric ratio.

Acknowledgement:

The authors are grateful to K. Lam for having performed the XPS measurements.

List of captions for figures and tables: Table 1. Peak analysis arising from the spectral deconvolution of the C1s XPS spectrum of the initial and nitric acid treated fluorinated samples.

Figure 1 .

 1 Figure 1. C1s XPS spectra, after background subtraction, of the a) pristine SWCNTs, b) SWCNTs

[ 2 ,Figure 2 .

 22 Figure 2. F1s XPS spectra, after background subtraction, of the a) SWCNTs fluorinated for 2h at 300

Figure 3 .

 3 Figure 3. FTIR spectrum of the precursor fluorotubes (left) and final oxyfluoro-compound obtained

Figure 4 .

 4 Figure 4. From left to right: TEM micrographs obtained from the pristine (bundle), fluorinated (bundle),

Figure 1 .

 1 Figure 1. C1s XPS spectra, after background subtraction, of the a) pristine SWCNTs, b) SWCNTs

Figure 2 .

 2 Figure 2. F1s XPS spectra, after background subtraction, of the a) SWCNTs fluorinated for 2h at 300

Figure 3 .

 3 Figure 3. FTIR spectrum of the precursor fluorotubes (left) and final oxyfluoro-compound obtained

Figure 4 .

 4 Figure 4. From left to right: TEM micrographs obtained from the pristine (bundle), fluorinated (bundle),

Table 1 .

 1 Peak analysis arising from the spectral deconvolution of the C1s XPS spectrum of the initial and nitric acid treated fluorinated samples.

	Sample	Binding energy (eV) Carbon environment Relative intensity
	Fluorinated precursor	284.5	C-C-C (a)	37.0 %
		286.1	C-CF	10.8 %
		288.8	C-F	45.1 %
		291.1	CF2	5.1 %
		292.8	CF3	2.0 %
				Composition
		From assignment of C1s peaks	CF0.61
			From peak area ratio	CO0.02F0.52
	Acid treated material	285.3 286.1	C-CO C-OH + C-CF	] 72.9 %
		287.4	C-OC or C=O (b)	9.3 %
		289.3	CF or O=C-OH (b)	9.9 %
		291.0	CF2	5.0 %
		293.0	CF3	2.9 %
				Composition
		From assignment of C1s peaks	COyF0.29
			From peak area ratio	CO0.47F0.29

a C indicates the atom responsible for the photoemission signal, each time.

  . Because of excessive peak overlap at low energy, reliable relative intensities in this region can not be confidently extracted, but taking the global oxygen content and the sufficiently

	resolved	ether	signal	as	references,	the	following	approximate	quantitation
	C≈0.30(CF)0.10(CF2)0.05(CF3)0.03(C2O)≈0.05(COH)≈0.42 has been obtained, i.e. more than 50% of the carbon
	atoms seem functionalised.


Victor Anaya
email: vanaya@cigip.upv.es

Giuseppe Berio
email: giuseppe.berio@univ-ubs.fr

Mounira Harzallah
email: mounira.harzallah@univ-nantes.fr

Patrick Heymans

Raimundas Matulevičius

Andreas L Opdahl
email: andreas.opdahl@uib.no

Hervé Panetto
email: herve.panetto@cran.uhp-nancy.fr

Maria Jose Verdecho
email: mverdecho@cigip.upv.es

<andreas Opdahl

The Unified Enterprise Modelling Language -Overview and Further Work

The Unified Enterprise Modelling Language (UEML) aims at supporting integrated use of enterprise and IS models expressed using different languages. To achieve this aim, UEML offers a hub through which modelling languages can be connected, thereby paving the way for also connecting the models expressed in those languages.

This paper motivates and presents the most central parts of the UEML approach: a structured path to describing enterprise and IS modelling constructs; a common ontology to interrelate construct descriptions at the semantic level; a correspondence analysis approach to estimate semantic construct similarity; a quality framework to aid selection of languages; a meta-meta model to integrate the different parts of the approach; and a set of tools to aid its use and evolution. The paper also discusses the benefits of UEML and points to paths for further work.

Introduction

Emerging information and communication technologies are becoming increasingly model-driven. An important driving force behind the model-driven trend is to provide ICT solutions that are both adaptable and integrated at the same time. One idea is that model-driven system can easily be adapted at the model level, so that a change to the system model automatically effects a corresponding change of the running system, without requiring resourcedemanding and error-prone manual re-design and re-implementation. Another idea is that two model-driven systems can be easily integrated at the model level, so that a mapping from one system model to another automatically configures middleware (such as enterprise application integration software) that integrates the running systems, again without human intervention. For example, a customer-relationship management (CRM) system in an enterprise may in the future be driven by a set of models that represent, e.g., the relevant human roles and types of products. And the same enterprise may possess a product-line management (PLM) system driven by a set of models that represent, e.g., the products and their features, product variants and the dependencies between them. Having model-driven systems for CRM and PLM is highly beneficial because it makes the systems easier to change whenever new requirements are identified. In addition, the two systems become easier to integrate when the representations of products in the two system models are kept complete and consistent.

But the above scenario works best for systems that are driven by models expressed in interoperable languages, meaning that it is possible to compare and otherwise relate the models automatically. When model-driven information systems are driven by models expressed using non-interoperable languages, the models easily become inconsistent with one another as they evolve, because they cannot be automatically compared or otherwise related to one another. This will make it much harder to integrate the running systems they drive. Model-driven technologies

may thus end up reinforcing -rather than alleviating -existing interoperability problems. In the above scenario, the modelling languages that drive the CRM and PLM systems may not be interoperable. For example, the CRM models may be expressed in a language with many specialised modelling concepts for people (as customers, users, salesmen etc.) in addition to products, whereas the PLM models are expressed in another modelling language that is particularly rich on concepts for expressing product features, variants and dependencies. This makes it difficult to ensure that products and their variants are represented in compatible ways in the two systems: every change to how products are represented in the CRM system must be immediately reflected in the PLM system and vice versa, but it becomes hard to provide tool support for this process. Manual model updates are slow and error prone and, as more model-driven systems are added to the picture, the number of dependencies between models grows faster than linearly. It is not easy for the enterprise to standardise its use of modelling languages either, because it may cut the enterprise off from the newest model-driven systems that are driven by the richest, most specialised models. The situation creates a need for theories, technologies and tools that allow information systems to be adapted and evolve, each driven by the most suitable languages for their purposes and context, while allowing the information systems and the models that drive them to be used in an integrated manner. the existing models as they are and, in addition, establishing correspondences between them in an explicit and usable way. Examples of useful services are consistency checking, automatic update reflection and model-to-model translation across modelling language boundaries. Figure 1 shows a selection of model types commonly used in modern enterprises for a wide range of purposes. Each of them requires modelling languages with different properties. UEML is intended as a hub for connecting these and other types of languages, eventually along with models expressed in those languages. To achieve this aim, UEML comprises:  a structured approach to describe enterprise and IS modelling constructs syntactically and semantically,  an evolving common ontology to interrelate the semantics of different modelling constructs,  a correspondence analysis approach that uses the common ontology to identify and quantify semantic similarities between modelling constructs,  a quality framework to define and evaluate the quality of enterprise and IS modelling languages in order to aid language selection for specific purposes,  a modular meta-meta model to organise the overall UEML framework and  a set of tools to aid its use and evolution.

The purpose of this paper is to present an overview of UEML and to discuss paths for further work. The paper is organised as follows: Section 2 presents UEML's background and its vision. Section 3 explains how languages and constructs are described in UEML, whereas Section 4 shows how descriptions of constructs are tied together by a common ontology. Section 5 discusses how correspondences between languages and constructs can be established and used, e.g., to support model-to-model translation across languages. Section 6 shows how enterprise and IS modelling languages are classified and selected in UEML according to specific goals. Section 7 presents the metameta models that hold the UEML framework together, whereas Section 8 reviews the various prototype tools supporting its use and evolution. Section 9 discusses UEML in its present state, before Section 10 concludes the paper and offers paths for further work.

Background

The idea of a Unified Enterprise Modelling Language first emerged during the ICEIMT'97 conference [START_REF] Goossenaerts | Formal Semantics of Enterprise Models[END_REF], with the aim of providing an underlying formal theory for enterprise modelling languages. A major motivation was the "Tower of Babel" situation that hindered proliferation of enterprise modelling in industry [START_REF] Vernadat | UEML: Towards a Unified Enterprise Modelling Language[END_REF]. The first development version of a unified enterprise modelling language was delivered by the UEML Thematic Network (UEML-TN 2002[START_REF] Moody | Measuring the Quality of Data Models: an Empirical Evaluation of the Use of Quality Metrics in Practice[END_REF], funded by the EU's FP5 [START_REF] Jochem | Common Representation through UEML -Requirement and Approach[END_REF][START_REF] Panetto | A Unified Enterprise Modelling Language for enhanced interoperability of Enterprise Models[END_REF][START_REF] Mertins | User oriented Enterprise Modeling for Interoperability with UEML[END_REF][START_REF] Berio | Supporting Enterprise Integration through a Unified Enterprise Modeling Language[END_REF].

UEML development has since continued within the Interop-NoE (2003[START_REF] Tu | Ontological Evaluation of BMM and i* with the UEML Approach[END_REF] Network of Excellence, funded by EU's FP6, which produced two further development versions of UEML, 2.0 and 2.1 (Berio, Opdahl, Anaya & Dassisti 2005a[START_REF] Berio | Deliverable DEM2[END_REF], 2006).

The following scenarios illustrate the UEML vision:

 Exchanging information contained in enterprise and IS models across modelling language boundaries. This is the central motivation behind UEML, which explains its focus on interoperability between modelling languages as a prerequisite for integrated use of the models that are expressed in those languages.

 Creating new problem-and/or domain-specific methods by combining elements from existing modelling techniques. UEML aims to make it easier to combine modelling languages and associated techniques and tools depending on the problem at hand, an ambition resembling that of method engineering [START_REF] Brinkkemper | Assembly Techniques for Method Engineering[END_REF][START_REF] Henderson-Sellers | Method Engineering and COTS Evaluation[END_REF], Ralyé & Rolland 2001). In particular, UEML aims to support local tailoring/adaptation of languages and constructs to fit local practices and needs, possibly producing new domain-specific languages as a result.

 Systematic, quality-driven, reuse of existing enterprise and IS modelling languages. Combining techniques and tools across modelling languages has the side benefit of making the languages available for the domains where they are most suited, without limitations posed by modelling tools and other technologies.

 Defining a core language for enterprise and IS modelling. As UEML stabilises, it may become possible to extract a core set of modelling construct to use as the starting point for a new enterprise/IS modelling language. Such a UEML core language should be composed of those constructs that have proven most useful for practical, integrated model use. However, the core language scenario should be understood as a longer term objective that is beyond the scope of this paper.

 Facilitating a web of languages and of models is another long-term objective. Whereas much research and development effort has gone into techniques and tools for integrated management of structured data (e.g., relational database theory) and of semi-structured data (e.g., XML and other web technologies), there is a lack of theory and technology for integrating information resources in the form of diagrammatic models.

UEML could contribute to growing a web of languages and of models in a way that resembles the touted semantic web of semi-structured data (Berners-Lee, Hendler & Lassila 2001).

Although UEML is intended as a hub for connecting different languages and different models expressed in those languages, it should not necessarily be the only means of making enterprise and IS languages and models interoperable. Other theories, technologies and tools may be better suited for certain integration needs and should possibly be made usable alongside UEML.

Language and Construct Description

UEML facilitates integrated model use by making semantic correspondences between the modelling constructs of different languages clear. Making the languages interoperable is seen as a first step towards also making the models expressed in those languages interoperable. A central part of UEML is therefore a standard, integrative and evolvable approach to describing enterprise and IS modelling constructs. By standard we mean that it provides a structured path to describing modelling languages, diagram types and constructs. By integrative we mean that, as soon as the languages, diagram types and constructs have been described in the UEML way, they have also become prepared for assessment of semantic correspondences, possibly across languages. And by evolvable we mean that UEML will be able to grow and adapt by incorporation and modification of additional modelling languages and constructs without becoming overly complex and thus unmanageable.

The descriptions of individual modelling constructs are particularly important, because it is this level that connects different modelling languages. Hence construct descriptions are more complex than descriptions of languages and diagram types. Specifically, in UEML, two distinct descriptions need to be made for each construct [START_REF] Opdahl | The UEML Approach to Modelling Construct Description[END_REF]):

 Presentation (or concrete syntax), which deals with the presentation of the modelling construct as part of model diagrams or in serialised form, e.g., in an XML file.

 Representation (or semantics), which accounts for which enterprise phenomena the construct is intended to represent (in particular covering reference, a central aspect of semantics).

Whereas a construct can have many presentations, it can have only one representation. This paper will focus on the representation part, which has so far been more developed than presentation.

In UEML, semantics is described by a representation mapping of each modelling construct into a common ontology, based on earlier work by [START_REF] Opdahl | A Template for Defining Enterprise Modelling Constructs[END_REF][START_REF] Krogstie | Evaluating UML Using a Generic Quality Framework[END_REF]. The UEML uses separation of reference to break individual modelling constructs into their ontologically atomic parts, along the following six axes:

1. Which class(es) of things is the construct intended to represent? Most modelling constructs somehow represent one or more classes of things. Even when the primary purpose of a construct is to represent certain properties, states or transformations, the construct implicitly also represents a property of, state of or transformation in, one or more classes of things. (A transformation may correspond either to an atomic event or a complex process.) 2. Which properties is the construct intended to represent? Most modelling constructs somehow represent one or more types of properties, which may either be intrinsic properties (belonging to only one thing) or relationships (properties that are mutual to several things). Some intrinsic properties are laws that restrict other properties. Even if the primary purpose of a construct is to represent classes, states or transformations, it represents classes, states or transformations that involve one or more types of property.

3. Which states is the construct intended to represent? Some modelling constructs are intended to represent a more or less restricted state in one or more classes of things. The state law that restricts the state can be described in terms of the properties of those classes. Whereas most modelling constructs represent one or more properties and, at least, one or more classes, not all constructs are intended to represent a state. 4. Which transformations is the construct intended to represent? Some constructs are intended to represent a simple or complex transformation of one or more classes of things from one state to another. The transformation law that effects the transformation can be described in terms of the states of those classes.

Again, not all constructs are intended to represent a transformation. Although some constructs are apparently not intended to represent behaviour at all, other constructs represent particular states, transformations.

Which instantiation levels is the construct intended to represent?

A modelling construct represents classes, properties, states and transformations at either the instance or type level or both.

6. Which modality (or mode) is the construct intended to represent? We usually think of enterprise and IS models as assertions of facts about a domain, e.g., assertions that something is or is not the case in the enterprise. But some model elements may instead state that someone wants something to be the case, or that someone is not permitted to do something, or that someone knows something is the case¸ or that something will be the case some time in the future.

Hence, whereas the two first axes deal with structure, the next two deal with behaviour. Together, these four axes describe the semantics of a modelling construct by describing a state of affairs, or a scene, played by several classes, properties and, perhaps, states and transformations together. The final two axes supplement the scene with information about the construct's intended use, i.e., its instantiation level and modality/mode. Example. We will use the Goal constructs from the GRL [START_REF] Yu | Towards Modeling and Reasoning Support for Early-phase Requirements Engineering[END_REF] and KAOS (van Lamsweerde & Willemet 1998) languages as our running example. Figure 2 shows how the KAOS.Goal construct is broken down into its semantically atomic parts using separation of reference (Matulevicius, Heymans & Opdahl 2006. 2007a, 2007b). A Goal in KAOS represents a pair of things belonging to different classes. The goalOwner is a thing that wants the goal to be achieved, and the concernedObject is the thing, usually a complex system, that the goal is about. A KAOS.Goal also represents a few properties of these two things. One such property is theGoal itself. This property belongs to the goalOwner and describes those states of the concernedObject in which the KAOS.Goal is achieved.

The goal property is described further in terms of its subproperties that, e.g., attribute a Name to theGoal and indicate which object the goal is about (i.e., the concernedObject). Because KAOS.Goals are considered structural in this example, there is no behavioural part with represented states and transformations. The instantiation level is either type or instance and the modality is intentional from to the goalOwner side and obligational for the concernedObject. ▢

The Common Ontology

To tie modelling-construct descriptions together, UEML uses a common ontology into which the represented classes, properties, states and transformations of each construct are mapped. The common ontology thereby comes to interrelate the construct descriptions at the semantic level.

The UEML ontology is organised into four taxonomies: The classes in the ontology are organised in a conventional generalisation hierarchy. Properties, on the other hand, have their places in a precedence hierarchy, where a property precedes another if every thing that possesses the second property necessarily also possess the first. (For example, associated-with precedes having-content, because everything that is having-content is also associated-with that content.) There are similar generalisation hierarchies of states and of transformations too. Classes, properties, states and transformations -including the state and transformation laws -all have attributes. For example, they all have unique names and there are cardinality constraints and role names on the associations between classes and properties. [START_REF] Bunge | Ontology I: The Furniture of the World[END_REF][START_REF] Bunge | Ontology II: A World of Systems[END_REF]) and which will keep growing as more modelling languages and constructs are added to UEML.

Figure 5. The current UEML taxonomy of properties, which has evolved from Bunge's ontological model [START_REF] Bunge | Ontology I: The Furniture of the World[END_REF][START_REF] Bunge | Ontology II: A World of Systems[END_REF] and which keeps growing along with the class taxonomy in Figure 4.

Example. Figures 4 and5 show the current UEML taxonomies of classes and of properties respectively. The two taxonomies, and the corresponding ones for states and transformations, are not static, but will keep evolving as more languages and constructs are incorporated into UEML.

In Figure 4, the most general class is Anything, used to describe constructs that are intended to represent any type of thing. The subclasses of Anything are more specific. Composite is used to describe constructs that represent things that are composed of parts, and its subclass System is used for constructs whose parts affect one another's behaviour.

The Component class is used to represent constructs that represent parts of Composite things, whereas the AssociatedThing is used for constructs that represent things that are somehow related to one another.

ChangingThing is used to describe constructs that represent dynamic behaviour, whereas AttributedThing is used to describe constructs that represent things to which humans have assigned particular properties, such as a name or sort. These more specific classes are further subclassed. The UEML ontology was first populated with a set of initial classes, properties, states and transformations derived directly from Mario Bunge's ontological model [START_REF] Bunge | Ontology I: The Furniture of the World[END_REF][START_REF] Bunge | Ontology II: A World of Systems[END_REF] and the Bunge-Wand-Weber representation model of information systems, the so-called BWW model (Wand & Weber 1988a, 1988b[START_REF] Wand | On the ontological expressiveness of information systems analysis and design grammars[END_REF][START_REF] Wand | On the deep structure of information systems[END_REF]. Since then, it has evolved and grown as new constructs have been added. Currently, UEML incorporates a selection of academic and industrial modelling languages, such as ARIS [START_REF] Dossogne | Evaluation of ARIS and BPMN using the UEML approach[END_REF], BMM [START_REF] Tu | Ontological Evaluation of BMM and i* with the UEML Approach[END_REF], BPMN [START_REF] Dossogne | Evaluation of ARIS and BPMN using the UEML approach[END_REF], coloured Petri nets, GRL (Dallons, Heymans & Pollet 2005[START_REF] Heymans | A Template-Based Analysis of GRL: Book chapter[END_REF][START_REF] Matulevičius | Comparison of Goal-oriented Languages using the UEML Approach[END_REF], 2007a[START_REF] Tu | Ontological Evaluation of BMM and i* with the UEML Approach[END_REF]), IDEF3 [START_REF] Harzallah | Incorporating IDEF3 into the Unified Enterprise Modelling Language (UEML)[END_REF], ISO/DIS 19440, KAOS [START_REF] Matulevičius | Comparison of Goal-oriented Languages using the UEML Approach[END_REF], 2007a, 2007b), UEML 1.0 and selected diagram types from UML (OMG-UML 2009), version 2.0. In consequence, the most general concepts in the common ontology are ontologically committed, in the sense that they have grown out of Bunge's ontology and the BWW model, whereas the more specific ones have emerged through language and construct analyses. that it has sub-properties (some of which it constrains as a LawProperty). ▢

Language and Construct Correspondences

To support integrated use of models, UEML must offer ways to exploit the mappings to identify and manage correspondences among language constructs and among model elements. Correspondences between any pair of constructs can be examined by comparing their mappings into the common ontology. If two modelling constructs are identical, they will map into the exact same ontology concepts. If two modelling constructs do not overlap at all, they will map into concepts that are not closely related in their respective taxonomies. However, the most common situation will most likely be where the modelling constructs map into some common ontology concepts, into some concepts that are closely related and into some that are not. Table 1. Detailed comparison of the GRL.GOAL and KAOS.Goal modelling constructs via their mappings into ontological concepts.

Example. Figure 8 shows how the Goal construct from another goal-oriented language, this time GRL [START_REF] Yu | Towards Modeling and Reasoning Support for Early-phase Requirements Engineering[END_REF], is broken down in the same manner as KAOS.Goal and similarly mapped to classes and properties in the common UEML ontology. Comparing Figures 7 and8 via their mappings into the same ontological concepts provides us with a precise description of exactly how GRL.Goal and KAOS.Goal are similar and exactly how they differ. Table 1 compares the two based on their construct descriptions, showing how the UEML descriptions points towards automatic translations from GRL to KAOS Goals. As shown in Figure 9, the ontology mappings indicate that the Name of a GRL.Goal maps directly into its KAOS counterpart, and similar for GRL.Goal Descriptions, which map to KAOS.Goal Defs. The ontology mappings also suggest that GRL.Actor may correspond to both KAOS.GoalOwner and KAOS.Agent, but that this cannot be established from the ontological mappings alone. Further work will have to investigate how reasoning techniques based on language structure and other information can be used to identify even more precise language correspondences. Finally, the comparison indicates that the FormalDef and Category attributes of a KAOS.Goal are not covered specifically by a GRL.Goal and cannot be provided when a KAOS model is derived from a GRL model alone. Accordingly, these attributes would be lost if a KAOS model were to be transformed into GRL. In this way, the UEML framework even makes it clear which information is missing and lost when model information is moved across language boundaries.  Generalisation occurs when one modelling construct represents a state of affairs that generalises the state of affairs represented by another. When one construct generalises another, the general construct can replace the special one in a model-to-model translation (with some loss of information), but the inverse replacement is only appropriate under specific circumstances.

Of course these simple kinds of correspondences are not independent. For example, constructs that are equal will trivially contain and generalise one another. There are also complex correspondences, e.g., when one construct represents a state of affairs that generalises a part of the state of affairs represented by another, thus combining containment and generalisation. There are also overlapping constructs, each of which contains part, but not all, of the other. However, a complete typology of correspondences and how they combine stills needs to be worked out.

Correspondences are also characterised by different degrees of precision. For example, it is possible to only take into account how each construct is mapped into ontology concepts, ignoring how the concepts are related within the construct description. More precise correspondences can be identified by taking into account both ontology concepts and the relations between them, but ignoring the roles that the concepts may play in the relations. Finally, both the ontology concepts, the relations between them and the roles played can be taken into account. Because correspondences are generally ways to assess to what extent constructs are similar or dissimilar (under a precision degree), it might be possible to characterise correspondences by using correspondence measures (CM). In this sense, a CM is a function:

CM: UEML C UEML C →
In this function, UEML C represents the set of constructs incorporated into UEML. CM results from explicit selections ranging on the following five parameters: correspondence type, precision degree, technique, type of data and evaluation method, as shown in Figure 10. The form of the function is related to the correspondence type to be identified (e.g. equality). There are three well-known forms of function that can be used, i.e., Jaccard, Recall and Precision [START_REF] Gower | Metric and Euclidean Properties of Dissimilarity Coefficients[END_REF]. The type of data taken as input by the function is varying depending on the precision degree required. Type of data constrains the specific technique that can be used for effectively evaluating function results as well (using, e.g., structure-based, graph-based or attribute-based techniques) [START_REF] Lin | An Information-Theoretic Definition of Similarity[END_REF][START_REF] Rodrýguez | Determining semantic similarity among entity classes from different ontologies[END_REF][START_REF] Blanchard | A Tree-Based Similarity for Evaluating Concept Proximities in an Ontology[END_REF]. Finally, the measure should be meaningful. To this end, an evaluation method should be defined to evaluate the measurement accuracy. According to [START_REF] Budanitsky | Lexical Semantic Relatedness and its Application in Natural Language Processing[END_REF], accuracy of the measure can be evaluated by comparing the measurement results with correspondences found in three alternative and distinct ways: 1) theoretical investigation 2) human judgement and 3) knowledge about a particular application.

Correspondence measures can also be used to validate the representation mappings and the common ontology, when correspondence measures derived automatically from the common ontology is compared to expert estimates of the same correspondences. Deviations indicate that the representation mapping for a construct is wrong and/or that there are weaknesses in the common ontology. There may be concepts missing from the common ontology, or there may be taxonomical relations between ontology concepts missing, e.g., a missing generalisation relation from a sub-to a superclass. If left undetected, missing taxonomical relations can lead to redundancies in the common ontology when the same subclass is added several times because it cannot be retrieved as a specialisation of its superclass. In this way, correspondence measures can also aid elimination of redundancy in the common ontology.

Correspondence measures as representative of correspondences are useful as high-level guides for model-to-model translation and other cross-language services. The representation mappings and common ontology provide the details for how to translate between modelling constructs belonging to different languages, as soon as the pair of modelling constructs to translate between have been decided. But it offers less help with deciding which constructs in one language to translate into which constructs in another. The correspondence measures can help by suggesting, for each construct in a language, which constructs in the other language that are most suitable as targets for, e.g., translation, leaving the final choice to be made by the model manager. When the construct-to-construct correspondences at the language-level have been established in this way, the representation mapping and common ontology are there to support the detailed construct-level mappings.

Language Quality Framework

Together, the representation mappings, common ontology and correspondence measures contribute towards integrated use of models expressed in different languages. But there is also a need to select suitable languages to include in the UEML in the first place. For example, to quickly enrich the common ontology, it may be better to incorporate a much used and relatively complete language early on than a narrower language used only by specific communities. Later, when using UEML, there is also a need to select suitable languages for particular purposes among the many available. UEML therefore includes a language quality framework [START_REF] Anaya | Evaluating Quality of Enterprise Modelling Languages: The UEML Solution[END_REF]) that aids language selection by:  defining the concept of quality of a modelling language;  supporting methodical, goal-dependent evaluation of the quality of enterprise and IS modelling languages.

The current quality framework has adapted and extended the SEQUAL quality framework [START_REF] Krogstie | Using a Semiotic Framework to Evaluate UML for the Development for Models of High Quality[END_REF][START_REF] Krogstie | Evaluating UML Using a Generic Quality Framework[END_REF], which provides a model of the quality of models, later extended to also account for the quality of languages.

SEQUAL identifies 8 quality types for characterising what quality is: physical quality, empirical quality, syntactic quality, semantic quality, perceived semantic quality, pragmatic quality, social and organisational quality. For example, semantic quality is the correspondence between the model and the domain. SEQUAL also identifies several types of appropriateness, each indicating a language aspect that must be considered when assessing whether a language is appropriate for a particular purpose [START_REF] Krogstie | Using a Semiotic Framework to Evaluate UML for the Development for Models of High Quality[END_REF][START_REF] Krogstie | Evaluating UML Using a Generic Quality Framework[END_REF]. For example, comprehensibility appropriateness reflects the ease with which the language its model can be understood by a certain audience. In SEQUAL, each quality type is related to one or more appropriateness types and vice versa. For example, domain appropriateness is used to assess physical and semantic qualities. Therefore, the different types of appropriateness provide the context for evaluating the related quality types.

In addition to SEQUAL, the UEML quality framework has been inspired by two additional quality frameworks: Moody's framework (2003) and ISO/IEC 9126 international standard for assessing software product quality (ISO/IEC 2001). These two frameworks have been adapted and aligned with SEQUAL's appropriateness types through a generalisation hierarchy [START_REF] Berio | Deliverable DEM2[END_REF].

The resulting appropriateness types in UEML's quality framework remain too general to allow concrete evaluations [START_REF] Anaya | Evaluating Quality of Enterprise Modelling Languages: The UEML Solution[END_REF]. Therefore, the framework also covers requirements and criteria. Requirements are collected from users (actors or experts), asking them how enterprise modelling should contribute towards enterprise integration and interoperability, based on a requirements base established in the previous UEML Thematic Network (UEML-TN 2002[START_REF] Moody | Measuring the Quality of Data Models: an Empirical Evaluation of the Use of Quality Metrics in Practice[END_REF]. Criteria are the operational, or measurable, counterparts of requirements. Each criterion can in turn be related to one or more appropriateness types, making it clear to which quality types the criterion contributes. The framework provides two complementary ways of collecting data for evaluating criteria.

The language template is used to gather general and factual information about a language, such as its notations and meta models, whereas the language-evaluation questionnaire comprises both questions derived from current criteria and an associated glossary [START_REF] Verdecho | Language Evaluation Questionnaire for Enterprise Modelling Languages[END_REF].

The framework also covers language descriptions, which cover, e.g., a language's owner and version; goals, which are aggregations of criteria for the purpose for evaluating language quality; metrics-for-goal, which are selected metrics relevant to a specific goal (metrics are needed to perform criteria assessment); metric evaluations, which are specific evaluations (for instance, a value) of a single metric on a specific language; combined metrics evaluations, which are combined evaluation of several metrics evaluations for a given language and a given goal (an explicit combined metrics evaluation makes explicit how several single metrics are combined, e.g., with a weighted formula, to evaluate the quality of a language with respect to a given goal; additionally, it is useful because the same metrics evaluation can be used several times if needed). The UML class diagram in Figure 11 shows the key concepts used to evaluate the quality of modelling languages in UEML. The associated quality evaluation method gives a clear picture of how to evaluate and select one or more enterprise and/or IS modelling languages for a specific purpose. The first task is to define the goal as an aggregation of criteria and then select suitable metrics for each criterion. A list is made of languages to be evaluated. The language template is used to collect factual information about each language, and the language-evaluation questionnaire is used to collect subjective opinions. Hence, whereas only a single filled-in language template is needed for each language, multiple filled-in questionnaires from language users are usually needed. Once the selected criteria are assessed by using selected metrics and storing these assessments as metrics evaluations, combined metrics evaluations are calculated and stored. Finally, languages must be suitably selected based on the results stored as combined metrics evaluations. Before its use, an enterprise may undertake a customisation of the quality framework: This simply means to define additional requirements, appropriateness types, criteria and metrics.

Table 2. Examples of criteria for language appropriateness, along with their descriptions.

Example. Table 2 provides examples of of criteria for language appropriateness, along with their descriptions.

Meta-Meta Models

The UML class diagrams of the language and construct description approach (Section 3), of the common ontology (Section 4), of the correspondence analysis approach (Section 5) and of the quality framework (Section 6) are all meta-meta models. They are meta-meta models because models of modelling languages are meta models and because Figures 3,6 and 10-11 are models of how to model aspects if modelling languages (thus of how to model meta models). The UML diagrams are intended as illustrations only. For example, Figures 3 and6 do not show attributes and omit several association classes and abstract classes. More detailed meta-meta models can be found in [START_REF] Opdahl | The UEML Approach to Modelling Construct Description[END_REF].

Whereas the representation mappings connect Figures 3 and6, the meta-meta models of the correspondence analysis and language quality frameworks in Figures 10-11 are currently connected to Figure 3 only through the language description in Figure 6. Further work should establish a single combined, yet modular, meta-meta model that covers all constituents of the UEML framework, the overall UEML meta-meta model.

The meta-meta models, in particular the construction description approach and the common ontology in Figures 3 and6, serve the same purpose for UEML as the OMG's MetaObject Facility (OMG-MOF 2009) does for UML.

However, the two meta-modelling approaches differ in two ways: in how they deal with semantics and in how coarsely they describe modelling constructs. At the semantic level, the UEML meta-meta model distinguishes between the ontological concepts of things, properties, states and transformations, which are considered ontologically fundamental for enterprise and IS models. In contrast, the OMG's MOF makes weaker ontological assumptions, representing modelling constructs in terms of meta classes (MOF::Classes) along with their properties, associations and association roles. In consequence, MOF meta models tend to focus first on representing syntactical information about languages. To the extent that problem-domain semantics are also represented, they are grafted onto the primary (abstract and/or concrete) syntactical meta-model structure. Indeed, MOF does provide some builtin semantics, but these are semantics for MOF-based repositories, i.e., semantics required for creating objects according to MOF specifications, not problem-domain semantics that describe which phenomena in the problem domain a modelling construct is intended to represent. This contrasts UEML's language and construct descriptions, which only deal with problem-domain semantics. At the semantic level, UEML and MOF are thus complementary: they focus on distinct aspects of languages, the first on the ontological problem-domain semantics, the second on repository semantics.

At the construct-description level, UEML's use of separation of reference leads to descriptions of modelling constructs that are more fine grained than most MOF descriptions. Indeed, Opdahl & Henderson-Sellers (2005) argue that the quality of MOF's meta models is compromised by the many referentially redundant modelling constructs that result from using MOF, where a referential redundancy occurs when multiple modelling constructs or model elements represent the same thing or property in the problem domain. The UEML meta-meta model, in contrast, has been explicitly designed to discourage referential redundancies, leading to language descriptions that better support activities such as consistency checking, automatic update reflection and reusing model contents across modelling languages and notations.

Tools

UEML is supported by a set of prototype tools realised using a selection of existing technologies. There are currently five tools in the set:

 UEMLBase Repository is a Protege-OWL realisation of the representation and ontology meta-meta models of Figures 3 and6, translated into OWL.

 UEMLBase Editor is an emerging set of Eclipse GMF-based editors for browsing and updating the contents of the UEMLBase repository.

 UEMLBase Manager is a Java-plugin for Protege-OWL that provides merging, reporting and other housekeeping functions for the repository.

 UEMLBase Verifier is a set of Prolog rules and a Prolog rule checker that support formal verification of the contents in the UEMLBase repository, for example to check cardinality constraints and ensure that the construct descriptions are concrete. Prolog was chosen instead of newer technologies, such as SWRL, because of its high availability, robustness and general versatility [START_REF] Mahiat | A Validation Tool for the UEML Approach[END_REF].

 UEMLBase Analyser is another Java-plugin, which uses the repository to compute similarity measures between UEMLBase constructs based on the meta-meta model in Figure 10. It thus paves the way for consistency checking, automatic update reflection, model-to-model translation across languages, as well as other integrated model uses.

Each tool strives to be consistent with the meta-meta models of Figures 3, 6 and 10-11, although they realise more specific implementation models, such as OWL, Eclipse EMF, Java classes and Prolog facts. Hence, the meta-meta models is used to support interoperability within the UEML tool set.

Discussion

The paper has presented the main constituents of the UEML and explained how they are related. Languages, possibly selected with the aid of the quality framework, are described using separation of reference according to Section 3. The descriptions of the states of affairs are then mapped into the common ontology of Section 4. It thereby becomes possible to establish correspondences between different constructs in terms of their mappings into the common ontology as in Section 5. The selection of modelling languages is guided by the quality framework of Section 6. In the long term, the most used and useful concepts in the common ontology can be used to form a core UEML language for enterprise and IS modelling. In the long tern, UEML could also contribute towards developing a web of languages and of models in a way that resembles the touted semantic web of semi-structured data (Berners-Lee, Hendler & Lassila 2001), which is currently emerging in areas such as e-science and e-government [START_REF] Shadbolt | The Semantic Web Revisited[END_REF].

From an initial set of around 25 concepts taken more or less directly out of Bunge's ontology and the BWW model, the common UEML ontology has grown to comprise 110 concepts. Most of them have resulted from analyses of individual modelling constructs using separation of reference. (A few initial higher-level remain to organise and structure the four taxonomies.) As part of the Interop-NoE work, 130 constructs from the following 10 languages have been mapped into this ontology: ARIS, BMM, BPMN, GRL, IDEF3, ISO/DIS 19440, KAOS, coloured Petri nets, UEML 1.0 and selected diagram types from UML 2.0. However, they are not all described in equal detail and none of them are yet fully validated. The languages, constructs, mappings and ontology have all been stored in the UEMLBase Repository, supported by the Editor, Manager, Verifier and Correspondence Analyser tools.

The standardised approach to language and construct description has turned out to have several advantages, in particular at the modelling construct level. The structured descriptions become complete, consistent, cohesive and, thus, more learnable and understandable. It therefore becomes easier to compare them to one another. The structured approach also offers systematic and detailed advice on how to proceed when analysing individual language constructs. It encourages highly-detailed construct description, which leads to languages that are integrated at a fine level of detail. It supports ontological analysis in terms of particular classes, properties, states and events, and not just in terms of the concepts in general.

Instead of starting from scratch by building a new integrated modelling language, UEML leverages existing investments in enterprise modelling-language design and in their supporting tools by integrating existing languages with one another through a common hub. This contrasts the UML approach for software modelling, which built a new language with a limited set of diagram types from the bottom up (although the new language was extensible through stereotyping, tags and constraints, and it was based on selected existing notations like use cases). We suggest that enterprise and IS modelling and software modelling may need different integration strategies because the types of phenomena (things, properties, states and transformations) to can be part of an enterprise or information system is virtually unlimited, calling for fundamentally open-ended language integration approaches. Software modelling also deals with a highly complex domain, but one that is in the end limited by the evolution of software technology. Software modelling may therefore be better served by a closed, but potentially also more tightly integrated modelling language built from the bottom up.

The UEML framework has positive network externality, in the sense that incorporating an additional construct or language becomes:  more valuable the more constructs and languages that have already been incorporated, because the additional language becomes interoperable with a larger number of other languages;

 less costly because reusing an enriched common ontology and existing representation mappings provide good reference examples and because the cost of maintaining tools and infrastructure can be shared by more UEML users.

Similar positive network externality effects can be expected at the model level beside the language level discussed here, although this needs to be explored in further work. Indeed, the most extensive benefits can be expected at the model level, where UEML will enable integrated use of models expressed in different languages. Taking an analogy from traditional architecture and construction, it is likely that many of our most beautiful and useful buildings would have been impossible to design and build had different and semantically unconnected languages been used for all the parts of the building and stages of the building process.

Early experience with the construct description approach indicated that it was difficult to use because it was based on a novel, unconventional way of thinking about the semantics of modelling constructs. It was sometimes hard to find the appropriate classes, properties, states and events in the common ontology to use when describing a construct. Also, it was sometimes hard to determine exactly which part of a language that constitutes a modelling construct. As part of the Interop-NoE, tools and tutorials were developed that have seemingly resolved many of these problems. Also, early drafts of the common ontology have become available along with exemplary representation mappings. As a result, the first draft of several of the most recent language incorporations could be made by students with little direct supervision.

The language quality framework is also helpful for users that need to select the most suitable language for a practical setting. The framework captures the users' perspectives on the setting in the form of user requirements, and guides the use of requirements for evaluating languages for that particular setting.

Conclusion and Further Work

UEML is an ambitious, long-term effort that will require several years of cooperation between academia and industry. The overall challenge for further work is to extend the theory and tools developed by the Interop-NoE network to support practical integrated use of models and languages. In order to make UEML a working hub for exchanging information contained in models across modelling languages, further research must therefore focus particularly on how industrial enterprise and IS models can be automatically converted into UEML form and back to conventional model form, but in a different language. Although several paper-and-pencil trials have demonstrated the feasibility of our ideas [START_REF] Berio | Deliverable DEM2[END_REF]Matulevičius, Heymans, Opdahl, 2007;[START_REF] Harzallah | Incorporating IDEF3 into the Unified Enterprise Modelling Language (UEML)[END_REF], detailed methods for integrated model use still need to be developed and implemented.

For UEML-supported integrated model use to be tested in large-scale, realistic settings, the common ontology and representation mappings must be verified, validated and improved. The current ontology and mappings have been contributed by several Interop-NoE research teams working in a distributed manner. The most immediate challenge is to improve the ontology and mappings in two directions. Firstly, the Editor and Verifier tools are being extended and improved. Secondly, the Correspondence Analyser tool is used to compare correspondences calculated from the common ontology and the representation mappings with correspondence estimates provided by human experts. The comparisons are used to identify weaknesses in the representation mappings. For example, when two constructs are considered similar by human experts, but not by the Correspondence Analyser, the reason might be that one or more ontology concepts have been duplicated. Accordingly, when the Analyser, but not the human experts, deem two constructs similar, the reason may be weaknesses in the generalisation hierarchies in the ontology. In this way, verification not only supports improving the representation mappings but also controls the quality of the common ontology.

As for the overall UEML framework, an obvious path for further work is to connect the meta-meta models for language and construct description and for the common ontology with the one for the quality framework. Also, the combined meta-meta model must be extended to account for the presentation part of language and construct description and for construct correspondences. In addition to tying together the overall approach, this work can be expected to reveal further possibilities, such as deriving quality and appropriateness metrics for languages, not only at the language level, but also at the construct level from the detailed UEML ontology and mappings. A further extension would be to aid users in selecting not only the most suitable languages to use in practical setting, but also which models to integrate. The users' perspectives on the model level could be captured in terms of usage and business benefits, suggesting how integrated use of models can address key business requirements and, most importantly, suggesting which models that are worth connecting using UEML. The latter point is important for assessing cost-effectiveness, as it unlikely that UEML will be able to support fully automatic (and thus effortless) integrated use of models in the near term.

These and other possible future developments have been organised in a UEML roadmap comprising several research directions, each detailed by specific actions [START_REF] Opdahl | A Roadmap for the UEML[END_REF]): 1. Language breadth -include more languages; 2. Ontological depth -refine the common ontology; 3. Ontological clarity -elaborate the common ontology language; 4. Presentation -extend the support for presentation issues; 5. Mathematical formality -define UEML semantics formally; 6. Tool support -develop prototype tool with GUI and validation support; 7. Model management -provide support for model management in addition to language management; 8. Validationstructural and behavioural language and model validation; 9. Dissemination -make UEML known in industry and academia and as a standard; 10. Community -establish and maintain a committed and cohesive community for managing and evolving the UEML. Additional directions that deal specifically with the language quality framework are: 1. Continuing the development of the quality framework by introducing new criteria and extending the questionnaire accordingly; 2. Continuing the accommodation of existing quality frameworks by specialising appropriateness; 3. Gradually developing supporting tools based on the meta-meta model, starting from the current simple support for filling-in the questionnaire to complete functionality to define and evaluate metrics; 4. Launching use of the quality framework and especially by performing evaluations of languages for developing a core language; 5. Extending the scope of the quality framework to cover model quality in addition to language quality using a corresponding overall approach. For example, more specific quality frameworks can be used to systematically introduce new appropriateness measures and to specialise existing ones. The roadmap still needs to be extended to account better for correspondence analysis.

The UEML approach may even be useful outside enterprise and IS modelling, e.g., for software modelling.

Significantly, none of the central components of the UEML framework are specific to enterprise modelling. They may therefore be used for a wider set of modelling domains.

Figure 1 .

 1 Figure 1. A selectin of model types commonly used in modern enterprises, each of them ideally requiring dedicated modelling languages.

Figure 2 .

 2 Figure 2. A break-down of KAOS' Goal modelling construct (van Lamswerde & Willemet 1998).

Figure 3 :

 3 Figure 3: The main classes of the UEML representation meta-meta model, used to describe the semantics of modelling constructs.

Figure 4 .

 4 Figure 4. The current UEML taxonomy of classes, which has evolved from Bunge's ontological model (Bunge

Figure 5

 5 Figure 5 shows the corresponding taxonomy of properties. The most generic property is AnyProperty, which has 7 immediate successors. Of these, a PartWhole relation associates a Composite thing with its Components. A MutualProperty associates two or more AssociatedThings. A MutableProperty is characteristic of a ChangingThing etc. StateLaws and TransfomationLaws are more specific properties that are used to describe modelling constructs with dynamic behaviour in further detail. Hence, although it is now shown in the figures, each property in Figure 6 is characteristic of a class in Figure 5. For example Anything, the most general class, is characterised by the most generic property, AnyProperty. ▢

Figure 6 :

 6 Figure 6: The main classes of the common UEML ontology, into which construct descriptions are mapped.

Figure 7 .

 7 Figure 7. The ontological concepts used to describe the KAOS.Goal construct are mapped into the four taxonomies of the common UEML ontology.

Figure 8 .

 8 Figure 8. The ontological concepts used to describe the GRL.Goal construct are mapped into the four taxonomies of the common UEML ontology.

Figure 9 .

 9 Figure 9. The comparison of ontology mappings suggests how a GRL.Goal can be transformed into a KAOS.Goal to support, e.g., model-to-model translation across modelling languages. Three kinds of correspondences between modelling constructs have been identified as part of the UEML framework. Each of them can be precisely formulated in terms of the ontology classes, properties, states and transformations into which the constructs in the correspondence map:  Equality occurs when two or more constructs represent the exact same state of affairs, as explained in Section 3. If two constructs are equal, one can always replace the other without loss of information, e.g., for model-to-model translation.  Containment occurs when the state of affairs represented by one construct has the state of affairs represented by another as a part. When one construct contains several others, the former can be replaced by a combination of the others during model-to-model translation.

Figure 10 :

 10 Figure 10: The main classes of the UEML correspondence analysis framework, used to identify and manage correspondences between modelling constructs.

Figure 11 :

 11 Figure 11: The main classes of the UEML language quality framework, used to classify and select modelling languages.

Acknowledgment

The authors are indebted to all the partners of Interop-NoE and, in particular, to the researchers participating in its Domain Enterprise Modelling. The authors are indebted to the many students who have contributed to the work, including Emmanuel Blanchard, Aurelie Dossogne, Cedric Jeanmart, Alf Harry Karlsen, Jeremy Mahiat, Christophe Tu, Torbjørn Vefring and Tomas Zijdemans. This work was partially funded by the Interop Network of Excellence and by the Interuniversity Attraction Poles Programme, Belgian State, Belgian Science Policy.