Mnacho Echenim

Nicolas Peltier

Sophie Tourret
email: sophie.tourret@mpi-inf.mpg.de

Prime Implicate Generation in Equational Logic (extended abstract) *

, enriched with rules that add new hypotheses on demand during the proof search. Experimental results are presented, showing that the proposed approach is more efficient than state-of-the-art systems.

Introduction and Motivations

Abductive reasoning is the process of inferring, given a set of axioms A and a formula φ, a set of assertions H such that A ∪ H |= φ. The set H may be viewed as a set of hypotheses that are sufficient to ensure the validity of the entailment A |= φ, or as a set of explanations of φ. Such hypotheses must be economical and plausible, in particular H must be minimal w.r.t. logical entailment and A ∪ H must be satisfiable. Abductive reasoning has many applications in artificial intelligence, verification and debugging, e.g. for computing missing pre-conditions, spotting and correcting errors in a logical specification, or for dealing with approximative, incomplete or spurious information. The problem has been thoroughly investigated in propositional logic [START_REF] Marquis | Consequence finding algorithms[END_REF], and very efficient algorithms have been proposed [START_REF] Simon | [END_REF][START_REF] Previti | [END_REF], but only a few approaches handle more expressive logics [START_REF] Knill | [END_REF]Marquis, 1991;[START_REF] Mayer | Marta Cialdea Mayer and Fiora Pirri. First order abduction via tableau and sequent calculi[END_REF][START_REF] Nabeshima | SOLAR: an automated deduction system for consequence finding[END_REF]. In particular, none of them is able to deal with the equality predicate in an efficient way.

In the present paper, we tackle the problem of generating such a set H, when A ∪ {φ} is a set of first-order formulas with equality and H is a set of ground unit clauses. In this case, by duality, ¬H is a clausal logical consequence of A ∪ {¬φ}, i.e., an implicate of A ∪ {¬φ}, and the problems boils down to efficiently generating sets of (entailment-minimal) implicates or prime implicates.

We illustrate our approach by an example in verification. Consider the following toy program, redirecting the tail of a nonempty list l 1 to a list l 2 of length 1. Assume we want to check that l 1 is of length 2 after the program is executed. This post-condition does not hold, which may come as a surprise for some programmers. Indeed, if l 1 = l 2 , then the tail of l 1 is redirected to l 1 yielding a cyclic list (hence length(l 1 ) is either 1 or undefined, depending on the definition). The problem can be stated in first-order logic with equality as the following set of clauses S, where the tail function is represented by a function tail : heap × list → list, and where h, h : heap are constant symbols denoting the initial and final states of the heap and x, y : list, z : heap are universally quantified variables.

% Definition of the tail redirection operation % The tail of x is redirected to y: x nil ∨ tail(SetT ail(z, x, y), x) y % The tail of the other lists is not affected by the redirection:

x nil ∨ x nil ∨ x x ∨tail(SetT ail(z, x, y), x ) tail(z, x ) % Definition of length length(z, nil) 0 x nil ∨ length(z, x) s(length(z, tail(z, x))) % Pre-conditions length(h, l1) 0 length(h, l2) s(0) % Negation of the post-condition length(h , l1) s(s(0)) % Translation of the program h = SetT ail(h, l1, l2)
The set S is satisfiable, the problem is to show that S is unsatisfiable under the hypothesis l 1 l 2 , or equivalently that l 1 l 2 is an implicate of S.

Normalized Ground Clauses

Terms, atoms, literals and clauses are defined inductively as usual over a set of function symbols Σ and variables V. We assume, w.l.o.g., that the equality is the only predicate symbol. We use the symbol to denote either or . Substitutions are functions mapping variables to terms, extended to any expression (terms, atoms, clauses, etc.) in the natural way and written in postfix notation. We assume given a reduction order , i.e., an order among terms that is closed under substitution and context embedding, and contains the subterm ordering (this entails that ≺ is well-founded). The order ≺ is extended to atoms or literals by interpreting them as multisets of terms, and to clauses by the usual multiset extension. For any expression E, we denote by E c the nnf of the negation of E, formally defined as follows:

(s t) c = s t, (s t) c = t s, ( n i=1 l i ) c = n i=1 l i c and ( n i=1 l i ) c = n i=1 l i c .
Definition 1 Given a clause C, we define the relation ≡ C on terms as follows: for all terms s, t, s

≡ C t iff C c |= s t. The C-representatives of a term s, lit- eral l and clause l 1 ∨ • • • ∨ l n are respectively defined by: s C def = min ≺ {s | t ≡ C s} (s t) C def = s C t C (l 1 ∨ • • • ∨ l n ) C def = l 1 C ∨ • • • ∨ l n C Definition 2 A ground clause C is normalized if: 1. every literal l in C is such that l C\l = l;
2. there are no two distinct positive literals l, m in C such that m l c ∨C -is a tautology;

3. C contains no literal of the form t t.

A conjunction of literals X is normalized if the clause X c is normalized.

Proposition 3 Any ground falsifiable clause C admits a unique equivalent normalized clause C ↓ , which is the ≺smallest clause equivalent to C. Consequently, two clauses are equivalent iff either they are both tautological or they have the same normalized form.

A Constrained Superposition Calculus

This section contains the definition of the calculus for generating implicates, named cSP. It is based on the Superposition Calculus SP (see for instance [Nieuwenhuis and Rubio, 2001]) which is the most successful proof procedure for first-order logic with equality. The principle underlying cSP consists in applying the inference rules of SP to the set of clauses under consideration along with ground unit clauses that are added during proof search and that act as hypotheses.

To keep track of the hypotheses that were used to derive a clause, the former are attached to the clauses as constraints. This yields the following definition:

-Superposition (i), (ii), (iii) [t s ∨ C | X ] [u[t ] v ∨ D | Y] [u[s] v ∨ C ∨ D | X ∪ Y]σ c-Factoring (iv), (ix) [t u ∨ t v ∨ C | X ] [t u ∨ u v ∨ C | X ]σ c-Reflection (v), (ix) [t t ∨ C | X ] [C | X ]σ Positive Assertion (vi), (vii) [u[t] v ∨ C | X ] [u[s] v ∨ C | X ∧ t s]σ Negative Assertion (ii), (viii), (x) [t s ∨ C | X ] [u[s] v ∨ C | X ∧ u[t ] v]σ
where the following conditions hold:

For all rules: σ = mgu(t, t );

(i): (u[t ] v)σ ∈ sel((u[t ] v ∨ D)σ) and vσ u[t ]σ;
(ii): (t s)σ ∈ sel((t s ∨ C)σ) and sσ tσ;

(iii): X ∪ Y ∈ X;

(iv): The set of inference rules defining cSP are given in Figure 1. The notation u[t] is used to denote a term containing a subterm t (u denotes the context). We may then write u[s] to denote a term obtained from u[t] by replacing t by s. The symbol ( or ) must denote identical symbols in the premise and in the conclusion of the rule. The rules are parameterized by the order ≺ and by:

(t u)σ ∈ sel((C ∨ t u ∨ t v)σ); (v): (t t )σ ∈ sel((t t ∨ C)σ); (vi): s ≺ t , vσ u[t]σ and (u[t] v)σ ∈ sel((u[t] v ∨ C)σ); (vii): X ∧ t s ∈ X; (viii): v ≺ u[t ]; (ix): X ∈ X; and (x): X ∧ u[t ] v ∈ X.
• A selection function sel that maps every clause C to a set of selected literals in C. The set sel(C) must contain all -maximal literals or at least one negative literal. • A set of normalized constraints X, closed under subset.

Intuitively X denotes the set of abductible formulas, i.e., formulas that are allowed to be added as hypotheses.

The use of and sel is standard, it aims at pruning the search space by restricting inferences, whereas the set X allows one to control the addition of hypotheses into the search space.

The reader may consult [Nieuwenhuis and Rubio, 2001] for missing definitions and more details about the superposition calculus.

A crucial feature of the Superposition calculus is the availability of a general criterion for detecting redundant clauses. In SP, a clause is considered redundant if all its instances are entailed by ≺-smaller instances of existing clauses. The definition for cSP is similar, with two differences: first the constraints of the entailing clauses must be included in that of the considered clause, and second the literals occurring in this constraint can also be used in the entailment test, provided they are smaller than the considered clause. Formally: Definition 5 If X is a constraint and C is a clause, we denote by X | C the set of literals in X that are smaller than or equal to C.

A c-clause [C | X ] is redundant w.r.t. a set of c-clauses S if either X is unsatisfiable or for every ground substitution σ of the variables in C, there exist c-clauses

[D i | Y i ] ∈ S (1 ≤ i ≤ n) and ground substitutions θ i (1 ≤ i ≤ n) such that:
• ∀i ∈ {1 . . . n}, Cσ D i θ i and Y i ⊆ X , and

• X | Cσ , D 1 θ 1 , . . . , D n θ n |= Cσ.
A set of c-clauses S is cSP-saturated if every c-clause deducible by the rules of cSP in one step is redundant w.r.t. S.

A cSP-saturation of a set of c-clauses S is a set of c-clauses S * such that: (i) every c-clause in S is redundant w.r.t. S * , (ii) every c-clause in S * is obtained from those in S by a finite number of applications of the rules in cSP, (iii) S * is cSP-saturated.

The following theorem states the soundness and deductive completeness of cSP. Theorem 6 Let S be a set of standard clauses and S * be a cSP-saturation of S. For every X ∈ X, X c is an implicate of S iff S * contains a c-clause of the form [ | X ] with X ⊆ X .

On the Storage of Implicates

Sets of implicates are huge, thus being able to store those sets in a compact way and to detect redundant implicates efficiently is a critical feature. We begin by devising an efficient algorithm for testing entailment between ground equational clauses.

Definition 7 Let C, D be two falsifiable ground clauses. The clause D E-subsumes C, written D ≤ E C, iff the two following conditions hold:

1. for every negative literal t s ∈ D, t C -= s C -; 2. for every positive literal l ∈ D, there exists a positive literal m ∈ C such that m C -∨l c is a tautology.

Theorem 8 Let C and D be two ground clauses. If C and D are falsifiable, then

D |= C iff D ≤ E C.
Based on the entailment test of Definition 7, we define a trie-like data structure to store implicates and algorithms to remove redundancy inspired from [START_REF] Kleer | [END_REF]. A clausal tree is a tree whose edges are labeled by literals and whose leaves are labeled by either ⊥ or . Each path from the root of the tree to a leaf can be associated with a clause defined as the disjunction of all the literals labeling the edges along the path. The set of clauses associated with the tree is the set of clauses associated with a path from the root to a -leaf. This representation ensures that the prefixes of the clauses will be shared, thus reducing the amount of consumed memory. Note that the edges pointing to a ⊥-leaf are useless and may be deleted (a node with no successor may be labeled by ⊥).

We consider a total ordering < π on ground literals, defined as follows: if l 1 is a negative literal and l 2 is a positive literal then l 1 < π l 2 , and if l 1 , l 2 are literals with same polarity then l 1 < π l 2 iff l 1 ≺ l 2 . To enforce maximal sharing and minimize the size of the tree, we assume that the literals occurring along a path in the tree are ordered w.r.t. < π , i.e., for any path e 1 , . . . , e n in the tree, if e 1 , . . . , e n are edges labeled by literals l 1 , . . . , l n respectively, then l 1 < π . . . < π l n .

When a new implicate C is generated, we need to test whether it is a consequence of a previously generated implicate (forward subsumption). If this is the case, then C is redundant and can be dismissed, otherwise we need to delete in the clausal tree all branches corresponding to an implicate that is a logical consequence of C (backward subsumption). We briefly sketch algorithms for performing these two tasks. The formal definitions of the algorithms can be found in [START_REF] Echenim | Mnacho Echenim, Nicolas Peltier, and Sophie Tourret. Prime Implicate Generation in Equational Logic[END_REF] together with detailed proofs of their properties.

Forward Subsumption. Beside the new generated clause C and the clausal tree T , we also consider two input clauses N and M that are both initially empty. The clause N contains the literals occurring in the parent nodes in the recursive calls and the clause M permits to keep track of the negative literals of C in recursive calls after having used them a first time to rewrite literals in the tree.

The algorithm is based on a depth-first traversal of the tree which is best described as a non-deterministic recursive algorithm. The algorithm returns true if the tree contains a single node labeled by (representing the empty clause) and backtracks if the tree is not and C = (base cases). Otherwise, an edge e starting from the root of the tree is chosen. Let l be the literal labeling e and let T be the subtree pointed by e:

• If it is clear that l |= M ∨ C, then we add l into N and we proceed to T . This entailment condition is tested by checking that l M is a contradiction (if l is negative) or that C M ∨l c contains a tautological literal (if l is positive).

• If the relation between l and M ∨C is not currently determined (because l is < π -greater than the literal currently considered in C and thus may entail literals that remain to be examined), then the minimal literal of C is added to M before restarting the exploration of the branch corresponding to e.

• Lastly, if it is clear that l |= C, which is the case e.g. when l is ≤ π -smaller than all the literals in C, then the algorithm backtracks.

Backward Subsumption. This handles the removal from a clausal tree T of all the clauses D that are E-subsumed by a given c-clause C, under the assumption that C itself is not subsumed by a clause stored in T . As the previous one, the algorithm performs a depth-first traversal of T with a rewriting of literals. The main difference is that the roles of C and T are switched: the literals of a branch of T are rewritten using the negative literals of C. When the subsumption test 1 compares Zres, primer and SOLAR with cSP flat and cSP on the random non-flat benchmark. For each system, we isolate the benchmarks for which the system is able to generate all implicates, and we specify for all systems the failure rate on those benchmarks (i.e., the percentage of formulas for which the system is not capable of generating all implicates in the allocated time, namely 5 min.), the time needed to generate all prime implicates in case of success, the number of inferences and the number of implicates generated. As shown in the 'successes' column, cSP is the obvious winner in terms of the number of tests handled before timeout. More detailed experimental results are presented in [START_REF] Echenim | Mnacho Echenim, Nicolas Peltier, and Sophie Tourret. Prime Implicate Generation in Equational Logic[END_REF].

Definition 4 A

 4 constraint is a conjunction (or set) of ground literals. The empty (tautological) constraint is denoted by . A constrained clause (or c-clause) is a pair [C | X ] where C is a clause and X is a constraint. The c-clause [C | ] is simply represented as C, and referred to as a standard clause. Intuitively X denotes the set of hypotheses used to derive C. If C is empty, then [C | X ] is equivalent to X c , and X c is an implicate of the clause set under consideration.

  c

Figure 1 :

 1 Figure 1: Inference Rules for cSP.

  (a) cSP vs. cSP flat (b) primer vs. cSP flat (c) primer vs. cSP

Figure 2 :

 2 Figure 2: Time comparison of cSP, cSP flat and primer; random flat benchmark

Table 1 :

 1 Test results summary; random non-flat benchmark Table

succeeds, the algorithm cuts the corresponding branch in T before exploring the remaining branches.

Experimental Results

Our prime implicate generation method has been implemented in a research prototype called cSP, written in OCaml, based on the LogTk library [Cruanes, 2014] for term ordering and congruence closure. We also implemented another version of the program, called cSP flat, that only handles flat clauses, i.e., clauses not containing function symbols of an arity strictly greater than 0, with additional refinements that only apply to this fragment.

We compared cSP and cSP flat with the most efficient available systems for generating implicates of logical formulas, namely primer [START_REF] Previti | [END_REF] and Zres [START_REF] Simon | [END_REF], two propositional prime implicate generation tools based on satisfiability encoding and resolution respectively, and SOLAR [Iwanuma et al., 2009], a prime implicate generation tool for first order logic based on semantic tableaux. Equality is not built-in in these systems, thus the equality axioms had to be added into the considered formula: reflexivity, commutativity, transitivity and substitutivity. For Zres and primer, these axioms must also be grounded and transformed into propositional logic by flattening.

We compared the systems on two randomly generated sets of (flat and non-flat respectively) equational ground clauses of small size. Figure 2 compares the execution time of cSP on the random flat benchmark with that of cSP flat and primer. It shows that cSP flat is the most suitable tool to handle such problems.


researchIng local sports InItIatIves for young mIgrants from a polItIcal perspectIve: methodologIcal and practIcal challenges el estuDio De iniciativas Deportivas locales para jóvenes Migrantes DesDe una perspectiva política: retos MetoDológicos y prácticos Noemi García-Arjona To cite this

* Noemi Garcia Arjona is lecturer at the Faculty of Sports Sciences, University of Rennes 2 (France). She is member of the research group VIPS² (Violences, Innovations, Politiques, Socialisations & Sports). She is expert in Intercultural and Social Mediation (Universidad Autónoma de Madrid). Main research themes are centered on integration policies through local sports initiatives and migrants' sports, physical activities and leisure experiences.

Abstract:

The processes of incorporation of young migrants have been studied using a range of new approaches. Among them, sports and physical activity have been claimed as a space for social and cultural integration. To date, most research has been based mainly on ethnographic and grassroots perspectives to better understand the experiences of sports practices of migrants and their families. However, fewer contributions have focused on the political discourse on sports as a field of integration. This article explores methodological challenges arosen when choosing sports policies as a field of study. The main methodological challenges considered include the contested conceptualizations of the target population in sports initiatives and the development of comparative selection

introduCtion

In recent years, the processes of incorporation of young second generation migrants into their receiving societies have been studied using new approaches that are far removed from traditional methods or areas of research, as is the case of sport and physical activity. The sports field has been understood as an area used for different forms of identity claim and ethnic-cultural belonging, or even as a kind of "social laboratory" for experimenting with sports programmes and their influence on the resolution of socio-cultural and coexistence conflicts [START_REF] Coakley | Sport in Society: Issues and Controversies[END_REF][START_REF] Maza | El deporte y su papel en los mecanismos de reproducción social de la población inmigrada extranjera[END_REF][START_REF] Gasparini | Le sport et la diversité: construction et circulation d'une catégorie de pensée[END_REF]. However, criteria for different levels of institutional participants. An indepth analysis of these methodological issues can help to reflect on the ideological constructs of sports as a field of integration and highlight the contribution of the political sociological perspective to existing migration studies. Keywords: sports; physical activity; integration; political sociology; methodological challenges.

Resumen: Los procesos de incorporación de los jóvenes migrantes han sido estudiados desde nuevas aproximaciones. Entre éstas, la actividad física y deportiva se ha reivindicado como espacio para la integración social y cultural. La mayoría de las investigaciones se han basado principalmente en perspectivas etnográficas para conocer mejor las experiencias reales de práctica deportiva de los migrantes y sus familias. Sin embargo, existen menos ejemplos enfocados en el análisis del discurso político. Este artículo explora algunos de los retos metodológicos que pueden surgir cuando se elijen las políticas deportivas como tema de estudio. Los principales retos metodológicos considerados incluyen, en primer lugar, entender cómo la población objetivo de estas iniciativas deportivas es definida y etiquetada y, en segundo lugar, desarrollar una selección de criterios comparativos para los diferentes niveles de participantes institucionales. Un análisis en profundidad de estos retos metodológicos puede ayudar a reflexionar sobre los constructos ideológicos del deporte como espacio de integración y subrayar la contribución de la perspectiva de la sociología política a los estudios migratorios existentes.

Palabras clave: deporte; actividad física; integración; sociología política; retos metodológicos. despite being perceived from the rather unitary and functionalist image of its socialising virtues, the sports field needs to be analysed carefully because "it designates a complex reality: its apparent unity conceals the diversity of ways of practising it" (Gasparini and Vieille Marchiset, 2008:17 1 ).

Before going further, it is important to clarify the term 'integration', as it is rather controversial and ambiguous, and explain how it will be considered in this article. According to the French sociologist Dominique [START_REF] Schnapper | Qu'est-ce que l'intégration[END_REF], integration is a term that entails confusion and two meanings must be distinguished: integration policies (i.e. the set of measures used to define and apply a political will to incorporate the migrant population into the receiving country) and the sociological phenomenon of the incorporation process. For the study on which this article is based, the first meaning was more accurate, since I followed a methodological approach based on a political perspective. Here thus, integration needs to be understood from this political perspective and in relation to the 'integration policies' related to the field of sports.

This article draws from the findings of my doctoral research project, which had two main objectives. The first was to analyse the formulation of policies aimed at the socio-cultural integration of young immigrants through physical and sporting activities in socially disadvantaged areas in Paris and Madrid. The second aim was to evaluate the articulation of this political approach within the associative network at the local level. In order to analyse how sports have potentially been used as a tool for the integration of young immigrants, I focused on the initiatives conceived and driven by political actors and associative networks, and the articulation between the two. For this reason, the sociology of organisations was chosen as an appropriate theoretical paradigm. Having as the main reference the work of [START_REF] Crozier | L'acteur et le système: les contraintes de l'action collective[END_REF], the sociology of organisations follows an individualistic methodology. From this perspective, society is built on the multiple strategies, interests and relationships established between individuals and the social system. The relevance of this perspective is based on its attempt to overtake the limits of culturalist approaches that conceive a homologous relationship between the specific organisation studied and the global society, as well as to prevent a deterministic view of social change [START_REF] Crozier | The regulation of complex organized systems[END_REF]. As Crozier and Friedberg (1977:456 2 ) argue: "it is not only a matter of evaluating, even criticising, the observed practices, but of understanding them". Therefore, the relationships, alliances and strategies established between political and social sports actors become the core of the study. Thus, various levels of participants need to be involved: from the political decisionmaking level to the management of the sports initiatives in the field (public programmes, sports clubs, associations and sociocultural entities). This multilevel conception of political action also takes as its reference the concept of governance applied to sports policies in [START_REF] Henry | Transnational and comparative research in sport: globalisation, governance and sport policy[END_REF] analysis. According to this approach, policies are not only conceived from a unilateral direction (top-down), but all stakeholders are taken into account both for the design of proposed policies and for their implementation.

In my doctoral study, both political and associative actors were considered and sports policies were analysed from the moment of their formulation (laws, integration plans, reports) to their practical implementation (sports programmes for each district or city). Two main approaches were adopted for data collection. Firstly, a policy documentary analysis of diverse sources of information was conducted (decrees, action plans, internal documentation, statistics, association statutes, and the local press). Secondly, 72 semi-structured interviews were conducted with two types of actors: associative (clubs and local sports associations) and institutional, covering various levels of political decision-making, including monitors and educators that directly implemented the sports schemes.

The present article argues that a political and organisational approach based on political sociology can enhance the study of sports as a tool for integration. This approach can complement existing perspectives focused on lived experiences of sports practices based mainly on ethnographic and grassroots approaches. Besides, few studies can be found in this area that analyse and compare two different contexts in political terms, and even fewer examples give voice in a more detailed way to the interactions between the different actors involved in the way proposed by the sociology of organisations.

To develop this main argument, the first section provides a general overview of the ways in which political authorities view sports as an integrative tool. This overview helps to show the need for further studies that critically appraise the ideological construction of sports as an integration tool as well as its effects when implemented. In the second section, a brief literature review considers different methodological approaches in this area of research to evidence the scarce presence of comparative and multilevel studies undertaken from a political perspective. In the third section, I address the main methodological challenges encountered during my doctoral project due to the chosen research design. These methodological challenges provide the opportunity to reflect on the existing gap between political discourse and practical implementation; to critically appraise how decision-making actors construct categories to label the target population of these sports initiatives; and to showcase the contribution of the political and organisational approach to better understand the relationships between government and associative actors in sports initiatives for migrants.

physiCal aCtivity and sports as integration tools

Politicians have considered sports, seen as a cultural phenomenon in modern societies, as a potential integration tool. Since its origin, contemporary sport has had a connotation of control strategy. For example, in England in the Public Schools of the nineteenth century, children of the upper classes practised rugby and football as a vehicle for moral transmission and desirable behaviour in the future leaders of the nation [START_REF] Ellis | Thomas Arnold, «Christian manliness and the problem of boyhood[END_REF]. With the "sportivisation" of society, state intervention in sport increased, especially in European countries. Authoritarian movements such as fascism, communism or Francoism in the first half of the 20th century used sport as a tool for political and moral control [START_REF] González Aja | Sport y autoritarismos: la utilización del deporte por el comunismo y el fascismo[END_REF]. Sport was also used during the Cold War, and especially in the Olympic Games, as an ideal showcase for demonstrating the supremacy of each political model [START_REF] Redihan | Sport as battleground in the U.S. -Soviet rivalry[END_REF]. However, the political use of sport was not exclusive to authoritarian governments, as France and Great Britain also used sport to promote national values through international events [START_REF] Arnaud | Sport and international politics. The impact of fascism and communism on sport[END_REF].

Thus, the use of sport for political purposes is not exclusive to totalitarianisms, but also evolves in democratic states for positive purposes. Here the idea of "sport for all" is acclaimed: state intervention in sport is legitimised through a provision of sports practice seeking democratisation and equality of opportunities, through the meritocratic system on which the contemporary sports phenomenon is based [START_REF] Queval | S'accomplir ou se dépasser: essai sur le sport contemporain[END_REF]. In this sense, the link between the state and society through sport has been decentralised, especially in the European context, with a local scope (municipal and regional policies) in constant interaction with other social actors in the field, especially clubs and sports associations [START_REF] Henry | Transnational and comparative research in sport: globalisation, governance and sport policy[END_REF][START_REF] Gasparini | Le sport dans les quartiers: pratiques sociales et politiques publiques[END_REF].

In this process of democratisation of sport, Western countries have forged the idea that sport is a privileged field for diversity, and understand sports participation:

As a (partial) solution to social problems within a functionalist perspective that assumes that institutions have a specific function in society (…); sport is an ideal institution for stimulating or enhancing the social integration of marginalised groups, such as ethnic minorities, the elderly, the physically challenged, and the unemployed (Elling, Knoppers & Knop, 2001:415).

However, it is pertinent to point out that the rate of participation of these young people in organised sports is below that of the main socio-cultural group, which means a lower level of sports practice, in both French and Spanish contexts. This lower participation is more evident in participants of African origin [START_REF] Atime | Fomento de la integración a través del deporte[END_REF][START_REF] Coulangeon | Les loisirs des populations issues de l'immigration, miroir de l'intégration[END_REF][START_REF] Arjona Garrido | Immigration, school, physical activity and sport. Analysis of sport acculturation in Spain[END_REF]. However, other sports realities converge in the same urban space, as shown by the significant presence of immigrant sports associations in disadvantaged neighbourhoods [START_REF] Granata | Le funzioni sociali dell'associazionismo sportivo per gli immigrati in due contesti urbani europei[END_REF][START_REF] Llopis-Goig | El fútbol une bastantísimo aquí»: las ligas de fútbol de la Asociación de Latinoamericanos y Ecuatorianos en Valencia[END_REF][START_REF] Müller | Local relations and transnational imaginaries: football practices of migrant men and women from Andean countries in Spain[END_REF][START_REF] Weiss | Tel père, tel fils!" -Les clubs de football "turcs" en France et en Allemagne[END_REF].

Sports can offer a space and a time for coexistence, in which to establish friendships and construct an intercultural dialogue in a ludic framework [START_REF] Coakley | Sport in Society: Issues and Controversies[END_REF]. In contrast, analysing whether sports are really an integration vehicle, a number of authors respond with skepticism and the belief that sport integrates per se has been questioned [START_REF] Gasparini | L'intégration par le sport. Genèse politique d'une croyance collective[END_REF], criticising the integrative social functions attributed to it as automatically transmitted values [START_REF] Elling | The social integrative meaning of sport: a critical and comparative analysis of policy and practice in the Netherlands[END_REF]. Some of these authors insist on the fact that sports offer the illusion of escape from social exclusion, as defended by [START_REF] Bourdieu | Deporte y clase social[END_REF]. French studies, in particular, criticise the social function of sport presented by the authorities as a panacea to combat difficulties in the integration of young immigrants [START_REF] Falcoz | Intégration par le sport: representations et réalités[END_REF]El Houssaine, 2001;[START_REF] Gasparini | L'intégration par le sport. Genèse politique d'une croyance collective[END_REF][START_REF] Gasparini | Le sport dans les quartiers: pratiques sociales et politiques publiques[END_REF]. In the case of Spain, for example, several authors agree that, despite the growing importance of programmes and political will, sport used as a means of social and cultural integration is still at an early stage, with no complete coordination with the sports bodies. Sports programmes (tournaments or events of one or a few days) are generally sporadic, they are implemented only at a regional or local level and their impact is moderate or even unknown [START_REF] Balibrea Melero | Deporte en los barrios: ¿integración o control social? Valencia[END_REF][START_REF] Kennett | Deporte e inmigración en España: el papel del deporte en la integración de los ciudadanos[END_REF]. This is certainly the crux of integration through sports initiatives: the fact that important elements in implementation still need to be explored in a more profound manner and, therefore, an important gap between theory and practice is still present. Some essential implementation elements are, among others, how to target the population, what sports modalities are more suitable, the level of organisation of these practices (informal or structured in clubs), the timing to achieve real outcomes, the types of funding or the lack of training of monitors and coaches facing cultural diversity. These issues are still a major matter of debate and need to be part of a further analysis.

It is precisely the methodological approach followed by the study on which this article is based that can contribute to filling the gap between theoretical constructions of integration though sports and their effects when implemented. Therefore, this conceptual framework shows that there is still a challenge for researchers to explore to what extent the conception of sports for young migrant integration is "more an idea than a practical reality" (Balibrea Melero & Santos Ortega, 2010: 93 ). In the next section, I try to demonstrate how existing studies do not usually follow political and multi-level approaches to answer these crucial issues.

applied methodologies with sports as field of researCh: a brief literature review

The aim of this literature review is to bring to light the methodology applied by previous researchers in the field of sport for integration, and thus, show how the methodology proposed in this article can fill the gaps and contribute to a deeper examination of this subject from a political and organisational perspective. In the literature review I privileged studies of Spanish and French contexts for obvious reasons, but examples from other countries have also been analysed to contrast reseach designs [see Table 1].

There are more exhaustive literature reviews on sport and integration that must be noted here. Firstly, [START_REF] Long | Reviewing research evidence and the case of participation in sport and physical recreation by black and minority ethnic communities[END_REF] present a detailed meta-analysis of sport participation in young BME (Black Minority Ethnic) in the UK. Secondly, the literature review of studies and conferences that [START_REF] Domínguez | Revisión de los principales estudios analizados en deporte e inmigración a nivel nacional e internacional[END_REF] have compiled by Spanish regions (Madrid, Catalonia and Valencia) and other countries of immigrant reception must be highlighted. Finally, attention is drawn to the in-depth analysis of studies carried out in France from the 1980s until today by [START_REF] Charrier | Prévention, animation et insertion par le sport en zones urbaines sensibles: la reconstruction du processus historique des analyses[END_REF], around three large axes: institutional actors, organisers and educators, and the target participants.

There is a growing group of investigations focusing on the role of sport in the integration of people from different cultural backgrounds, particularly about the socialising aspects of sports practice (clubs, associations or local sports programmes). This literature comes from the main immigrant receiving countries, such as the United States, United Kingdom, Germany, France and the Netherlands, and in the last few decades, recent contexts of immigration reception such as Italy or Spain [START_REF] Stodolska | The role of recreational sport in the adaptation of first generation immigrants in the United States[END_REF][START_REF] Henry | Transnational and comparative research in sport: globalisation, governance and sport policy[END_REF][START_REF] Grimminger-Seidensticker | Intercultural education in physical education: results of a quasi-experimental intervention study with secondary school students[END_REF][START_REF] Weiss | Tel père, tel fils!" -Les clubs de football "turcs" en France et en Allemagne[END_REF][START_REF] Gasparini | L'intégration par le sport. Genèse politique d'une croyance collective[END_REF][START_REF] Müller | The integrative power of sport: imagined and real effects of sport events on multicultural integration[END_REF][START_REF] Granata | Le funzioni sociali dell'associazionismo sportivo per gli immigrati in due contesti urbani europei[END_REF][START_REF] Balibrea Melero | Deporte en los barrios: ¿integración o control social? Valencia[END_REF]2010). These studies have focused on understanding how sports, conceived as a research field, might contribute to the knowledge of everyday life experiences, and how sports experiences help to better understand social and cultural adaptation to the receiving country. Italy & Spain [START_REF] Granata | Le funzioni sociali dell'associazionismo sportivo per gli immigrati in due contesti urbani europei[END_REF] Comparative analysis between Spanish and Italian sports and cultural associations of South American migrants

Interviews with sports club organisers

The main distinguishing feature in Table 1 is the methodological perspective from which the studies were conceived. Group 1 corresponds to quantitative studies, which use statistical methods to explore the level of sports practice according to the cultural background of the participants. These studies are rare. The first approaches come from political and associative institutions, which seek to find out how migrant populations and sports practice are related. In Spain the survey on sports practice by the Ministry of Education, Culture and Sport (2015) under the scientific direction of Manuel García Ferrando can be highlighted. This is the longest national longitudinal survey on sports practice in Spain, which started in 1980 and is carried out every 5 years. In 2010, for the first time, the variable "foreign population" was included using the criterion of nationality. [START_REF] Muller | La pratique sportive des jeunes dépend avant tout de leur milieu sociocultural[END_REF], but the cultural or ethnic origin category in the study of sports habits is not present in any case. Studies that analyse the sporting habits of a particular ethnic or cultural group outside a statistical perspective are very rare [START_REF] Stodolska | The role of recreational sport in the adaptation of first generation immigrants in the United States[END_REF]. Group 2, the largest one, corresponds to studies that have addressed the role of sports as a means of social and cultural integration with qualitative methods. First, there are examples of case studies that analyse pilot programmes or sports practices in very specific urban contexts (a neighbourhood or a city). [START_REF] Maza | El deporte y su papel en los mecanismos de reproducción social de la población inmigrada extranjera[END_REF] and [START_REF] Soler | El programa 'Bellugant-nos': actividad física para mujeres inmigrantes y autóctonas del barrio Collblanc-La Tarrasa (Hospitalet)[END_REF] in Barcelona, Balibrea Melero and Santos Ortega (2010) in Valencia or [START_REF] Chantelat | Les groupes de jeunes sportifs dans la ville[END_REF] in Lyon are relevant examples. Data collection is based mainly on ethnography, using participant observation and semi-structured interviews. Secondly, with a similar methodology, the migrant sports associations are the focus of study. Here the following can be highlighted: the studies of Muller (2013), Llopis [START_REF] Llopis-Goig | El fútbol une bastantísimo aquí»: las ligas de fútbol de la Asociación de Latinoamericanos y Ecuatorianos en Valencia[END_REF] on the Latino leagues in Spain, sports migrant associations in Italy by [START_REF] Granata | Le funzioni sociali dell'associazionismo sportivo per gli immigrati in due contesti urbani europei[END_REF] or the analysis of football clubs of Turkish origin in France and Germany by [START_REF] Weiss | Tel père, tel fils!" -Les clubs de football "turcs" en France et en Allemagne[END_REF]. Association presidents, tournament organisers and the players themselves are frequently the participants interviewed in these studies.

In this same group, another common object of study can be observed: the analysis of institutional sports programmes. Some researchers have been interested in the formulation and implementation of these initiatives by analysing both the discourse and the praxis, usually presenting their results as an evaluation and proposing theories to better understand these sports practices [START_REF] Henry | Transnational and comparative research in sport: globalisation, governance and sport policy[END_REF][START_REF] Gasparini | Le sport dans les quartiers: pratiques sociales et politiques publiques[END_REF][START_REF] Charrier | Activités physiques et sportives et insertion des jeunes[END_REF]. In these cases, the main data source is the institutional documentation at different levels of government (municipal, regional and national), official statistics and reports examining sports schemes. [START_REF] Gasparini | Le sport dans les quartiers: pratiques sociales et politiques publiques[END_REF] propose a typology of sports associations in neighbourhoods, [START_REF] Charrier | Activités physiques et sportives et insertion des jeunes[END_REF] presents a wide range of the social effects of sports programmes, and [START_REF] Henry | Transnational and comparative research in sport: globalisation, governance and sport policy[END_REF] proposes an ambitious attempt at modelling the sports policies in each member state of the European Union, according to criteria such as the heterogeneity of the population and the type of migration policies (in a range between assimilationist to intercultural policies).

Group 3 presents "mixed" studies. They are less frequent and combine both quantitative and qualitative techniques. For example, [START_REF] Grimminger-Seidensticker | Intercultural education in physical education: results of a quasi-experimental intervention study with secondary school students[END_REF] propose the evaluation of a programme of Physical Education based on intercultural education from an intervention with pre and post questionnaires, video analysis and interviews with participants. [START_REF] Müller | The integrative power of sport: imagined and real effects of sport events on multicultural integration[END_REF] propose another significant case in the combination of methods and types of actors involved in data collection by regarding the celebration of the AWC (Amsterdam World Cup) multicultural sports event. From a Foucaldian perspective, the authors analyse the discourse, motivations and power relations among the actors involved (organisers, spectators, players of immigrant origin) using survey data, in-depth interviews and ethnographic field notes.

Overall, it should be noted that the comparative dimension between local contexts of two or more countries is also present. Some examples can be found of sports clubs of Latin American origin between Seville and Madrid [START_REF] Müller | Local relations and transnational imaginaries: football practices of migrant men and women from Andean countries in Spain[END_REF] and between Italy and Spain [START_REF] Granata | Le funzioni sociali dell'associazionismo sportivo per gli immigrati in due contesti urbani europei[END_REF], or the Turkish football clubs in France and Germany [START_REF] Weiss | Tel père, tel fils!" -Les clubs de football "turcs" en France et en Allemagne[END_REF]; [START_REF] Arnaud | Le sport, entre citoyenneté et assujettissement culturel[END_REF] compares the sports policies for integration purposes in the cities of Lyon (France) and Birmingham (UK) as both cities have a significant presence of young immigrants.

In conclusion, the literature review reveals a variety of studies undertaken from different methodological perspectives and with a variety of techniques: quantitative, qualitative and mixed. Nevertheless, some gaps must be considered. The first gap is the scarcity of studies from a political sociological perspective. Those found analyse global definitions of sports policies using official documentation, but there are no examples where this definition is contrasted in the field. The second gap is the limited examples of multi-level analysis of contexts and actors. Only the research by [START_REF] Müller | The integrative power of sport: imagined and real effects of sport events on multicultural integration[END_REF] can be considered a notable case, since these authors try to grasp motivations and power relations among the multiple actors involved (organisers, spectators, players of immigrant origin) in the AWC sports event. However, they only limit their research to this one-off sports event.

In line with the dialogue that existing studies have started on sport as a tool for integration, the study on which the present article is based aimed to enrich the political sociological perspectivs. This perspective takes into consideration several elements that can enhance a holistic and comparative approach to studying two different sports contexts; including, on the one hand, the entire process of political construction (from formulation to implementation); and, on the other, the way that the ideological construct of integration through sport has been transferred into practice by different types of decision-making actors.

main methodologiCal Challenges enCountered in the field

Adopting a political sociological perspective to studying migrant integration and sports presents a range of methodological challenges. Firstly, it is difficult to define and evaluate the real role of sports as a tool of integration of young migrants. The idea of "integration through sport" has been built from the political sphere, but migrant associations and clubs 4 have also used this political construct in order to claim visibility for their identity and cultural background. Secondly, a major challenge exists when comparing two different reception contexts, as in this case between sports initiatives in Paris and Madrid, due to the difference in the integration models of France and Spain and the wide diversity of existing sports and cultural practices. In this section, I consider the lessons learned in my study to illustrate some of these main challenges, including:

1. The process of characterising the young target population in terms of their ethnic or cultural identity by the organisers of sports initiatives. 2. The issues encountered in adopting a multilevel qualitative design in two different sports contexts and thus, establishing comparative selection criteria for choosing equivalent types of actors at different decision-making levels.

first challenge: characterising the target population of sports initiatives

The first methodological challenge I faced was to understand how and why the organisers defined and targeted the participants of the sports activities, who were mainly adolescents and young people, usually aged between 12 and 18 5 . The way of referring to this population is not free from ambiguity and an extensive amalgam of labels is used to define the target population: "troubled youth", "disorganised youth", "young people in difficulty", "young people issu d'immigration" 6 , "vulnerable youth", "youth at risk" and "unadapted youth". On other occasions, a territorial or urban reference to where they live is used by policy makers to define them: "young people from the neighbourhood or banlieue 7 ", "young people from difficult neighbourhoods", "young people from disadvantaged neighbourhoods" or "young people from ZUS 8 ". However, the cultural or ethnic origin is rarely used to identify the origin of the participants, especially in France. In the French context, the issue of immigration and ethnic origin is enourmously sensitive. The political model of integration prefers not to apply affirmative action to avoid any type of ethnic or cultural discrimination; instead, its policies are implemented to resolve social disadvantages, so the intervention is planned in specific territories. Access to information on the immigrant population already entails a problem due to 5

The age range varies by sports programme. Two strands can usually be defined, based on a review of institutional documentation and bibliography: activities for adolescents (12-16 years old) and for young people, also called young adults (over 16, and up to 25 years of age).

6

In the French context the expression issu d'immigration is used to refer to the descendants of immigrants, either second generation (an immigrant father and/or mother) or later generations. Banlieue means suburb in French. In the case of large French cities, such as Paris, Lyon or Marseille, this term is used to refer to peripheral urban areas inhabited by a population with low economic resources and a high percentage of immigrant origin [START_REF] Vieille Marchiset | Des loisirs et des banlieues. Enquête sur l'occupation du temps libre dans les quartiers populaires[END_REF].

8

In French, ZUS (Zones Urbaines Sensibles) [Sensitive Urban Zones]. Since the urban policies created in the 1990s, ZUS refers to the system of territorial cataloging of urban areas with urban and economic, but also social and cultural difficulties. In Spain, this category depends on the social policy of the region or the city. In Madrid, interventions in the underpriveledged urban neighbourhoods are called Planes de Barrio.

"statistical blindness" 9 , much more evident in recreational or sport migrant practices; as the literature review highlighted, there is a scarcity of studies of this type.

Spain seems to follow a model of ethnic and cultural categorisation more similar to the Anglo-Saxon model; the country of origin has been postulated as the main criterion for the analysis of the situation of immigrants. The current legislation defines "foreign" as "those who lack Spanish nationality" (BOE, 2000, art.1). For Iglesias de Ussel (2010), this confirms the distinction between national and non-national for "foreigners" or "resident foreigners", giving a clear difference of treatment according to their legal status. This can be observed in the survey on sports habits by the Ministry of Education, Culture and Sports (2010). Here the variable of nationality was used ("Spanish" or "foreign"), and within the subcategory of "foreign", a subdivision into "European", "American" and "African" was applied. Without detracting from the milestone implied by the fact that this benchmark study in Spain included nationality as a variable, its approach to the migrant reality ended up being too simplified.

The French case is particularly sensitive to the use of ethnic or cultural categories, and that is why special attention should be devoted to it. According to the republican vision of integration, the practice of making the cultural or ethnic origin explicit has been widely avoided, both from the public administration and the academic world. The basic idea here is that not using ethnic categories will preserve the principle of equality among the population and thus avoid the possibility of exclusion by race, ethnic or cultural affiliation in the public or private sphere. France is thus different from other similar contexts with a long migratory tradition, such as the United States or Great Britain, where the use of ethnic and racial categories in population censuses is common practice. Nevertheless, some authors critizise the absence of cultural or ethnic categories in the studies of migration in the French context (Schnapper;2000;[START_REF] Tribalat | Les Yeux grands fermés. L'immigration en France[END_REF]. They argue that these categories do not have to entail a racist or "anti-Republican" position (in the French sense of the idea of Republican values as universal categories, and thus the 9

The publication of Michèle [START_REF] Tribalat | Les Yeux grands fermés. L'immigration en France[END_REF], "Les Yeux grand fermés" (Eyes Wide Shut), perfectly illustrates this "blindness" regarding the situation of migrants: a huge media and debate presence but at the same time an absence of statistical studies. avoidance of stigmatisation); and also maintain that the abscence of ethnic or cultural categories results in the invisibilization of migrants' day-to-day lives.

In my doctoral study, I identified two strategies used by sports managers in defining their target population. The first strategy avoided making explicit references to the ethnic or cultural background of the young participants. Instead, as noted above, two other criteria were used to define the target population: territorial references and the situation of vulnerable youth. This way of referring to and managing the target population was present in the Paris SDP programme (Sport Découverte Proximité) and in the sports associations, except for the immigrant ones. The question of origin was invisible (no reference to the origin, or notions such as integration, or diversity in the sports plans). Morevoer, it was a very sensitive topic during interviews, with some decision-making actors even refusing to mention the cultural background of the targeted population. In any case, there was relative unanimity among actors from both sports clubs and council sports programmes in wanting to convey that the criterion of choice of participants is more universal, and not because of cultural or ethnic belonging. One of the coordinators of the municipal sports programme expressed it this way:

The only criterion is to live in the neighbourhood, to be residents of the neighbourhood. These neighbourhoods are multicultural because there are all nationalities in Paris, so there are people from different horizons [mainly North African and Sub-Saharan]. Our goal is to propose [the programme] to all these people. In contrast, there are certain ethnic clubs among us, but at the associative level (SDP Coordinator, 18th district, Paris10 ).

In Madrid this strategy was used too, but not so unanimously; there are nuances that differentiate it from the Parisian case. This strategy was used by social workers from the Intercultural Co-Existence Services in Madrid, where the neighbourhood was the main reference to define the target population. The participant in these sports activities was the neighbour, but at the same time the cultural background of the young beneficiaries was visible, as opposed to Paris, where it was deliberately omitted.

The second strategy was to make explicit the cultural or ethnic origin. This approach is diametrically opposed to the first strategy, since the criterion underlined by the sports scheme is precisely the ethnic difference. This unique approach to sports activities "for immigrants" was present in documents from Madrid (integration plans, financial support for the immigrant population associations). In this case it was possible to identify the origins by the names of the associations or sports clubs; they were in general from Latin America -and especially Ecuador-, and could be identified with relative ease. There were association names that referred to geographical or cultural origin in various forms. For example, a reference to Ecuadorian regions of origin such as the Association Lojanos in Madrid or the Association Llano Grande; also the country name, like in APEM (Ecuadorian's People Association), the Colombian Sports League, LIDEBOL (Bolivian Sports League), or the Paraguayan Association of women's football.

Cultural references were present too, like the Rumiñahui 11 Spanish-Ecuadorian Association. In other cases the reference to the origin of the membership was linked to the Latino community, such as the Latin Strength Association; an allusion to the unity and solidarity of the group was also present, such as the United Ecuadorian League for Sport, United Cultures League or The Unity League. On other occasions, migrants had introduced a reference to the urban context in which they resided, as in the case of APOCID (Association El Pozo 12 for Intercultural Co-Existence and Sport).

Here the ethnic claim is obvious. A desire for Latin origin visibility was found not only in the name of the club or sports league, but also in the presence of typical cultural traits and customs of origin. Frequently in the opening ceremonies of these sports leagues, traditional dances and folk costumes were evident, as well as food and drinks from Ecuador or Latin America, along with the display of the flags of the country of origin.

The institutional organizers did not hesitate to refer to the cultural background of the participants, and they also consciously used it to show the different origins. Perhaps the best example was the Basketball Immigration World Cup (Mundialito de la Inmigración), organised by the government of Madrid and the Foundation of the Spanish Basketball Federation. In the rules of 11 A historical Ecuadorian figure .   12 El Pozo del Tío Raimundo is a formerly a shantytown in Madrid, and an actual working-class neighbourhood located on the east side of the city.

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Noemi García-Arjona this tournament, there is an explicit requirement to form teams representing different countries, where at most 5 players come from the same origin and the rest from other countries (FEB Foundation, 2014). For the organisers, this measure would help to speed up processes, in some way, through the rules of the game, forcing the young people from different backgrounds to play together, but in any case it was seen as a first step or "lesser evil" for the short term.

In Paris, the situation was quite different. The only cases in which there was an explicit reference to origin were found within immigrant associations, for example the FCBA (French Chinese Basketball Association), the Malgache Sports Association (from Madagascar) or the Club Foot Antillais (from the French Antilles). In other cases, the reference was subtler. For example, the basketball club Paris Basket 97-3, refers to its Guyanese origin in its own name, as 97-3 is the code that identifies departmental French Guiana in the French DOM-TOM territories13 . The sports project objective is defined as "the implementation of actions to help develop basketball within the Guyanese community" (Paris Basket 97-3, 2017). However, in the interview, its president, a former basket player, emphasised the fact that, although players with Guyanese origins established the association, its current target population is culturally very diverse.

Possibly a paradigmatic example is the football club Espérance Paris 19ème. This club, founded in 1974 by Algerian immigrants, a priori does not reveal its origin; perhaps the green colour of the shirt and the word "espérance" (hope) may bring a veiled reference to an Arab and Muslim belonging. The main reference is territorial, i.e. the 19th district, where the club headquarters are located, in the northeast of Paris. In its statutes the club does not make any allusion to searching to promote ethnic belonging. Article 2 states that "the association aims to organise and develop sport in the 19th district" (Espérance Paris 19ème, 2010:1). Nor was the aim of bringing young people of Arab or Muslim origin together mentioned in the interview with its current president. Still, it is revealing that in the club statutes the explanation of the founding Arab origins of the club can be found; it is stated in Article 18 that "the association regroups, by merger, members of the following associations: Club omnisport Espérance Arabe (Arab Hope Club) and Union Sportive Saint-Georges XIXème" (Espérance Paris 19 ème , 2010:5).

As shown in previous examples, decision-making actors show significant disparities in defining the target population. It is crucial to consider how, from a political sociological perspective, the discourse of the interviewees is fundamental to conceiving the categories of migrant or second generation young people that participate in the sports initiatives. It is through their discourse and decisions in the field that a sports initiative is "made for" one type of population or another. Even more, both local government actors and sports club managers contribute to defining, constructing or misinterpreting migrant categories. This question is even more evident in Paris when it comes to addressing the ethnic background of the participants in these sports practices, which are officially invisible but actually present in the sports activities. [START_REF] Noiriel | À quoi sert «l'idéntité nationale[END_REF] even affirms that the category of "immigrant" is only a socioadministrative invention, that is to say, it has been historically used with a purpose of measurement and control by the established power as a form of domination or exclusion of minorities; furthermore, it is not the result of a process of self-identification by the immigrants themselves. In the case of Madrid, the acceptance of a visible and direct reference to cultural or geographical origin within the sports initiatives could be perceived in a negative way, and seen to foster endogamy or communitarian closure 14 . Some authors, such as Taguieff (2005), however, claim the crucial need to clearly deconstruct the meaning of this notion as a negative perception of the presence of migrant, ethnic and/or religious communities in receiving societies.

Thefore, the methodology used for this study permits us to problematise how the targetting or labelleing of the population by the integration policies and their actors is not a mere discussion of 14 In French the term is communautarisme. It defines the group of values shared by a community (ethnic, religious, cultural, social, political, sports, etc.), seen as important, or even, more relevant than universal values of freedom and equality. Political actors have largely used (and manipulated) this concept, especially the far-right Front National (FN) party. [START_REF] Costa-Lascoux | L'intégration "à la française": une philosophie à l'épreuve des réalités[END_REF] uses the term "sociologism of the difference", in vogue during the 80s policies but still present, to refer to a form of political government and media coverage that try to put the accent on the ethnicity of the population as the core problem of society, and as a result, the cultural stigmatisation of underpriviledged areas. semantic nuances: the use of certain concepts and notions already determines or limits a way of conceiving this reality, and much more so when dealing with the question of identity and alterity during the process of migrant integration.

second challenge: comparative selection criteria for decision-making actors

The interest of analysing two different contexts was justified by the potential enrichment that this could provide for the research. The example of France, with successes and failures throughout its migration experience, could provide encouragement and guidance in the Spanish context for the creation of sports integration policies and social and cultural integration; hence the interest in proposing an analysis in two different contexts.

However, adopting a comparative approach across two different political contexts raises important methodological challenges. Here I exemplify a particular challenge faced when using this approach. This practical issue was how to establish comparative selection criteria for choosing equivalent types of actors at different decisionmaking levels. At the same time, this issue brought an added value to the analysis of the object of study. Firstly, it contributed to drawing a holistic frame of political and associative relations at the local level in two different contexts; secondly, the choice to take into consideration new actors involved in the decision making process helped to explore unknown aims and strategies, and therefore, to better understand the implementation of sports initiatives.

The typology of participants described below is based on previous multi-level approaches, mainly those of [START_REF] Müller | The integrative power of sport: imagined and real effects of sport events on multicultural integration[END_REF] and [START_REF] Gasparini | Le sport dans les quartiers: pratiques sociales et politiques publiques[END_REF]. The contribution of the present study, in comparison to these previous works, was to also take into consideration a governance approach in sports policies [START_REF] Henry | Transnational and comparative research in sport: globalisation, governance and sport policy[END_REF]. This meant analysing all possible actors involved in the process of decision-making policies, from their formulation to their effects when implemented. Thus, for institutional participants, 3 levels were distinguished, according to the rank of responsibility of the position and the proximity to the field [ For the participants from associations, not only sports clubs involved in the process of social and cultural integration were included, but also other organisations present in the neighbourhood such as foundations, NGOs, youth groups, and social assistance associations for the immigrant population that had developed sports programmes. The selection was based on the typology of sports initiatives at the local level proposed by [START_REF] Gasparini | Le sport dans les quartiers: pratiques sociales et politiques publiques[END_REF]: 1) traditional sports clubs present in the district, 2) sports associations for social purposes, and 3) nonsports associations that use physical sports activity in their projects (foundations and NGOs, neighbourhood associations, cultural and youth institutions).

The innovative contribution of this study was to include a fourth type of local association initiatives: immigrant or ethnic sports clubs. Their inclusion has proved to be essential because of the importance of such initiatives within the associative framework and its special relationship with local authorities. This methodological decision was a key factor for getting access to more information about the way in which the sports field was a place of contact between immigrant clubs and sports neighbourhood associations. It was observed especially in Madrid, as in the Parisian context the existence of these clubs was critised by both politicians and other types of associations; who considered that this type of ethnic sports events and competitions should remain relegated to the private sphere, without public support and, therefore, no government funding.

In the Madrid sports field, in contrast, there were examples where the existence of the Latin American Leagues was convenient in economic terms. For example, when addressing the collaboration between public organisations and these associations, the interest of the public administrations to have the organisers of the Latin League as regular "clients" for renting sports facilities, especially turf football pitches, was revealed. These strategic alliances were also observed between associations, as in the case of some neighbourhood clubs, in deep financial difficulties, that were literally saved by these leagues because they sublet the sports facilities. In addition, as stated by Müller and Ludwigs (2008), the Latin leagues represent an economic niche, by providing income through the leagues management (clubs registration fees, ethnic business support and sponsorship). There was also the possibility of being recognised as relevant social actors to attract the attention of institutions and private companies. This fact was crucial to question the homogeneous image of these clubs by other sports managers, usually labelled as ghettoes and promoting ethnocentric sports practices. On the contrary, many of these associations were already integrated within the municipal sports system or had the intention to join it. [START_REF] Müller | Local relations and transnational imaginaries: football practices of migrant men and women from Andean countries in Spain[END_REF] critises this non-recognition of the role of sport, as it is a facilitator of the social and cultural capital of immigrants thanks to two effects: the bonding of social networks and intra-community solidarity on the one hand, and the possibility of social recognition on the other. As a final illustrative example of the contribution of this study in arguing for the inclusion of ethnic clubs as key informants, an example in Madrid in the district of Carabanchel (San Isidro neighbourhood) can be mentioned. In this district, sports events in parks and outdoor areas by immigrant associations were at the core of local conflicts, not because of the sports practice itself, but especially because of the side effects of the activities: accumulation of noise and waste, unauthorised street trading, illegal sports bets and fees for the use of public sports facilities, alcohol abuse, violent altercations or lack of security in the facilities. The first approach to resolve the conflict focused on complaints and fines by the police, but it did not solve the problem of coexistence. The conflict was only resolved through a mediation process in a three-way partnership between Latino associations, neighbourhood associations and social workers from the city council. Sports facilities with innovative sports practices were adapted, such as Ecuavolley 15 , programmes and neighbourhood parties also included these practices, and possibly the greatest structural change was the creation of a new mixed sports club as a result of the merger of two associations with the same status and recognition as the rest of the neighbourhood associations.

ConClusions

The innovation and contribution of the approach I have proposed in this article exemplify the potential of a political sociological perspective to enhance studies on sports as a field for integration. Therefore, some learning points can be highlighted.

Firstly, sports face similar problems to other areas of integration policies, specifically when sports initiative managers and policy makers define the target population. In the selected sports initiatives in Paris, the invisibility of migrants or participants from diverse cultural backgrounds was patent, as well as the reluctance to consider the presence of ethnic sports clubs as positive for the process of incorporation in the receiving society. On the contrary, the examples of the sports initiatives in Madrid brought the possibility to make cultural diversity visible, like a display to show a shared identity; furthermore, sometimes it was claimed as a positive example to learn from and to be transferred to society. The contribution of the present study relies on the problematisation 15 Ecuavolley is a sport with adapted rules from volleyball and football, which has a great popular following as an informal sport in Ecuador, and is played in the streets of the country.

of the ambiguous and even contradictory categories that policy makers and sports club managers use to construct their definitions of a target population, which, in turn, have a direct effect on the field. It should be highlighted that the process of decision-making that actors followed in the field was directly and continously linked to the social discourse on migrant issues, which was strongly conditioned by each national model of integration. In fact, actors reflect and transmit through their decisions different perspectives: one perspective is "universalist" and avoids cultural identification of ethnic minorities, reducing the visibility of migrant identities; the other perspective, more intercultural, seeks cultural dialogue and ethnic recognition through sports, but real examples of successful implementation are still scarce. Possibly the example mentioned of a mixed sports association in a district of Madrid with immigrant and non-immigrant participants may illustrate the potential uniqueness of the sports field for bringing a universal language and a positive context of co-existence.

Secondly, an innovation of this methodological approach is the consideration of a comparative perspective with different actors, both associative and political, as participants in the study within a micro-perspective environment (the district). This study can enrich knowledge on comparative research because, as discussed in the literature review, there are few examples of this kind in the field of sports. In this case, although the selection of two district contexts in Paris and Madrid was a challenge for several reasons, particularly in the search for equivalent selection criteria for participants, in the end it has been fundamental to a better understanding of the network of relationships and interests in both contexts.

The initial complexity of a research design with various levels of actors resulted in an unexpected richness of results and the possibility of understanding the role of sports as a tool for integration in greater depth. In contrast to the reviewed literature that normally considers the analysis of these actors separately, the innovation of the present study relied on the inclusion of a multilevel perspective. Moreover, ethnic clubs as key actors in the sports dynamics of a particular context permitted to understand better complex situations of opposing objectives and interests in the sports field. Thanks to this methodological decision, it was possible to find out how links are established between sports organisers, the reasons for neighbourhood conflicts generated because of sports activities, and how sports may help to build a shared space for living together.

The learning derived from this study, based on a multi-level and comparative analysis, provides a more nuanced understanding of the role of the sports field in integration policies for migrants, and highlights the contribution of a political sociological perspective analysis to migration studies.

  researchIng local sports InItIatIves for young mIgrants from a polItIcal perspectIve: methodologIcal and practIcal challenges el estuDio De iniciativas Deportivas locales para jóvenes Migrantes DesDe una perspectiva política: retos MetoDológicos y prácticos noeMi García-arjona* MIGRACIONES 42 (2017). ISSN: 2341-0833, DOI: mig.i42.y2017.003 43-70

7

 7

*

  In París, Sport and Youth policy was managed by the DJS (Direction de la Jeunesse et des Sports) [Youth and Sports Area]. In Madrid, Youth policies are included in the Area of Familia y Asuntos Sociales [Family and Social Services]. **In Paris, Immigration policies belong to DPVI (Délégation à la Politique de la Ville et à l'Intégration) [Urban Affairs and Integration Area]. In Madrid, Immigration policies are carried out by the same area as Youth (see above).

  Furthermore, Dominguez et al. (2010) used questionnaire to determine the sports practice of the Ecuadorian population in Madrid, applying Berry's model of acculturation and crossing the results of type of practice (frequency, sport modality, knowledge of sports provision, use of facilities) with sociodemographic variables. In the case of France, however, it is difficult to find examples. The INSEE (Institut national de la statistique et des études économiques) has statistically analysed the difference in sports practice by socio-economic level

	Group	Country/City	Author/s (year)	Main theme	Method(s)
		France & Germany	Weiss (2013)	Comparative analysis between Turkish football clubs and cultural associations of South American migrants	Documentary analysis (sports articles, political sports reports), field notes, interviews with the sports leagues organisers
		France & UK	Arnaud (1998)	Comparative analysis between local sports policies of Lyon and Birmingham	Observations (sports councils meetings), interviews (local politicians, sports organisers), documentary analysis
	2	France	Charrier (1997)	Analysis and evaluation of sports programmes in	Research-action (Documentary analysis,
				underprivileged urban areas	interviews)
				Analysis of sports	Documentary analysis
		France	Gasparini & Vieille Marchiset (2008)	programmes (institutional and associative) in France aimed to integrate youngsters	(local and national sports policies, associations sports programmes, evaluation
				through sports	reports, laws)
		UK -European Union	Henry (2007)	Comparative analysis between European sports policies on integration	Documentary analysis (national sports policies, evaluation reports, laws)
			Grimminger, E.	Evaluation of a Physical	Experimental intervention
		Germany	& Möhwald, A.	Education programme based	with mixed evaluation:
			(2016)	on intercultural reflexivity	questionnaire, video analysis
	3
		The Netherlands	Müller, Van Zoonen & De Roode (2008)	Analysis and evaluation of an intercultural event in Amsterdam (AWC)

a

Table 2

 2 ].

		table 2
		LEVELS OF INSTITUTIONAL PARTICIPANTS
	Level	Description	Local government area
		Elected representatives of the government in the selected
	Level 1	government areas (sports, immigration, youth, social affairs),
		responsible for the analysed sports schemes
		Technical and administrative coordinators or employees
		present in the different municipal institutions. These are	Sport
	Level 2	intermediate positions in charge of managing public policies, from the moment they are formulated to their implementation.	Youth* Immigration/ Social
		This would include district policy makers on sports and	Services **
		immigration policies and coordinators of sports schemes.
		Sports educators, instructors and promoters of sports
	Level 3	programmes. They have direct contact with the participants of the proposed programmes. In some cases, these institutional
		actors are also coordinators of the activity.

Author's translation.

Author's translation.

Questionnaire & interviews (event organisers, participants), documentary analysis

Author translation.

DOM-TOM refers to Overseas French territories.

aCknowledgements

I would like to thank Pr. Teresa González Aja, my thesis director, for her support during my research. I would also like to thank Dr Martha Montero-Sieburth, Dr Rosa Mas Giralt and Dr Joaquín Eguren for their meaningful advice and for the opportunity to publish this article.