Nathalie Villa
email: nathalie.villa@math.ups-tlse.fr

Fabrice Rossi
email: fabrice.rossi@inria.fr

A comparison between dissimilarity SOM and kernel SOM for clustering the vertices of a graph

Keywords: kernel SOM, dissimilarity, graph

Flexible and efficient variants of the Self Organizing Map algorithm have been proposed for non vector data, including, for example, the dissimilarity SOM (also called the Median SOM) and several kernelized versions of SOM. Although the first one is a generalization of the batch version of the SOM algorithm to data described by a dissimilarity measure, the various versions of the second ones are stochastic SOM. We propose here to introduce a batch version of the kernel SOM and to show how this one is related to the dissimilarity SOM. Finally, an application to the classification of the vertices of a graph is proposed and the algorithms are tested and compared on a simulated data set.

Introduction

Despite all its qualities, the original Self Organizing Map (SOM, [START_REF] Kohonen | Self-Organizing Maps, 3rd Edition[END_REF]) is restricted to vector data and cannot therefore be applied to dissimilarity data for which only pairwise dissimilarity measures are known, a much more general setting that the vector one. This motivated the introduction of modified version of the batch SOM adapted to such data. Two closely related dissimilarity SOM were proposed in 1996 [START_REF] Kohonen | Self-organizing maps of symbol strings[END_REF][START_REF] Ambroise | Analyzing dissimilarity matrices via Kohonen maps[END_REF], both based on the generalization of the definition of the mean or median to any dissimilarity measure (hence the alternative name Median SOM). Further variations and improvements of this model are proposed in [START_REF] Kohohen | Self-Organizing maps of symbol strings[END_REF][START_REF] Conan-Guez | Fast algorithm and implementation of dissimilarity selforganizing maps[END_REF][START_REF] Golli | Une adaptation des cartes autoorganisatrices pour des données décrites par un tableau de dissimilarités[END_REF].

Another way to build a SOM on non vector data is to use the kernelized version of the algorithm. Kernel methods have become very popular in the past few years and numerous learning algorithm (especially supervised ones) have been "kernelized": original data are mapped into an high dimensional feature space by the way of a nonlinear feature map. Both the high dimensional space and the feature map are obtained implicitly from a kernel function. The idea is that difficult problems can become linear ones while being mapped nonlinearly into high dimensional spaces. Classical (often linear) algorithms are then applied in the feature spaces and the chosen kernel is used to compute usual oper-ations such as dot products or norms; this kernelization provides extensions of usual linear statistical tools into nonlinear ones. This is the case, among others, for Support Vector Machine (SVM, [START_REF] Vapnik | The Nature of Statistical Learning Theory[END_REF]) which corresponds to linear discrimination or Kernel PCA ( [START_REF] Schölkopf | Nonlinear component analysis as a kernel eigenvalue problem[END_REF]) which is built on Principal Component Analysis. More recently, kernelized version of the SOM has been studied: [START_REF] Graepel | Selforganizing maps: generalizations and new optimization techniques[END_REF] first proposes a kernelized version of SOM that aims at optimizing the topographic mapping. Then, [START_REF] Andras | Kernel-Kohonen networks[END_REF][START_REF] Donald | The kernel self organising map[END_REF] present kernel SOM that applies to the images of the original data by a mapping function; they obtain improvements in classification performances of the algorithm. [START_REF] Lau | Kernel selforganising maps for classification[END_REF][START_REF] Yin | On the equivalence between kernel selforganising maps and self-organising map mixture density networks[END_REF] also studied these algorithms: the first one gives a comparison of various kernel SOM on several data sets for classification purposes and the second proves the equivalence between kernel SOM and self-organizing mixture density network.

In this work, we present a batch kernel SOM algorithm and show how this algorithm can be seen as a particular version of the dissimilarity SOM (section 2). We target specifically non vector data, more precisely vertices of a graph for which kernels can be used to define global proximities based on the graph structure itself (section 3.1). Kernel SOM provides in this context an unsupervised classification algorithm that is able to cluster the vertices of a graph into homogeneous proximity groups. This application is of a great interest as graphs arise naturally in many settings, especially in studies of social networks such as World Wide Web, scientific network, P2P network ( [START_REF] Bornholdt | Handbook of Graphs and Networks -From the Genome to the Internet[END_REF]) or medieval peasant community ( [START_REF] Boulet | Partitionnement d'un réseau de sociabilité à fort coefficient de clustering. In 7èmes Journées Francophones[END_REF][START_REF] Villa | Clustering a medieval social network by SOM using a kernel based distance measure[END_REF]). We finally propose to explore and compare the efficiency of these algorithms to this kind of problems on a simulated example (section 3.2).

A link between kernel SOM and Dissimilarity SOM

In the following, we consider n input data, x 1 , . . . , x n from an arbitrary input space, G. In this section, we present self-organizing algorithms using kernels, i.e. functions k :

G × G → R such that are symmetric (k(x, x ′ ) = k(x ′ , x))
and positive (for all m ∈ N, all x 1 , . . . , x m ∈ G and all α 1 , . . . , α m ∈ R, m i=1 α i α j k(x i , x j ) ≥ 0). These functions are dot products of a mapping function, φ, which is often nonlinear. More precisely, it exists an Hilbert space, (H, ., . ), called a Reproducing Kernel Hilbert Space (RKHS), and a mapping function φ : G → H such that k(x, x ′ ) = φ(x), φ(x ′ ) . Then, algorithms that use the input data by the way of their norms or dot products are easily kernelized using the images by φ of the original data set: φ and H are not explicitely known as the operations are defined by the way of the kernel function.

On-line kernel SOM

A kernel SOM based on the k-means algorithm has been first proposed by [START_REF] Donald | The kernel self organising map[END_REF]. The input data of this algorithm are the images by φ of x 1 , . . . , x n and, as in the original SOM, they are mapped into a low dimensional grid made of M neurons, {1, . . . , M }, which are related to each others by a neighborhood relationship, h. Each neuron j is represented by a prototype in the feature space H, p j , which is a linear combination of {φ(x 1 ), . . . , φ(x n )}:

p j = n i=1 γ ji φ(x i ).
This leads to the following algorithm: Algorithm 1: On-line kernel SOM

(1) For all j = 1, . . . , M and all i = 1, . . . , n, initialize γ 0 ji randomly in R;

(2) For l = 1, . . . , L, do [START_REF] Bornholdt | Handbook of Graphs and Networks -From the Genome to the Internet[END_REF] assignment step: x l is assigned to the neuron, f l (x l ) which has the closest prototype:

f l (x l ) = arg min j=1,...,M φ(x l ) -p l-1 j (4)
representation step: for all j = 1, . . . , M , the prototype pj is recomputed: for all i = 1 . . . , n,

γ l ji = γ l-1 ji + α(l)h(f l (x l ), j) δ il -γ l-1 ji
End for.

where step (3) leads to the minimization of

n i,i ′ =1 γ l-1 ji γ l-1 ji ′ k(x i , x i ′ ) -2 n i=1 γ l-1 ji k(x i , x l ).
As shown in [START_REF] Yin | On the equivalence between kernel selforganising maps and self-organising map mixture density networks[END_REF], the kernel SOM can be seen as a result of minimizing the energy

E = n j=1 h(f (x), j) φ(x) -p j 2 stochastically.
Another version of the kernel SOM is also proposed by [START_REF] Andras | Kernel-Kohonen networks[END_REF]: it uses prototypes chosen in the original set and then computes the algorithm with the images by φ of this prototype. It comes from the minimization of the following energy

E = n j=1 h(f (x), j) φ(x) -φ(p j ) 2 .

Dissimilarity SOM with dissimilarities based on kernels

Dissimilarity SOM ( [START_REF] Kohohen | Self-Organizing maps of symbol strings[END_REF][START_REF] Conan-Guez | Fast algorithm and implementation of dissimilarity selforganizing maps[END_REF][START_REF] Golli | Une adaptation des cartes autoorganisatrices pour des données décrites par un tableau de dissimilarités[END_REF]) is a generalization of the batch version of SOM to data described by a dissimilarity measure. We assume given, for all i, i ′ = 1, . . . , n, a measure δ(x i , x i ′ ), that is symmetric (δ(x, x ′ ) = δ(x ′ , x)), positive (δ(x, x ′ ) ≥ 0) and such that δ(x, x) = 0. The Dissimilarity SOM proceeds as follows:

Algorithm 2: Dissimilarity SOM

(1) For all j = 1, . . . , M , initialize p 0 j randomly to one of the element of the data set {x1, . . . , xn};

(2) For l = 1, . . . , L, do (3) assignment step: for all i = 1, . . . , n, xi is assigned to the neuron, f l (xi) which has the closest prototype:

f l (xi) = arg min j=1,...,M δ(xi, p l-1 j ) (4)
representation step: for all j = 1, . . . , M , the prototype pj is recomputed:

p l j = arg min x∈(x i ′ ) i ′ =1,...,n n i=1 h(f l (xi), j)δ(xi, x)
End for.

As shown in step ( 4), the purpose is to choose prototypes in the data set that minimize the generalized energy [START_REF] Conan-Guez | Fast algorithm and implementation of dissimilarity selforganizing maps[END_REF][START_REF] Golli | Une adaptation des cartes autoorganisatrices pour des données décrites par un tableau de dissimilarités[END_REF] propose variants of this algorithm: the first one allows the use of several prototypes for a single neuron and the second describes a faster version of the algorithm.

E = M j=1 n i=1 h(f (x i ), j)δ(x i , p j ).
In [START_REF] Villa | Clustering a medieval social network by SOM using a kernel based distance measure[END_REF], a dissimilarity based on a kernel is described: it is designed for the clustering of the vertices of a graph. To construct their dissimilarity, the authors take advantage of the fact that the kernel can be interpreted as a norm; then computing the distance induced by this norm leads to the definition of a dissimilarity measure on {x 1 , . . . , x n }:

δ med (x, x ′ ) = φ(x) -φ(x ′ ) (1) = k(x, x) + k(x ′ , x ′ ) -2k(x, x ′ ).
We can also define a variant of this dissimilarity measure by, for all x, x ′ in G,

δ mean (x, x ′ ) = φ(x) -φ(x ′ ) 2 (2) = k(x, x) + k(x ′ , x ′ ) -2k(x, x ′ ).
We now show that the dissimilarity SOM based on this last measure can be seen as a particular case of a batch version of the kernel SOM.

Batch kernel SOM

Replacing the value of the dissimilarity (2) in the representation step of the Dissimilarity SOM algorithm leads to the following equation:

p l j = arg min x∈(x i ′ ) i ′ =1,...,n n i=1 h(f l (x i ), j) φ(x i ) -φ(x) 2 .
In this equation, the prototypes are the images by φ of some vertices; if we now allow the prototypes to be linear combinations of {φ(x i )} i=1,...,n as in the kernel SOM (section 2.1), the previous equation becomes p

l j = n i ′ =1 γ l ji ′ φ(x i ′ )
where

γ l j = arg min γ∈R n n i=1 h(f l (x i ), j) φ(x i ) - n i ′ =1 γ i ′ φ(x i ′ ) 2 .
(3) Equation ( 3) has a simple solution:

p j = n i=1 h(f l (x i ), j)φ(x i ) n i=1 h(f l (x i ), j) (4)
which is the weighted mean of the (φ(x i )) i . As a consequence, equation ( 3) is the representation step of a batch SOM computed in the feature space H. We will call this algorithm kernel batch SOM:

Algorithm 3: Kernel batch SOM
(1) For all j = 1, . . . , M and all i = 1, . . . , n, initialize γ 0 ji randomly in R;

(2) For l = 1, . . . , L, do (3) assignment step: for all i = 1, . . . , n, xi is assigned to the neuron, f l (xi) which has the closest prototype:

f l (xi) = arg min j=1,...,M φ(xi) -p l-1 j (4)
representation step: for all j = 1, . . . , M , the prototype pj is recomputed:

γ l j = arg min γ∈R n n i=1 h(f l (xi), j) φ(xi)- n i ′ =1 γ i ′ φ(x i ′ ) 2
End for.

where, as shown in (4), the representation step simply reduces to

γ l ji = h(f l (x i ), j) n i ′ =1 h(f l (x i ′ , j))
.

Like in the on-line version, the assignment is run by directly using the kernel without explicitly defining φ and H: in fact, and all x ∈ {x i , . . . , x n }, it leads to the minimization on j ∈ {1, . . . , M } of

n i,i ′ =1 γ ji γ ji ′ k(x i , x i ′ )- 2 n i=1 γ ji k(x, x i ).
Then, the kernel batch SOM is simply a batch kernel SOM performed in a relevant space so it shares its consistancy properties [START_REF] Cottrell | Batch and median neural gas[END_REF].

Finally, we conclude that the dissimilarity SOM described in section 2.2 can be seen as the restriction of a kernel batch SOM to the case where the prototypes are elements of the original data set. Formally, dissimilarity SOM is the batch kernel SOM for which the feature space is not Hilbertian but discrete.

Application to graphs

The fact that the prototypes are defined in the feature space H from the original data {x 1 , . . . , x n } allows to apply the algorithms described in section 2 to a wide variety of data, as long as a kernel can be defined on the original set G (for which no vector structure is needed). In particular, this algorithm can be used to cluster the vertices of a weighted graph into homogeneous proximity groups using the graph structure only, without any assumption on the vertices set. The problem of clustering the vertices of a graph is of a great interest, for instance as a tool for understanding the organization of social networks ( [START_REF] Bornholdt | Handbook of Graphs and Networks -From the Genome to the Internet[END_REF]). This approach has already been tested for the dissimilarity SOM on a graph extracted from a medieval database ( [START_REF] Villa | Clustering a medieval social network by SOM using a kernel based distance measure[END_REF]).

We use in the rest of the paper the following notations. The dataset {x 1 , . . . , x n } consists in the vertices of a graph G, with a set of edges in E. Each edge (x i , x i ′ ) has a positive weight w i,i ′ (with w i,i ′ = 0 ⇔ (x i , x i ′ ) / ∈ E). Weights are assumed to be symmetric (w i,i ′ = w i ′ ,i ). We call d i the degree of the vertex x i given by

d i = n i ′ =1 w i,i ′ .

The Laplacian and related kernels

In [START_REF] Smola | Kernels and regularization on graphs[END_REF], the authors investigate a family of kernels based on regularization of the Laplacian matrix. The Laplacian of the graph is the positive matrix L = (L i,i ′ ) i,i ′ =1,...,n such that

L i,i ′ = -w i,i ′ if i = i ′ d i if i = i ′
(see [START_REF] Chung | Spectral Graph Theory[END_REF][START_REF] Kondor | Diffusion kernels on graphs and other discrete structures[END_REF] for a comprehensive review of the properties of this matrix). In particular, [START_REF] Smola | Kernels and regularization on graphs[END_REF] shows how this discrete Laplacian can be derived from the usual Laplacian defined on continuous spaces. Applying regularization functions to the Laplacian, we obtain a family of matrices including

• Regularized Laplacian: for β > 0, K β = (I n + βL) -1 ; • and Diffusion matrix: for β > 0, K β = e -βL ; These matrices are easy to compute for graphs having a few hundred of vertices via an eigenvalue decomposition: their eigensystem is deduced by applying the regularizing functions to the eigenvalues of the Laplacian (the eigenvectors are the same). Moreover, these matrices can be interpreted as regularizing matrices because the norm they induced penalizes more the vectors that vary a lot over close vertices. The way this penalization is taken into account depends on the regularizing function applied to the Laplacian matrix.

Using these regularizing matrices, we can define associated kernel by k β (x i , x i ′ ) = K β ii ′ . Moreover, the diffusion kernels (see also [START_REF] Kondor | Diffusion kernels on graphs and other discrete structures[END_REF]) can be interpreted as the quantity of energy accumulated after a given time in a vertex if energy is injected at time 0 in the other vertex and if the diffusion is done along the edges. It has then become very popular to summarize both the global structure and the local proximities of a graph (see [START_REF] Vert | Extracting active pathways from gene expression data[END_REF][START_REF] Schölkopf | Kernel methods in computational biology[END_REF] for applications in computational biology). In [START_REF] Fouss | An experimental investigation of graph kernels on a collaborative recommendation task[END_REF], the authors investigate the distances induced by kernels of this type in order to rank the vertices of a weighted graph; they compare them to each others and show their good performances compared to standard methods.

Simulations

In order to test the 3 algorithms presented in section 2 for clustering the vertices of a graph, we simulated 50 graphs having a structure close to the ones described in [START_REF] Boulet | Partitionnement d'un réseau de sociabilité à fort coefficient de clustering. In 7èmes Journées Francophones[END_REF][START_REF] Villa | Clustering a medieval social network by SOM using a kernel based distance measure[END_REF]. We made them as follow:

• We built 5 complete sub-graphs (C i ) i=1,...,5 (cliques) having (n i ) i=1,...,5 vertices where n i are generated from a Poisson distribution with parameter 50; • For all i = 1, . . . , 5, we generated l i random links between C i and vertices of the other cliques: l i is generated from a uniform distribution on the set {1, . . . , 100n i }. Finally, multiple links are removed; thus the simulated graphs are "non-weighted" (i.e.

w i,i ′ ∈ {0, 1}).
A simplified version of these types of graphs is shown in Figure 1: we restricted the mean of x i to 5 and l i is generated from a uniform distribution on {1, . . . , 10n i } in order to make the visualization possible. Algorithms 1 to 3 were tested on these graphs by using the diffusion kernel and the dissimilarities (equations ( 1) and ( 2)) built from it. The grid chosen is a 3×3 rectangular grid for which the central neuron has a neighborhood of size 2, as illustrated in Figure 2.

We ran all the algorithms until the stabilization is obtained, which leads to:

• 500 iterations for the on-line kernel SOM (algorithm 1); • 20 iterations for the dissimilarity SOM with both dissimilarities (algorithm 2); • 10 iterations for the batch SOM (algorithm 3).

Then, to avoid the influence of the initialization step, the algorithms were initialized randomly 10 times. For each graph and each algorithm, the best classification, which Table 1: Computation times the on-line kernel SOM is very slow because it needs a high number of iterations to stabilize. For the batch kernel SOM, we initialize the prototypes with random elements of the data set (as in the dissimilarity SOM) in order to obtain a good convergence of the algorithm. Finally, we tested three parameters for the diffusion kernel (β = 0.1, β = 0.05 and β = 0.01). Higher parameters were not tested because we had numerical instabilities in the computation of the dissimilarities for some of the 50 graphs. In order to compare the classifications obtained by the different algorithms, we computed the following criteria:

• the mean energy (except for the dissimilarity SOM with dissimilarity (1) which does not have a comparable energy). Notice also that the energies computed for different values of β can also not be compared; • the standard deviation of the energy;

• the mean number of classes found by the algorithm;

• after having associated each neuron of the grid to one of the cliques by a majority vote law, the mean pourcentage of good classified vertices (vertices assigned to a neuron associated to its clique); • the number of links divided by the number of possible links between 2 vertices assigned to 2 neurons having distance 1 (or 2, 3, 4) between them on the grid.

The results are summarized in Tables 2 to 5 and an example of a classification obtained for the batch kernel SOM for the graph represented in Figure 1 is given in Figure 3.

First of all, we see that the quality of the classification heavily depends on the choice of β. For this application, performances decrease with β, with very bad performances for all the algorithms with the parameter β = 0.01. Then, we can also remark that the performances highly depend on the graph: the standard deviation of the energy is high compared to its mean. In fact, 5 graphs always obtained very bad performances and removing them divides the standard deviation by 20.

Comparing the algorithms to each others, we see that the batch kernel SOM seems to find the best clustering for the vertices of the graph: this is the one for which the mean number of classes found by the algorithm is the closest to the number of cliques [START_REF] Chung | Spectral Graph Theory[END_REF]. It has also the best pourcentage of good classified vertices and the smallest number of links for all neighborhoods, proving that the vertices classified in the same cluster are also frequently in the same clique. Then comes the on-line kernel SOM that suffers from a long computational time and finally, the dissimilarity SOM with slightly better performances for the dissimilarity (2). Comparing the first three Tables, we can say that the performance gain of the on-line kernel SOM is really poor compared to the computational time differences between the algorithms. Moreover, interpretation of the clusters mean- ing can take benefit of the fact that prototypes are elements of the data set. On the contrary, dissimilarity SOM totally fails in decreasing the number of relevant classes (the mean number of clusters in the final classification is always the biggest possible, 9); this leads to a bigger number of links between two distinct neurons than in the both versions of kernel SOM.

β = 0.1 β = 0.05 β = 0.

Conclusions

We show in this paper that the dissimilarity SOM used with a kernel based dissimilarity is a particular case of a batch kernel SOM. This leads us to the definition of a batch unsupervised algorithm for clustering the vertices of a graph. The simulations made on randomly generated graphs prove that this batch version of kernel SOM is both efficient and fast. The dissimilarity SOM, which is more restricted, is less efficient but still have good performances and produces prototypes that are more easily interpretable. We also emphasized the importance of a good choice of the parameter 1 of the kernel, a problem for which an automatic solution would be very useful in practice.

Figure 1 :

 1 Figure 1: Example of a simulated graph: the vertices of the 5 cliques are represented by different labels (+ * x o)

Figure 2 :

 2 Figure 2: SOM grid used (dark gray is the 1-neighborhood and light gray the 2-neighborhood of the central neuron)

Figure 3 :

 3 Figure 3: Example of a classification obtained for the batch kernel SOM on graph represented in Figure 1

Table 2 :

 2 Performance criteria for the on-line kernel SOM

		β = 0.1 β = 0.05 β = 0.01
	Mean energy	0.10	3.21	196
	Sd of energy	0.40	4.7	39
	Mean nb of classes	8.04	8.92	9
	Mean % of	79.84	78.28	39.72
	good classif.
	% of links for	54.5	58.4	51.3
	1-neighborhood
	% of links for	39.1	40.0	48.0
	2-neighborhood
	% of links for	34.9	33.1	45.6
	3-neighborhood
	% of links for	24.2	28.9	43.8
	4-neighborhood
		β = 0.1 β = 0.05 β = 0.01
	Mean energy	NA	NA	NA
	Sd of energy	NA	NA	NA
	Mean nb of classes	9	9	9
	Mean % of	77.34	40.49	29.56
	good classif.
	% of links for	48.6	45.4	52.5
	1-neighborhood
	% of links for	42.0	45.5	55.8
	2-neighborhood
	% of links for	38.0	48.1	57.1
	3-neighborhood
	% of links for	34.8	51.5	57.0
	4-neighborhood

Table 3 :

 3 Performance criteria for the dissimilarity SOM (dissimilarity (1))

Table 4 :

 4 Performance criteria for the dissimilarity SOM (dissimilarity (2)) β = 0.1 β = 0.05 β = 0.01

	01

Table 5 :

 5 Performance criteria for batch kernel SOM

Acknowledgements

This project is supported by "ANR Non Thématique 2005 : Graphes-Comp". The authors also want to thank the anonymous referees for their helpful comments.


Antoine Meillet

A partir de l'étude de 60 langues et en développant les travaux de Clairis et al., nous élaborons une typologie des structures syntaxiques (constructions connectives) qui permettent de satisfaire un besoin communicationnel général : l'attribution d'une qualité, l'identification ou la classification. Nous définissons les constructions connectives par la disjonction entre le noyau syntaxique et le noyau sémantique, ce qui les distingue des constructions nucléaires. Syntaxiquement les constructions connectives peuvent prendre la forme d'une connexion directe entre le qualifiant et le qualifié, d'une connexion via a un connecteur non verbal ou d'une connexion via un verbe. Plusieurs de ces possibilités peuvent être utilisées dans une langue donnée, chacune ayant ses propres contraintes. Nous proposons de classer les langues en cinq types sur la base des combinaisons possibles entre ces stratégies.

Introduction

This paper explores a specific domain in language communication: the attribution of a quality, identification and membership from the perspective of the syntactic constructions that express it crosslinguistically. In order to satisfy communication needs in the field of attribution, languages use syntactic resources which converge on many levels, but which also show specific constraints. Most frequently, the syntactic means used to establish attribution are not specialized. Rather, the languages adapt their general syntactic resources to the specificities of attributive constructions.

The theoretical framework

This study furthers reflections on copula clauses and non-verbal predication spanning the 20 th century, beginning with Meillet 1 (1906) and Benveniste 2 and more recently with the functional-typological studies by Stassen 3 and Pustet 4 based on the traditional parts of discourse in which 'predicate' is a logicalsemantic term.

We present here a functionalist approach, following Babiniotis & Clairis5 (1999) and Clairis et al. 6 . In this framework, a "connective syntax" was opposed to a "nuclear syntax". We suggest here a more elaborate definition of the two types of constructions, connective vs. nuclear, based on the disjunction or conjunction of the syntactic nucleus (the receiver of all the syntactic determinations) and the semantic nucleus (center of semantic specifications).

In the "nuclear constructions", the syntactic nucleus is also the center of the semantic specifications. In contrast, in the "connective constructions", a syntactic connection (direct or indirect) is established between two units, semantically corresponding to a "qualified" and a "qualifier". In this case, the syntactic nucleus is different from the center of the semantic specifications (see in detail Figures 2345).

In the first study by Babiniotis & Clairis (1999), based on Modern Greek, the so-called "connective syntax" was restricted to the verbal connectors. Verbal connectors included the traditional "copulas", "semi-copulas" and, more controversially, full-lexical verbs. In Clairis et al. (2005), the study was extended to 10 more languages, and non-verbal connective constructions were added. Connective syntax thus came to cover all the processes used by languages to express quality, identification and membership7 , and which form a complete sentence.

One of the outcomes of the 2005 pilot study was a continuum of connective constructions, ranging from direct connection to connections using non specialized verbs (definitions and examples in § 3-6): More than one of the various connective strategies are generally used in one language. Based on the possible combinations of connective strategies crosslinguistically, five types of languages are suggested in this paper (see § 7). Moreover, this study shows that the use of the available strategies in a language is determined by constraints relative to the types of predicates, the types of clauses and the TMA markers involved (see § 6).

Corpus

This paper is based on a sample of 60 languages 8 , including the 11 languages of the pilot study which were based on first-hand data (Clairis et al. 2005), and completed by data available in grammatical descriptions. As can be seen in the Map 1, the sample includes languages from a wide range of families: Africa (9), Asia (13), Eurasia (2), Europe (11), Australia and Oceania (11), North America (9), South America (7).

Types of units involved in connective constructions

We observe that not all types of units can be used as qualified units and qualifiers but that most units are specialized in one use or the other. Costaouec 9 establishes a hierarchy depending on the frequency of the various units used as predicates or qualified units (slightly modified here): This syntactic hierarchy reflects a semantic specialization where the most definite, specific units -expressed by personal pronouns and proper nouns 10 -are obligatorily qualified units. On the contrary, units expressing generic qualities, such as stative predicates and adjectives, are most frequently used as predicates. Nouns, on the other hand, can be used either as predicates or qualified units, with equal frequency.

Direct connection in the world's languages

Definition

"Direct connection" includes all cases where a syntactic relation is established between a predicate and a qualified unit with no other item involved.

Martinique French Creole (Creoles) (1.)  b 3SG handsome 'He's handsome.' (Jeannot-Fourcaud 11 : 128) This connection is established between two non-verbal units which together form a complete sentence (Clairis et al. 2005). But it can also occur between a nonverbal unit and a stative predicate, or between a non-verbal unit and a unit with mixed characteristics, as is often the case in languages with weak "noun-verb" ). The qualifier unit is both the predicate and the syntactic nucleus of the sentence, i.e. it is the bearer of the language's syntactic determiners (TMA, adverbs), restricted in some languages, and its semantic role is to qualify another unit (see Figure 2): Direct connection appears to be a very frequent strategy crosslinguistically, having very rich means distinguishing it from adjectival constructions.

Main or secondary strategy

Direct connection can be the main strategy in some languages, i.e. the strategy used for the most unmarked contexts:

Tseltal (Mayan) (2.) Bijteswanej -on teacher B1 'I am a teacher.' (Polian13 : 210) Frequently, direct connection is the main strategy but has restrictions that require the use of other strategies. For example, in Hungarian direct connection is the main strategy but it is restricted to either connections between nouns, between a noun and an adjective or between a noun and the third person pronoun (for the other grammatical persons, a connecting verb is necessary).

Hungarian

Equative constructions

A specific direct connection strategy is the equative structure. We use this term here not as a semantic term but rather to refer to a symmetric syntactic construction where the qualified unit is first presented, then qualified: Deuri (Sino-Tibetan) (13.) la popô-wâ su popô this tree-TH high tree 'This tree is a high tree.' (Jacquesson 2005 27 : 110)

Identification of direct connections vs. nuclear and adjectival constructions

Crosslinguistically, we observe that direct connections are distinct from the adjectival constructions through a variety of strategies:

Word order

Intonation

Little evidence is available for this strategy, probably due to lack of case studies. In Niger-Congo languages, different intonation patterns are realized depending on whether the utterance is a complete predicate or an incomplete sentence, a phenomenon also known as "predicative lowering". This general strategy is found in all types of sentences, and can also serve to distinguish between a complete predicative sentence and an incomplete adjectival construction. For example in Langi: 'My small goat.' 'My goat is small.'

Derivational processes

In Bijogo the stative predicate in the adjectival construction receives a suffix -a or -: Bijogo (Niger-Congo) (Segerer 2002 36 : 169) (29.) kɔ-tɛɲ kɔ-nɔy 'The meat is cooked.' (30.) kɔ-tɛɲ kɔ-nɔy-ɑ 'the cooked meat'

non-verbal connectors in the world's languages

Definition

Non-verbal connectors play the role of syntactic bridges between the predicate and the qualified unit but do not receive any syntactic determination (e.g. TMA markers): The use of specialized connectors is limited by various constraints depending on the use of TMA markers. Specialized connectors can be restricted to interrogative sentences or may only appear with specific types of qualified units. For example, in Koto and Zura, two Gula dialects, one finds a connector, dubbed a "predicative particle"  , specialized in interrogative connective sentences:

Gula (Nilo-Saharan) ( 34

Non-specialized connectors

Some non-verbal units, having full lexical meaning in other contexts, can be employed as connectors: personal pronouns, demonstratives, focus particles, relative pronouns, presentatives and locatives. Non-specialized connectors generally add a focalization effect to the sentence.

Personal pronouns

In Moroccan Arabic hu wa 'him' can be employed as a connector (loosing its properties as a pronoun) with additional focus as compared to direct connection: Moroccan Arabic (Afro-Asiatic) (37.

Connection via a verb

Definition

Following Babiniotis & Clairis (1999), as well as Clairis et al. (2005), the present study of connective constructions also includes the full lexical verbs. In the present study we distinguish two categories of verbs which participate in connective constructions: a) connective verbs, traditionally known as copulas: a verb of the type 'to be' or 'to become' or a verb with full lexical meaning ('to stand', 'to see', etc.) but frequently used with the meaning 'to be'; Zapotec (Oto-Manguean) (43.) n-ak=be maestro STAT.be=3INF teacher 'They are teachers.' (Sonnenschein 2005 47 : 178) b) non-connective verbs: verbs not specialized in connective constructions and adding lexical meaning to the attribution of quality ('to work as', 'to elect', etc.). Spanish (Indo-European) (44.) Actúa en tanto que presidente de la república 'He acts as president of the republic.' This is a simplification of the categories proposed in Babiniotis & Clairis (1999) and Clairis et al. (2005) which distinguish four levels: "connective verbs" ('to be', 'to become' copulas), "quasi-connective verbs" (for some verbs taking different case markings in Greek), "nuclear-connective verbs" (for transitive connective verbs) and "non-connective verbs" (for intransitive connective verbs). In practice though, this has proved to be far too complicated for a large scale typological project.

Connective verbs

Connective verbs can 1) be the only strategy used in a language, 2) be a secondary strategy with some specific constraints involved (e.g. TMA markers), or 3) be impossible in the language. Syntactically and semantically the use of a connective verb requires the presence of a predicate. In some cases, the predicate's determinations are restricted when used in nuclear constructions. Morphological factors can also help identify the predicate in some languages, for example the gender and number markers which agree with the subject in French.

'To be', 'to become'

The most well known strategy, although not necessarily the most frequent one crosslinguistically, is connection via a verb of the type 'to be' or 'to become', traditionally called a copula. In most studies 'to be' is not considered a real verb and therefore is dubbed copula or verb copula. The meaning of this term, from the Latin copula, shows that it is mostly considered for its syntactic role in connecting two units. The reason for this is that 'to be' frequently has no specific lexical meaning.

Various analyses have been proposed in the rich literature on the status of copulas. For Sapir 48 and Bally 49 the nucleus in the case of a 'to be' copula verb is a complex formed by the copula verb and the predicate. This is partially Martinet's analysis 50 who identifies a "complex predicate" for constructions involving a "full copula" (like 'to become'), but who considers, like Meillet 51 , that 'to be' is an "empty copula" which serves only to establish the connection between the two members. Lyons 52 also considers that the copula verb is only a recipient for TMA markers. The verb 'to be' is a semantically empty verb generated by the grammatical rules of the language and used as a link between the subject and the predicate in traditional logic. This is the approach followed by Dik 53 (p. 132), for whom the copula is no more than a grammatical device, and by Givón who names copular verbs "dummy verbs", acting as the syntactic head of the verb phrase but carrying a reduced lexical-semantic load (Givón 54 : 119). On the 48 Edward Sapir, 1992 [1921], Le langage, Paris, Payot. 49 Charles Bally, 1920[1932]), Copule zéro et faits connexes, Bulletin de la Société de Linguistique de Paris 23, p. 1-6. 50 André Martinet, 1985, Syntaxe générale, Paris, Armand Colin. 51 Antoine Meillet, 1964Meillet, [1934]], Introduction à l'étude comparative des langues Indoeuropéennes, Paris, Hachette. 52 John Lyons, 1970 [1968], Linguistique générale, Paris, Larousse. 53 Simon Dik, 1983, Auxiliary and copula be in a functional grammar of English, in F. Heny & B. Richards (eds), Linguistic Categories: Auxiliaries and Related Puzzles, Dordrecht, Reidel, p. 121-143. 54 Talmy Givón, 2001, Syntax I, Amsterdam, John Benjamins. contrary, for Benveniste 55 (p. 157) a sentence with 'to be' is a verbal sentence just like all other verbal sentences. This is the approach we follow here (see for a detailed discussion Clairis et al. 2005): a verb, be it a "copula" or not, is a unit belonging to a syntactic class with specific determinations (i.e. TMA) and which functions as a syntactic nucleus.

Here are some examples of connective verbs found crosslinguistically: Ubykh (Northwest Caucasian) (49.) ɑ -giζɑ-nɑ-š -qɑ they made.be tall 'They made him tall.' (Dumezil 1931: 22) Example of the so-called 'dynamic copula', 'to become': Ubykh (Northwest Caucasian) (50.) yedänä t`it-λooγusa-nǝ ašqa very man.hero became 'He became a hero.' (Dumezil 1931: 22) In Nahuatl, some superlative verbs, such as mo-cem-aquia 'to be, to fully become' can also be used in connective constructions (in this case the predicate follows the verb, contrary to the other types of predicative constructions):

Nahuatl (Uto-Aztecan) (51. ) Mo-cem-aquî nextic to.be.totally grey 'It is fully grey.' (Launey 1994 60 : 112) Verbs with full lexical meaning also used as copulas Among the connective verbs, we will mention the case of intransitive verbs which have also developed uses as connective verbs. For example in Australian languages, posture verbs -'sit', 'lie', 'stand'-as well as motion verbs e.g. 'go'-(Dixon 2002 61 : 22-23) have developed a "copula" meaning 'to be'. This is also the case in Papuan languages where the verbs 'say' and 'hit' also function as connective verbs: Kewa (Papuan) (52. ) Transitive nuclear verbs with an object or subject predicate Transitive verbs, in their connective uses, can introduce a subject or an object predicate depending on their diathesis, i.e. active/passive, active/reflexive, active/middle voice alternations. In Turkish on the other hand, the predicate (here an adjective) can receive a present or a past tense marker but for the future the connective verb ol-'to be/become' is necessary: The "tensedness" criterion was first put in relation to the non-verbal predication by Stassen (1997). This observation was developed by Eriksen (2005) 87 relating tensedness to the use of a copula. Eriksen points in his study that tensless languages generally don't require a copula since in a tensless language a sentence doesn't need to be about a point in time. On the contrary, in tensed languages, in which "all sentences must be assertions about a point in time" (Eriksen 2005: 63), a copula is usually required for adjectival and nominal predicates.

Clause types

It appears that connective strategies are frequently related to the type of clause: declarative, negative, or interrogative clause. For example, in Kryz (Nakh-Daghestanian) various connectors are specialized for each type of sentence: declarative -ya, interrogative -y(i)/-i, negative -da (Authier 2009 88 ). In Thulung (Sino-Tibetan), the "copula" tsha borrowed from Nepali cannot be used in interrogative sentences following the restrictions also valid in Nepali (Lahaussois 2002 89 : 179).

Likewise, in Badaga (Pilot-Raichoor 1991 90 : 569-572) direct connection is the main strategy except for negated predicates which require a copula.

Eriksen (2005) observes that the so-called "tensed" languages use one negation marker while "tenseless" languages may or may not use a specific negator for nominal predicates. Indeed, in several languages, specific negators are used in connective constructions. Vesselinova (2007) 91 also notes that negation can be expressed for some languages in the same way in declaratives, nominal sentences and existential sentences but it is common to observe that a specific negation is needed for each type of clause or for some of them.

For example, in Hayu (Sino-Tibetan), the negation marker varies according to the different uses of /no(t)/ 'to be, to exist': the nominal negation /maaŋ/ is used with the "copula", while the verb negation /ma/ is used for the existential (Michailovsky 1988 92 : 134-138).

Language types based on the combination of the connective constructions

Based on the combination of the connective strategies within a language we propose five types of languages:

Type A: Direct Connection (9 languages) This type includes languages that use direct connection as an unique strategy. It usually occurs in "tensless languages", including languages with a weak verbnoun opposition:

Araki, Berber, Mwotlap, Palau, Sakalava (Malagasy), Sikuani, Tagalog, Uldeme, Yurakaré.

Type B: Direct Connection, Non-verbal connection possible (6 languages) Type B includes languages that use direct connection as their main strategy but also that have the possibility to use a non-verbal connector as a secondary strategy:

Arawak (Guyana), East Futunan, Nêlêmwa, Tseltal, Nanafwe, Martinique French Creole. This language type includes the so-called "tensed languages" that may express a permanent quality through direct connection as long as it concerns an unmarked tense such as present or aorist. But, when further TMA precision is needed, those languages require a verb: Kambera, Qawasqar, Tehuelche, Nengee, Badaga, Cree Montagnais, I'saka, Bijogo, Deuri, Classical Nahuatl, Hungarian, Ixcatec, Kalaalisut, Kamayura, Nashta, Purepecha, Russian, Tinumiisut, Turkish, Wambaya, Yuwaalaraay, Zapotec.

Type D: Verbal Connection, Direct Connection marginal or impossible (16 languages)

This category includes the languages that function mainly with verbal connection and may use direct connection in specific contexts such as exclamative sentences. Otherwise, direct connection is not possible:

Basque, Breton, Chechen, French, Georgian, Hayu, Japanese, Korean, Kryz, Modern Greek, Romani, Saami, Spanish, Thulung, Ubykh, Welsh.

Type E: All possible (7 languages) For some languages a wide range of connective strategies is available and naturally each strategy responds to specific pragmatic needs (e.g. focus):

Mankon, Qiang, Gbanzili, Gula, Yemeni Arabic, Langi, Moroccan Arabic.

Languages with direct connection as a main strategy are the majority. Moreover, the most common type in our sample is Type C, for languages that use direct connection as an unmarked strategy but require a verb for extra TMA markers. The second most frequent strategy concerns the almost exclusive use of verbal connection, Type D.

Conclusion

Based on a sample of 60 languages belonging to a wide range of stocks, this study presents the various syntactic processes used crosslinguistically to express the attribution of a quality, identification and membership: direct connection, specialized non-verbal and non-specialized connectors, and full lexical verbs, both intransitive and transitive.

More than one of these strategies can be found in a given language. The choice of a strategy depends most frequently on the type of unit, clause type, use of TMA markers other than present or aorist, and the need to add pragmatic focus or an additional lexical argument.

Based on the uses of the three connective strategies five language types have been identified:

Figure 1 .

 1 Figure 1. Nuclear constructions: Conjunction of the syntactic and the semantic nucleus 1st participant (Subject) → Syntactic nucleus ← Other participants (Object, Circumstantial, etc.) \\ ================ ⇗ ⇖ ================ // Semantic specifications

Map 1 .

 1 The Language Sample 8 AFRO-ASIATIC Berber; Moroccan Arabic; Yemeni Arabic; Uldeme -ALACALUFAN Qawasqar -ALTAIC Turkish -ARAWAKAN Arawak (Guyana) -AUSTRONESIAN Araki; East Futunan; Kambera; Mwotlap; Nêlêmwa; Palau; Sakalava (Malagasy); Tagalog -AUSTRALIAN Wambaya; Yuwaalaraay -BASQUE Basque -CHON Tehuelche -CREOLES Martinique French Creole; Nengee -DRAVIDIAN Badaga -ESKIMO-ALEUT Kalaalisut; Tinumiisut -INDO-EUROPEAN Breton; French; Modern Greek; Nashta; Romani; Russian; Spanish; Welsh -JAPANESE Japanese -KARTVELIAN Georgian -KOREAN Korean -MAYAN Tseltal -ALGIC Cree Montagnais -NAKH-DAGHESTANIAN Chechen; Kryz -NORTH-CENTRAL NEW GUINEA I'saka -NORTHWEST CAUCASIAN Ubykh -NIGER-CONGO Bijogo; Gbanzili; Langi; Mankon; Nanafwe -NILO-SAHARAN Gula -OTO-MANGUEAN Ixcatec; Zapotec -PUREPECHA Purepecha -SINO-TIBETAN Deuri; Hayu; Qiang; Thulung -TUPIAN Kamayura; Sikuani -URALIC Hungarian; Saami -UTO-AZTECAN Classical Nahuatl -YURAKARE Yurakaré.

Figure

  Figure 2. Direct connection Qualified unit ←→ Predicate (syntactic nucleus) (adjective, noun, stative predicate…) ⇖ ======================= // Semantic specification

21

  Corinne Williams J., 1980, A Grammar of Yuwaalaraay, Canberra, Pacific Linguistics. 22 Timothy Jowan Curnow, 2000, Towards a Cross-linguistic Typology of Copula Constructions, in John Henderson (ed.), Proceedings of the 1999 Conference of the Australian Linguistic Society. 23 Lyle Campbell, 1985, The Pipil language of El Salvador, Berlin, Mouton Publishers, Mouton grammar library 1. 24 Marian Klamer, 1998, A Grammar of Kambera, Berlin-New York, Mouton de Gruyter. 25 Aaron Huey Sonnenschein, 2005, A Descriptive Grammar of San Bartolomé Zoogocho Zapotec, Munchen, Lincom GmbH. 26 Marie-Françoise Rombi & Jacqueline M.C. Thomas, 2006, Un continuum prédicatif. Le cas du gbanzili (Répulique Centrafricaine), Paris-Louvain-Dudley, Peeters, Selaf 420.

  ko-i this man-TH come-P 'This man is coming.'Non-predicate markerIn Palau, direct connection is distinct from adjectival use for which the marker ęl is required: 27 François Jacquesson, 2005, Le deuri : langue tibéto-birmane d'Assam, Louvain-Paris, Peeters, coll. Linguistique de la Société de Linguistique de Paris. 28 Evangelia Adamou, 2005, Syntaxe connective en nashta, Typologie de la syntaxe connective, p. 171-182. 29 François Jacquesson, 2005, Le deuri : langue tibéto-birmane d'Assam, Louvain-Paris, Peeters, coll. Linguistique de la Société de Linguistique de Paris.

  Langi (Niger-Congo, Dunham 2005 35 : 117) (28.a) (28.b) mbʊri yaanI ndudi mbʊri yaanI ndudi

Figure35

  Figure 3. Connection through a non-verbal connector

  the teacher.' Litt. : 'I him the teacher' (Chatar-Moumni 2005 42 : 65) Demonstratives Likewise the demonstrative   (formerly the imperative of the verb 'see'), when employed as a connector receives the third person singular pronoun and introduces the notion of concomitance: 40 Pierre Nougayrol, 1999, Les parlers gula. Centrafrique, Soudan, Tchad, Paris, CNRS Editions. 41 Samia Naïm, 2009, Yemeni, Louvain-Paris, Peeters, coll. Les langues du monde 1-Société de linguistique de Paris. 42 Nizha Chatar-Moumni, 2005, Syntaxe connective en arabe marocain, Typologie de la syntaxe connective, p. 55-72.

Figure

  Figure 4. Connection via a verb

46

  Salamatou Alhassoumi Sow, 2003, Le parler des Peuls Gaawoore. Niger Occidental, Louvain-Paris-Dudley, Ma, Peeters. 47 Aaron Huey Sonnenschein, 2005, A Descriptive Grammar of San Bartolomé Zoogocho Zapotec, Munchen, Lincom GmbH.

Basque'

  This house is the most beautiful.' (Coyos 2005 56 : 94) Ixcatec (Oto-Manguean) (46.) ʔi²na³na³ ša²ña²-ku¹-na³ na²ʔmi¹ 1SG be-ACC-1SG priest 'I am already a priest.' (Fernández de Miranda 1961 57 , glosses by Costaouec) Quite often, the connective verb intervenes when TMA markers are required, i.e. as a complementary strategy. For example, in Mankon the verb bé 'to be' is used when temporal specification is needed or with negation: F]-be bird-ME 'It was a bird (that made this noise).' (Leroy 2007 58 : 331) Verbs like 'to be' or 'to become' generally serve to qualify the subject; in causative constructions, it is possible to qualify an object: Ubykh (Northwest Caucasian) (48.) ɑ -giζɑ-š -qɑ he was tall 'He was tall.' (Dumezil 1931 59 : 22) 55 Emile Benveniste, 1966, La phrase nominale, Problèmes de Linguistique Générale 1, Paris, Gallimard, p. 151-167 56 Jean-Baptiste Coyos, 2005, Syntaxe connective en basque, Typologie de la syntaxe connective, p. 73-89. 57 Maria Teresa Fernandez de Miranda, 1961, Diccionario ixcateco, Mexico, Instituto nacional de antropología e historia. 58 Jacqueline Leroy, 2007, Le mankon. Langue bantoue des Grassfields (Province Nord-Ouest du Cameroun), Louvain-Paris, Peeters, Selaf 437. 59 Georges Dumézil, 1931, La langue des Oubykhs, Paris, Edouard Champion.

Figure

  Figure 6. Connection via a transitive verb Subject (qualified unit: passive, reflexive, middle voice)

Turkish

  'The house will be pretty.'(Divitcioglu-Chapelle 2005)

85

  Lajos Nyéki, 1988, Grammaire pratique du hongrois d'aujourd'hui, Gap, OPHRYS-POF. 86 Elif Divicioglu-Chapelle, 2005, Syntaxe connective en turc, Typologie de la syntaxe connective, p. 199-211. 87 Pål Kristian Eriksen, 2005, On the Typology and the Semantics of Non-Verbal Predication, Unpublished PhD Thesis, University of Oslo. 88 Gilles Authier, 2009, Grammaire kryz. Langue caucasique d'Azerbaïdjan, dialecte d'Alik, Paris-Louvain, Peeters.

89

  Aimée Lahaussois, 2002, Aspects of the grammar of Thulung Rai: an endangered Himalayan language, unpublished PhD thesis, University of California, Berkeley. 90 Christiane Pilot-Raichoor, 1991, Le Badaga : langue dravidienne (Inde). Description et analyse, Unpublished PhD thesis, Paris. 91 Ljuba Vesselinova, 2007, Towards a typology of negation in non-verbal and existential sentences, 7th Biannual Meeting of the Association for Linguistic Typology, Paris. 92 Boyd Michailovsky, 1988, La langue hayu, Paris, CNRS Editions.

Type C :

 : Direct Connection, Verbal Connection under constraints (22 languages)

Table 1 .

 1 The connective strategies

	Direct connection	Non-verbal connectors	Verbs
		a) specialized	a) connective
		b) non-specialized	b) non-connective

Table 2 .

 2 The hierarchy of the types of units used as predicates and qualified units

	Most frequently		Predicates	Always
	predicates		or qualified units	qualified units
	Stative predicates Adjectives	Numerals	Nouns	Proper	Personal
		Indefinites		nouns	pronouns
		Interrogatives
		Adverbs

Koh 18 2005). 3.3. Types of units

  In some languages, direct connection can be established between a clitic and a non-verbal unit. InCurnow (2000) 22 this is analyzed as an "inflectional copula

	Chechen (Nakh-Daghestanian)
	(4.) isb j ɑh̩	i		iljexwo
	impressive	PROX DEM	singer
	'Impressive this singer!' (Guérin 15 : 70)
	It can also appear in specific constructions, as in Kryz (Authier 2009 16 ), or in construction":
	Breton where it is only used in dependant clauses: Pipil (Uto-Aztecan)
	Breton (Indo-European) (9.) ni-ta:kat
	(5.) pemp 1SGSUBJ	buoc'h	he -man	d-oa	ha	i	treut
	five 'I am a man.' (Campbell 1985 23 : 54) cow 3SG.F 3SG-be/PST	and	3PL	thin
	'She owned five cows and all of them (were) thin.' Personal pronoun-Stative predicate litt. 'Five cows was her own and they thin.' (Avezard & Costaouec 17 : 115) Kambera (Austronesian)
	(10.) [Na ART 'That person (there) is a good (person).' (Klamer 1998 24 : 92) tau nuna] k nak-hàmu person DEI.3S 3SN-be.good In some languages direct connection is impossible (i.e. Korean, Following are some examples of the types of qualified and qualifier units Personal pronoun-Adjective
	involved in direct connections (Qualified item-Predicate): Zapotec (Oto-Manguean)
	Proper Noun-Noun (11.) gasgh	=ba'
	black Moroccan Arabic (Afro-Asiatic) =3AN (6.) h̩ med muɛɑllɩm 'It is black.' (Sonnenschein 2005 25 : 35)
	'Ahmed is a teacher.' (Chatar-Moumni 2005 19 ) Noun-Stative predicate
	Noun-Noun Gbanzili (Niger-Congo)
	Hungarian (Uralic) (12.) ndo ngo -nìʔ	ʔá	nzɛlɛ̄
	(7.) Barát-om pepper-DEF.DEM friend-POSS1 'The pepper is hot.' (Rombi & Thomas 2006 26 : 55) 3SG AOR/be.strong mérnök engineer
	(Uralic) 'My friend is an engineer.' (Nyéki 1993 20 )
	(3.) Ön Noun-Adjective tanár
	3SG Yuwaalaraay (Australian) professor
	'He is a professor.' (8.) burul nhama		dhayn
	or 'You (Respectful) are a professor.' (Nyéki 14 ) big that man
	It can be a possible but secondary option, i.e. a marked strategy from a pragmatic viewpoint (e.g. exclamation): 15 Françoise Guérin, 2008, La syntaxe connective en tchétchène, La Linguistique 44/2, p. 67-
	80.
	16 Gilles Authier, 2009, Grammaire kryz. Langue caucasique d'Azerbaïdjan, dialecte d'Alik,
	Paris-Louvain, Peeters.
	17 Cécile Avezard & Denis Costaouec, 2005, Syntaxe connective en breton, Typologie de la
	syntaxe connective, p. 91-106.

18 Huong-Won Koh, 2005, Syntaxe connective en coréen, Typologie de la syntaxe connective, p. 107-123. 19 Nizha Chatar-Moumni, 2005, Syntaxe connective en arabe marocain, Typologie de la syntaxe connective, p. 55-72. 20 Lajos Nyéki, 1988, Grammaire pratique du hongrois d'aujourd'hui, Gap, OPHRYS-POF. 'That man is big.' (Williams 1980 21 : 69) Personal pronoun-Noun

  kio pânaat 'It's not a stone.'(Bril 2002 31 : 91) Case marker In Russian an adjective can be predicate in a direct connection with a pronoun or a noun, in which case the qualified unit is marked by the nominative case and the predicative adjective can be unmarked: Patte 2008: 58-63) two personal pronoun paradigms exist: the first for agents of active verbs (lu in the example below); the second for patients and in stative predicates (i/no in the examples below):

	nuclear use
	In some constructions, the genitive case is used: (27.) huna-ena
	Palau (Austronesian) 'He will grump.' (Queixalós 2000: 33)
	direct connection Russian (Indo-European) (NB: Different personal paradigms also distinguish the two predication
	(17.) Ak (22.) on types).		sméchęr	vysokogo rosta
	PREFSUJ he.NOM.SG.M	be.ill	high.height.GEN
	'I am ill.' (Lemaréchal 1991 30 : 62) 'He is of a high height (i.e. tall).' (Avgustinova 2006: 2)
	adjectival use In adjectival constructions, the adjective must be marked by the nominative
	(18.) Blái case:	ęl	bęchés
	house * Russian (Indo-European) new
	'A house which is new…' (Lemaréchal 1991: 144) (23.) gordyj otec
	proud.NOM SG.M	father.NOM
	Negation marker 'a proud father…' (Avgustinova 2006: 8)
	In Nêlêmwa a specific negation marker, kio, can be an indication of connective
	use: Personal pronoun
	Nêlêmwa (Austronesian) In Arawak (Arawak (Arawakan) (24. ) lu-fara no 3SGM-kill 3SGF 'He kills her.' (Patte 2008 33 : 59) (19.) Russian (Indo-European) Arawak (Arawakan)
	(20.) otec (25. ) halekhebe-ka gord father.NOM proud.PRD-ADJ.SG.M i happy-ACC 3SGM	rezul'tatami results.INST.PL
	'Father is proud of the results.' (Avgustinova 2006 32 : 7) 'He's happy.' (Patte 2008: 62)
	In other sentences, both the predicate (noun or adjective) and the qualified TMA markers
	pronoun are marked by the nominative case: In Sikuani, future and iterative markers are suffixed in verbal predication (-ena
	and -biaba) but are independent in connective constructions (respectively tsane
	Russian (Indo-European) and tsabiani):
	(21.) on Sikuani (Tupian) he.NOM.SG.M fool.NOM.SG.M | fat.NOM.SG.M durak | tolstyj direct connection 'He is a fool / fat.' (Avgustinova 2006: 2) (26.) tahawihanü tsane
	'He will be my usual commercial partner.' 30 Alain Lemaréchal, 1991, Problèmes de sémantique et de syntaxe en palau, Paris, Editions du CNRS. (Queixalós 2000 34 : 33)
	31 Isabelle Bril, 2002, Le nêlêmwa (Nouvelle Calédonie). Analyse syntaxique et sémantique,
	Louvain-Paris-Dudley, Peeters, Selaf 403.

32

Tania Avgustinova, 2006, A Functional Typology of Copular 'Be': Towards an HPSG Formalisation, in Stefan Müller (ed.), Proceedings of the HPSG06 Conference, CSLI Publications.

  Yemeni Arabic connection is frequently effected via two specialized connectors, namely gad "declarative" and ād "durative", which receive the personal pronoun (subject):With these connectors, negation is marked by mā… and not by the mi/u or mā used in direct connection.Time can be lexically marked (e.g. by an adverb), but the grammatical expression of past needs connection via the verb kān 'be':

	Yemeni Arabic (Afro-Asiatic)
	(35.) ʕād-i			marat-ak
	PART-3SGF		wife-2SGM
	'Is she still your wife?' (Naïm 2009 41 : 175-176)
	Yemeni Arabic (Afro-Asiatic)
	(36.) mɑ̄ gɑd	kɑn-ʃ		msɑlliħ
	NEG PART be.3SGM-NEG	arm.PTCP
	'He was not armed.' (Naïm 2009: 175-176)
	. ) sē	á		dè'	gǝ̄	wà
	2PL	PRED	who	PL	INT
	'You, who are you?' (Nougayrol 1999 40 : 65)
	37 Amani Bohoussou & Stavros Skopeteas, 2005, Syntaxe connective en nanafwe,
	Typologie de la syntaxe connective, p. 155-169.

38 Nizha Chatar-Moumni, 2005, Syntaxe connective en arabe marocain, Typologie de la syntaxe connective, p. 55-72. 39 Amani Bohoussou & Stavros Skopeteas, 2005, Syntaxe connective en nanafwe, Typologie de la syntaxe connective, p. 155-169.

In

  For copulas deriving from verbs of posture in Tibeto-Burman languages see Noonan & Grunow-Hårsta 63 , Post 64 . Michael Noonan & Karen Grunow-Hårsta, 2002, Posture Verbs in Two Languages of Nepal, in John Newman (ed.), The Linguistics of Sitting, Standing, and Lying, Amsterdam-Philadelphia, John Benjamins.

	ni kadipi te-a
	I red	say-3SG.PRES
	'I am red.' (from the sun)
	(Franklin 1981 cited in Dixon 2002 62 )
	60 Michel Launey, 1994, Une grammaire omniprédicative. Essai sur la morphosyntaxe du
	nahuatl classique, Paris, CNRS Editions.
	61 Robert M. W. Dixon, 2002, Copula Clauses in Australian Languages: A Typological
	Perspective, Anthropological Linguistics 44, 1, p. 1-36.
	62 Robert M. W. Dixon, 2002, Copula Clauses in Australian Languages: A Typological
	Perspective, Anthropological Linguistics 44, 1, p. 1-36.

63

Georges Babiniotis & Christos Clairis, 1999, Τυπολογíα της συνδετικής σύνταξης (Typology of connective syntax). Proceedings of the 4 th international Conference on Greek Linguistics, Nicosie-Chypre, p. 180-185.

Christos Clairis, Claudine Chamoreau, Denis Costaouec & Françoise Guérin (dir.), 2005, Typologie de la syntaxe connective, Rennes, Presses Universitaires de Rennes.

Connective constructions are also frequently used for comparison, location (Leon

Leon Stassen, 2008, Predicative adjectives, in Martin Haspelmath, Matthew Dryer, David Gil & Bernard Comrie (eds), The World Atlas of Language structures on line (Wals), Feature 118, Munchen, Max Planck Digital Library. http://wals.info/feature/118

Gilles Polian, 2006, Eléments de grammaire du tseltal. Une langue maya du Mexique, Paris, L'Harmattan.

Lajos Nyéki, 1988, Grammaire pratique du hongrois d'aujourd'hui, Gap, OPHRYS-POF.

Marie-France Patte, 2008, Parlons Arawak. Une langue amérindienne d'Amazonie, Paris, L'Harmattan.

Huong-Won Koh, 2005, Syntaxe connective en coréen, Typologie de la syntaxe connective, p. 107-123.

Michel Launey, 1994, Une grammaire omniprédicative. Essai sur la morphosyntaxe du nahuatl classique, Paris, CNRS Editions.

Cécile Avezard & Denis Costaouec, 2005, Syntaxe connective en breton, Typologie de la syntaxe connective, p. 91-106.

Acknowledgements

This paper was presented in the 8th Conference of the Association for Linguistic Typology in Berkeley (2009) and benefited from the remarks of its participants. We gratefully acknowledge support for the preparation of this paper from the CNRS Federation of Typology and Linguistic Universals, directed by Stéphane Robert. We also wish to thank the colleagues who, when needed, kindly accepted to control the analyses concerning the languages they specialize in, even though we are responsible for any mistakes in this paper: I. Bril, G. Segerer, F. Jacquesson, A. François, C. Moyse, C. Pattin, V. de Colombel, A. Lahaussois and A. Fernandez-Garay.

Connective verbs are very frequently non-specialized. For example in Thulung (Sino-Tibetan) the native "copula" verb, bumu 'to be, to live, to stay' is used in connective, locational, existential and possessive functions, and as an auxiliary to form aspectual constructions such as progressives (Lahaussois 65 : 174-178). Moreover, Güldemann 66 shows that 'to be' or 'to become' verbs are often used as quotative markers across the languages.

Non-connective verbs

Non-connective verbs are mostly used in nuclear constructions and although they are not specialized in connective constructions, they can be used as such. In their connective use, they add extra lexical meaning to the connection between the predicate and the qualified unit. As nuclear verbs, they can be either intransitive or transitive, or both. Non-connective verbs usually show a change in meaning when used in connective constructions as well as a change in valency, requiring an additional predicate: e.g. Il passait pour le maître du pays 'He was considered the country's master' is distinct from the intransitive verb 'passer' as in Il passe dans la rue 'he's walking by in the street'. Moreover, non-connective verbs accept complementary determination such as adjectives, something not possible in their nuclear uses e.g. Il part furieux 'He leaves furious'. This category is rarely taken into consideration in descriptive studies and was the most difficult to document. Transitive nuclear verbs used in connective constructions (subject predicate) One of the observations made in Clairis et al. (2005) was the fact that connective constructions can also be transitive, contrary to the traditional distinction between transitive and intransitive predication (Stassen 1997) or transitive, intransitive and copula clauses (Curnow 2000, Dixon 2002: 1). Clairis et al. propose calling these verbs "nucléo-connectifs", in order to stress their ability to combine both nuclear and connective characteristics. In this case, a transitive verb can be the nucleus governing a subject and an object at the same time. Here are some examples of transitive verbs with a subject predicate:

Adpositions

Quite often non-connective verbs require an adposition when used in connective constructions. It is important to distinguish between comparative sentences and attributive sentences, as the same adposition may be used in both cases. Relative constraints should also be taken into consideration, e.g. the use of a definite article. In the following example, the definite article can only be used in the comparative structure:

Constraints in the use of the various connective constructions

The connective strategies presented above are most frequently used in parallel in a given language, though it is rare to find them all in a single language (in our sample 5/60). In general, one of the processes is the main strategy, used in temporally and pragmatically unmarked sentences. When the need for extra grammatical (aspectual, temporal, person), pragmatic (focus) or lexical information is involved, a second strategy is used. Strategies are also highly dependant on the type of predicate (definite vs. indefinite, stative predicate vs. noun) and on the clause type (negative, interrogative, affirmative, dependant clause).

Predicate types

Various constraints are found in the world's languages depending on the types of predicates. Specific qualified units, such as personal pronouns and proper nouns, behave differently from generic units, such as indefinite nouns and plural nouns.

For example, in Pulaar direct connection is only possible with personal pronouns: Restrictions related to the person can also be found. For example, in Kamayura the copula is restricted to use with the first and second persons only: Kamayura (Tupian) (82. ) paje ere-ko

Shaman

2SG-Copula 'You are the shaman.' (Seki 2000 80 : 158) Indeed, third person pronouns behave differently in a general mannor: for example Stassen (1997) and Eriksen (2005) 81 observe that there are no languages in which zero copula contructions are licensed for first person but not third person pronouns (Eriksen 2005: 27).

Definite and indefinite nouns as well as plural nouns also may behave differently and require different strategies: this is the case in Tseltal where definite nouns may take the non-verbal connector (also used as a focus marker) while indefinite nouns require direct connection. In Moroccan Arabic, whenever We should also mention that it is common for predicative adjectives to behave differently in a given language and have to be constrained in the connective strategies in which they can be involved. For example in Bijogo (Niger-Congo, Segerer 2002 83 : 168), predicative adjectives are obligatorily linked to one sort of strategy: while -koto 'old', of verbal origin, can be directly connected, -ʈiʈ 'small', requires the use of a copula -nam 'be'.

TMA markers

One of the most well known constraints in connective constructions concerns the use of TMA markers. In many languages direct connection is favoured when temporal and aspectual stability is involved but is no longer possible with all or some TMA markers (in the present study 20 languages out of 60). As Eriksen (2005 84 : 27), following Stassen (1997), observes if a language accepts a zero copula construction in the past it will also accept it in present.

Such is the case in Hungarian, where no TMA markers are allowed in direct connection: We believe it would be useful if future language descriptions were to include a chapter on connective constructions, which would examine all the means available in the language and the relevant constraints applying to them.

Abbreviations