Racial socialisation and negotiation of family mixedness among white parents of internationally adoptive children in France

Solène Brun

Chapitre paru dans Josiane Le Gall, Catherine Therrien et Karine Geoffrion (dir.), Mixed Families in a Transnational World, New York, Routledge, 2022, p. 130-149.

In France, international adoption has rarely been studied from the angle of racial mixedness. In the United States and the United Kingdom, the adoption debate is strongly focused around racial questions, notably the legitimacy of so-called 'transracial' 1 adoption, be it domestic or international [START_REF] Bartholet | Where do black children belong: The politics of race matching in adoption[END_REF][START_REF] Lee | The transracial adoption paradox[END_REF][START_REF] Sweeney | Race-conscious adoption choices, multiraciality, and color-blind racial ideology[END_REF][START_REF] Tizard | Black, white, or mixed race?: Race and racism in the lives of young people of mixed parentage[END_REF]. The French sociohistorical context, on the other hand, has shaped the adoption debate in a totally different manner. France is largely considered a 'colour-blind' society [START_REF] Brubaker | Citizenship and nationhood in France and Germany[END_REF][START_REF] Sabbagh | French color blindness in perspective: The controversy over 'statistiques ethniques[END_REF][START_REF] Simon | The choice of ignorance: The debate on ethnic and racial statistics in France[END_REF], and in studies of adoption, as elsewhere, the question of race is often replaced by that of 'culture' [START_REF] Fortier | Des gamètes de couleur': Phénotype, race ou ethnie?[END_REF][START_REF] Marre | We do not have immigrant children at this school, we just have children adopted from abroad': Flexible understandings of children's 'origins[END_REF][START_REF] Roux | L'utérus et la patrie. Adoption, origines et politique des identités[END_REF][START_REF] Roux | The colour of family happiness: Adoption and the racial distribution of children in contemporary France[END_REF]). Yet a large majority of adopted children in France come from countries colonised by Europe in the past, and are very likely to be racialised as non-whites. Adoptive parents, for their part, belong overwhelmingly to the majority population, and are racialised as white [START_REF] Guillaumin | L'Idéologie raciste[END_REF]. If international adoption de facto creates families in which different national origins coexist, it also creates, in most cases, racially mixed families, characterised by the coexistence of majority racial status (for the parents) and minority status (for the children). These families where children racialised as non-white are raised and socialised by parents from the white majority population can thus pro-vide valuable insights on racial boundaries and how they are negotiated at the microsociological level.

Moreover, as whiteness is generally unmarked, and is characterised by invisibility and unspeakability [START_REF] Dottolo | I never think about my race': Psychological features of white racial identities[END_REF][START_REF] Frankenberg | White women, race matters: The social construction of whiteness[END_REF][START_REF] Lewis | What group?' Studying whites and whiteness in the era of 'colorblindness[END_REF], and ultimately by normality, white parents of non-white children occupy a singular and heuristic position. Their situation can shed useful light on the mechanisms of racial socialisation, rendered all the more observable by the fact that the parents do not share the same racial positionality as their children and therefore cannot simply transmit their own experience. The disruption of the norm of intrafamilial racial homogeneity thus renders racial socialisation practices less self-evident, hence more discernible for the researcher. Childhood is a key period in the process of primary socialisation [START_REF] Berger | La construction sociale de la réalité[END_REF], and it is within the family and through socialisation that children learn ways of being and acting, as well as under-standing the world and their place in it as determined by their gender and their class, but also by their race. This chapter examines the contours of racial socialisation, a question all too rarely studied in France, in the context of international and transracial adoptive families. It thus contributes both to the literature on racial socialisation in adoptive families [START_REF] Barn | Doing the right thing': Transracial adoption in the USA[END_REF][START_REF] Crolley-Simic | Racial socialization practices of white mothers of international transracial adoptees[END_REF][START_REF] Deberry | Family racial socialization and ecological competence: Longitudinal assessments of African-American transracial adoptees[END_REF][START_REF] Khanna | We didn't even think about adopting domestically': The role of race and other factors in shaping parents' decisions to adopt abroad[END_REF][START_REF] Leslie | Racial socialization in transracial adoptive families: Does it help adolescents deal with discrimination stress?[END_REF][START_REF] Mohanty | Ethnic and racial socialization and self-esteem of Asian adoptees: The mediating role of multiple identities[END_REF][START_REF] Samuels | Being raised by white people': Navigating racial difference among adopted multiracial adults[END_REF]) and to that on mixed-race families [START_REF] Rollins | Racial socialization of biracial youth: Maternal messages and approaches to address discrimination[END_REF][START_REF] Song | What are the parenting practices of multiracial people in Britain?[END_REF][START_REF] Stone | Racial socialization practices of white mothers raising black-white biracial children[END_REF][START_REF] Twine | Brown skinned white girls: Class, culture and the construction of white identity in suburban communities[END_REF]2010), exploring social racialisation in situations where white parents raise non-white children. In both bodies of literature, the aim is to analyse how non-white children must 'learn to navi-gate racialised stigma' with parents who have no direct knowledge of what this means and implies [START_REF] Samuels | Being raised by white people': Navigating racial difference among adopted multiracial adults[END_REF], in an often normative perspective.

By focusing on the question of racial mixedness among international adoptive families in France, this chapter shows how white parents approach the racial socialisation of their non-white children in a colourblind context. After describing the data on which the chapter relies, and the singular con-text in France with regard to international adoption and racial questions, it examines the two dominant modes of socialisation that can be identified. While a minority of adoptive parents interviewed socialise their children through what I have called 'learning racial minority status', the majority tend to apply an assimilationist approach-in which racial mixedness within the family is dealt with through references to integration and assimilation of children, both in a national and racial perspective -adopting a colourblind rationale to socialisation and keeping race at a distance. The chapter concludes with an analysis of the determinants of these socialisation practices, examining the characteristics and social positioning of the adoptive parents.

Research methods

This chapter draws upon an ethnographic study conducted between 2015 and 2017 to explore how racial boundaries are negotiated within international adoptive families and families of mixed-race couples in France. The chapter focuses here on the first module of the study on international adoption, comprising 53 semi-structured interviews with adoptive parents (n=34) and with individuals adopted abroad (n=19). The adoptive parents were aged between 36 and 74 and had adopted children in 21 countries or territories (Benin, Haiti, Madagascar, Guatemala, Ivory Coast, Colombia, Ethiopia, Mali, Wallis and Futuna, Central African Republic, Kazakhstan, Vietnam, China, Russia, Nepal, Congo Brazzaville, Djibouti, Peru, Morocco, Senegal, and South Korea) between 1970 and 2016. One-third of the respondents were active members of an association of adoptive parents.

Most had adopted as a couple (n=22), and among those who adopted as a lone parent (n=12), 11 were women. Some of the interviews with people who adopted as a couple were conducted with both parents (n=6), and the remainder with one parent (6 with the father only and 10 with the mother only). With two exceptions, all the parents interviewed belonged to the French white majority population and had adopted at least one child in a country of Africa, the Caribbean, the Pacific, South America or Asia. A large share of parents was in highly qualified occupations, and none were manual workers. This imbalance is consistent with the profile of adoptive parents in France: the adoption survey conducted by the French Institute for Demographic Studies (INED) in 2001-2002 found that 32 per cent of adoptive parents are in higher-level occupations (versus 18 per cent in the general population according to data from INSEE, the French statistical office). Last, a large majority of respondents (n=30) were living in the Paris region at the time of the survey, although in towns with very diverse sociodemographic profiles. The remainder lived in a French overseas department, abroad, or in a small provincial town. 2 During the interviews, which lasted between 50 minutes and 3½ hours, respondents were asked about their decision to adopt and the adoption process, the child(ren)'s arrival in the family, the discussions held with them, cultural transmission strategies, choices of forenames, and the child(ren)'s integration in the family. Parents were also asked to recount any experiences of rejection, racism or discrimination to which their children had been exposed, and how they, as parents, had prepared them to deal with such situations. Last, the parents were asked about the members of their contact circle (friends and relatives), and those of their children, their place of residence and the schools attended.

Context: race and adoption in France

With its solid republican foundations, France is a country where the colourblind ideology is not only dominant, but also institutionalised, as noted by many authors [START_REF] Bessone | Sans distinction de race? Une analyse critique du concept de race et de ses effets pratiques[END_REF][START_REF] Brubaker | Citizenship and nationhood in France and Germany[END_REF][START_REF] Sabbagh | French color blindness in perspective: The controversy over 'statistiques ethniques[END_REF][START_REF] Simon | The choice of ignorance: The debate on ethnic and racial statistics in France[END_REF]. The term 'colourblindness' refers to the cognitive and epistemological paradigm whereby racial differences are ignored, and, in some instances, whereby the very existence of races, both biological and social, is refuted (D. Fassin, 2006a;E. Fassin, 2006b). In France, colourblindness thus takes the form of a 'legal and political' framework [START_REF] Sabbagh | French color blindness in perspective: The controversy over 'statistiques ethniques[END_REF], characterised, especially since the aftermath of the Second World War, by a strong reluctance to confront and name the race question or to acquire a vocabulary serving specifically to combat ethno-racial discrimination [START_REF] Safi | Promoting diversity in French workplaces: Targeting and signaling ethnoracial origin in a colorblind context[END_REF]. While the use of ethno-racial categories has been institutionalised in some countries, notably via the population census [START_REF] Morning | Ethnic classification in global perspective: A cross-national survey of the 2000 census[END_REF][START_REF] Schor | Compter et classer: histoire des recensements américains[END_REF][START_REF] Simon | La statistique des origines: l'ethnicité et la 'race' dans les recensements aux États-Unis, Canada et Grande-Bretagne[END_REF], this is not the case in France. In the post-war period, the use of the word 'race' became highly derogatory and is subject to taboo [START_REF] Dhume | De la race comme un problème. Les sciences sociales et l'idée de nature[END_REF][START_REF] Guillaumin | L'Idéologie raciste[END_REF][START_REF] Peretti-Ndiaye | Race, racisme, racialisation: Que nous disent les discours?[END_REF]).

Yet ethno-racial inequalities and discrimination are widespread in France, and their scale has been amply documented [START_REF] Brinbaum | Discrimination in France: Between perception and experience[END_REF][START_REF] Mcavay | Perceptions et expériences de la discrimination en France[END_REF][START_REF] Safi | Les discriminations ethniques et raciales dans l'enquête Trajectoires et Origines: Représentations, expériences subjectives et situations vécues[END_REF]. The results of the Trajectories and Origins survey conducted by INED and INSEE in 2009 provide valuable information on the experience of discrimination and racism among immigrants and their descendants, by country of origin. Discrimination is reported more frequently by people from the French overseas departments, Sub-Saharan Africa, North Africa and Turkey than by people of Asian origin, whose experience is more similar to that of European immigrants and their descendants as well as of the majority population [START_REF] Mcavay | Is there really such thing as immigrant spatial assimilation in France? Desegregation trends and inequality along ethnoracial lines[END_REF][START_REF] Safi | Les discriminations ethniques et raciales dans l'enquête Trajectoires et Origines: Représentations, expériences subjectives et situations vécues[END_REF].

These inequalities and the racialised hierarchy that they reveal mirror the hierarchies observed at a global level, and affect the world of international adoption accordingly. In 2014, around 69 per cent of adoptions concerned children born abroad. 3 Alongside the United States and Spain, France is among the world's top three receiving countries: these countries alone account for two-thirds of all international adoptions [START_REF] Mignot | L'adoption internationale dans le monde: Les raisons du déclin[END_REF]. While the number of international adoptions in France and elsewhere in the world has declined sharply, the flow remains almost exclusively unidirectional, from the Global South to the Global North. Between 2004 and 2019, the proportion of European adoptions remained small, ranging between 15 per cent and 24 per cent from year to year, with most adopted children being born in Africa or Asia. 4 In France, the proportion of adoptions from Africa is higher than elsewhere, with African countries accounting for the majority of inter-national adoptions by French people since 2007 (Mahéo, 2016, 157).

According to Denéchère, this 'French singularity' is explained by the country's colonial past and its French-speaking sphere of influence (Denéchère, 2009, 126). Historically, the first French international adopters turned mainly to Asian countries, as did those in the rest of Europe and the United States. In 1974, internationally adopted children in France came mainly from South Korea, Vietnam and India (Denéchère, 2009, 126). Today, a large majority of adopted children in France is born in former European colonies. This international adoption flow is thus associated with a process of racialisation, both in the 'choice' 5 of adoptees and in the formation of adoptive families in the receiving country.

The general economy of international adoption, the strong tensions generated by the increase in demand in Western countries and the decline in international adoption have given rise to a system whereby the children are classified by desirability, and the parents by their adoptive capacities. In France, while parents' adoptive capacities are ranked mainly on the basis of socioeconomic factors and social norms of 'good parenting qualities' (heterosexuality, youth, stability, etc.) [START_REF] Ramos | La réception des normes par les parents: Le cas de l'adoption[END_REF][START_REF] Roux | Parents at their best: The ethnopolitics of family bonding in France[END_REF], the desirability ranking of children operates largely along racial lines [START_REF] Brun | Trouble dans la race. Construction et négociations des frontières raciales dans deux types de familles mixtes en France[END_REF][START_REF] Roux | The colour of family happiness: Adoption and the racial distribution of children in contemporary France[END_REF]. For many French adopters, children born in South America and East Asia represent a compromise between what is undesirable (children who are black, no longer infants, or have special needs) and what is unattainable (healthy white babies) [START_REF] Brun | Trouble dans la race. Construction et négociations des frontières raciales dans deux types de familles mixtes en France[END_REF], as is also the case in the United States (Dorow, 2006a;2006b;[START_REF] Khanna | We didn't even think about adopting domestically': The role of race and other factors in shaping parents' decisions to adopt abroad[END_REF][START_REF] Perry | Transracial and international adoption: Mothers, hierarchy, race, and feminist legal theory[END_REF][START_REF] Raleigh | Selling transracial adoption. Families, markets, and the color line[END_REF][START_REF] Sweeney | Race-conscious adoption choices, multiraciality, and color-blind racial ideology[END_REF][START_REF] Zhang | Intercountry versus transracial adoption: Analysis of adoptive parents' motivations and preferences in adoption[END_REF].

Racial socialisation in the French context

The concept of racial or ethnic socialisation was first developed in the 1980s in the United States by social scientists studying the socialisation practices of African-American parents [START_REF] Peters | Racial socialization of young black children[END_REF][START_REF] Richardson | Racism and child-rearing: A study of black mothers[END_REF][START_REF] Spencer | Children's cultural values and parental child rearing strategies[END_REF]. It was later extended to other ethnic or racial minorities. Given that the main role of this socialisation is to provide children with dispositions for coping with, and even challenging, racism and discrimination, the concept is intrinsically linked to minority families, potentially exposed to racial prejudice.

In France, despite an abundant literature on socialisation, understood as 'the set of processes whereby individuals are constructed […] by the global and local society in which they live, and during which individuals acquire […] socially situated ways of doing, thinking and being' (Darmon, 2010, 6), race has rarely been addressed from this angle, unlike class or gender. Yet the role of socialisation in the formation of ethnic or racial identities is not a novel idea for European social scientists. Fredrik Barth already developed a similar notion, considering that ethnic identities are closely linked to imposed and internalised social roles which shape the rules of behaviour and the social sanctions incurred when individuals infringe these rules [START_REF] Barth | Ethnic groups and boundaries: The social organization of culture difference[END_REF].

While the existence of racial socialisation in all-white families is rarely considered, some surveys have examined the socialisation of children from ethnic and/or racial minorities raised by white parents. Studying families with bi-racial, multi-racial or adopted children, these surveys question the capacity of white parents to adequately accomplish such a socialisation [START_REF] Andujo | Ethnic identity of transethnically adopted Hispanic adolescents[END_REF][START_REF] Crolley-Simic | Racial socialization practices of white mothers of international transracial adoptees[END_REF][START_REF] Smith | White on black: Can white parents teach black adoptive children how to understand and cope with racism[END_REF], with an explicitly normative perspective that posits that there exists an 'adequate' way of racially socialising children, which would thus allow the development of a 'healthy' and 'positive' racial identity among minority children [START_REF] Butler-Sweet | A healthy black identity': Transracial adoption, middle-class families, and racial socialization[END_REF][START_REF] Thompson | Socialization to race and its relationship to racial identification among African Americans[END_REF]. In US studies, the term socialisation is often used simply as a synonym for education, with little focus on the less strategic and more unconscious dimensions of socialisation as a system of internalisation, or even incorporation, of dispositions. Rather than simply transferring the concept of racial socialisation to the French context, I position my perspective at the crossroads of these two conceptions. Without discarding the French concept of socialisation as a durable, and generally implicit incorporation of ways of 'feeling, thinking and acting' [START_REF] Bourdieu | The logic of practice[END_REF], I believe that its meaning can be broadened to include a more explicit-even strategic-dimension that brings it closer to the US understanding of the term.

The study conducted here showed that parental socialisation practices take two different forms. In some families, socialisation involves developing the children's awareness of their minority status, based on the parents' perception and anticipation of racism. This approach, applied only by a minority of the parents interviewed, reflects a desire to develop the children's consciousness of racism, and to provide them with the necessary coping dispositions while encouraging them to take pride in their minority identity. A second, more frequent approach that I call 'learning colourblindness' can be observed among parents with a colourblind attitude to racism; distancing strategies are applied to exclude racism from the family sphere and daily life. This second form of socialisation is itself characterised in practice by two modes of action. The first is a universalist form of socialisation in which preparation for racism is diluted in the development of more general dis-positions for confronting the difficulties of life and in which racism is dedramatised and de-individualised. The second is an assimilationist type of socialisation whereby racial mixedness within the family is managed through both the children's national and racial assimilation. It should be noted that the typology of socialisation practices described in this chapter is a typology of practices and not a typology of parents themselves: indeed, the different practices described are not mutually exclusive. However, while some parents apply several different socialising practices, promoting a sense of pride often goes hand in hand with an explicit preparation for discrimination, in what I call 'learning minority status', just as universalist socialisation is often coupled with assimilation strategies, in what I call 'learning colourblindness', highlighting that socialising practices and representations of racism are interlinked. After presenting and characterizing the different modes of socialisation, I will examine the factors that may explain parents' socialising rationale.

Learning racial minority status

Learning minority status, in the racialised sense of the term, is one parental mode of socialisation. Parents anticipate the implications of their children's racial minority status in the host society and help them to develop coping mechanisms. The fact that only a minority of the parents interviewed (n=5) mentioned practices of this kind is likely related to the dominance of colourblindness in France, a point I will return to later.

In the interviews, this anticipation is first expressed through explicit acknowledgement of the racialised dimension of the children's adoption. Associated with a hierarchical perception of race relations in France, this awareness prompts the parents to anticipate the children's possible future exposure to racism, often with the aim of preparing and protecting them. For example, Béatrice Reynard 6 (age 46, training center manager, adopted daughter born in Côte d'Ivoire, adoption as spouse) feels duty-bound to help her daughter confront such realities, notably with respect to police discrimination, which she frequently encounters through her work. When anticipating potential exposure to racism, some parents take measures to prepare their children for the racist remarks, incidents or attacks they may one day have to confront. Note that in comparison with the mixed-race couples interviewed, the practices of adoptive couples take a more direct and less tacit form; for a parent from a racial minority can transmit his or her experience directly to the children in a way that is, by definition, impossible for all-white adoptive parents.

For Jehanne and Arnaud Asselin (age 53, landscape gardener; age 45, journalist, adoption as spouses), who adopted their son in Mali, it is important, for example, to let him know that racism exists, and to try and teach him to 'defend himself' and to 'give as good as he gets'. Catherine Fournier (age 54, civil servant, daughter adopted in Haiti, as a lone parent), for her part, understands the difficulty of deconstructing what she calls 'ordinary racism' with her teenage daughter, while being told by her that she 'can't understand' because she is not directly exposed to racism herself. Catherine also plans to warn her daughter about the police, and the fact that they are 'not always well-intentioned' towards young black adults. Likewise, Flora Seblon (age 47, teacher, son adopted in Haiti, as a 'false' lone parent), 7 is aware that she and her wife cannot 'prevent' their son from being exposed to racism, and intends to 'give him verbal weapons at least […] to defend him-self'. In this way, through their words and attitudes, these parents try to help their children develop the necessary coping dispositions. By invoking the possibility of exposure to racism, and seeking to raise their children's aware-ness of this issue, they create a framework of socialisation which, they hope, will enable their children to develop the resources they need to live as a racial minority in society.

Among the survey respondents, adoptive parents seeking to foster explicit racial pride were even more rare, most reporting that it was easier for them to develop their children's interest in their birth culture (continued cultural ties with the country of origin, dietary adaptations, travel, etc.). 8 Only three parents mentioned socialising practices aimed at encouraging a sense of belonging to a minority racial group. Corinne Crespel (age 50, teacher, three children adopted in Haiti, as spouse), for example, high-lighted the need to convey a positive image of black people to her three children. During the interview, she explicitly referred to the Négritude movement 9 when she talked about her efforts to instil racial pride. For Corinne, it is also important to give them role models of black success in France. During the interview she recounts that her five-year-old daughter had asked 'why are all the men at store entrances black?' Unwilling for her daughter 'to only notice or only identify with the school cleaning woman or the supermarket security guard' Corinne is deliberately seeking to develop her children's racial awareness: she teaches them the history of slavery as 'their' history, highlighting stories of revolt, shows them films on the subject and highlights black success stories via famous black politicians and writers. Catherine Fournier, who lives in an affluent and racially homogeneous suburb of Paris, also wants to give her daughter positive examples of successful black people, and regrets that most of the black people her daughter encounters are in menial jobs ('it's simple, they [the blacks] are road sweepers, refuse collectors, whatever'). Corinne and Catherine's approach is dual: alongside a desire to provide role models that are not exclusively white, they want to give their children examples of socioeconomic success that correspond to their own social status. Clearly, the socialisation processes identified here are also a reflection of social class; in this case-given the over-representation of higher-level occupations among adopters (see above)-the dominant classes.

It is also with the intent of broadening her daughter's range of role models that Catherine felt it was important to buy black dolls for her when she was small. The process of socialisation via a wide range of references also takes place through toys and play, as it enables children to incorporate ways of doing and to build a representation of the world they inhabit.

Colourblindness and distancing: universalist socialisation and assimilation

Quite distinct from learning the minority status, the dominant modes of socialisation are framed in a 'colourblind' approach characterised by a distancing from the questions of race and racism. The majority of adoptive parents I interviewed adhere to a colourblind perspective on society or an essentially moral and individualistic understanding of racism-that Bonilla-Silva (1997) qualifies as an 'idealist view'. Among this group, several parents reported not seeing, or no longer noticing their children's skin colour -a literal example of colourblindness. This minimisation of physical difference, part of the process of naturalising the parent-child relationship, is common among adoptive parents (see, for example, [START_REF] Bergquist | Caucasian parents and Korean adoptees: A survey of parents' perceptions[END_REF][START_REF] Crolley-Simic | Racial socialization practices of white mothers of international transracial adoptees[END_REF][START_REF] Deberry | Family racial socialization and ecological competence: Longitudinal assessments of African-American transracial adoptees[END_REF]. Moreover, the replacement of terms used to designate racial categories by chromatic words considered more appropriate (such as 'brown' and 'beige', for example), contributes to the development of a colourblind perspective within the family, and a deliberate distancing from racial questions and their most widely used categories. Such questions are consigned to the public sphere, outside of the home and family where they are seen as irrelevant [START_REF] Karis | I prefer to speak of culture': White mothers of multiracial children[END_REF]. By separating the public and private spheres in this way, the parents define a colourblind domestic space in which to raise and socialise their children.

These colourblind attitudes and the way they are embodied by the parents create a reference space which partially delimits the children's framework of socialisation. They underpin a 'universalist socialisation' approach widely shared by the parents I interviewed. Under this approach, racial socialisation is diluted in the parents' efforts to prepare the children for the difficulties of life in general, and socialisation is explicitly colourblind, avoiding any mention of race. Several parents, for example, confirmed that they took no 'specific' steps to prepare their children to belong to a racial minority in society. For Clémence and Guillaume Demailly (age 36, urban planner, and teacher, two sons adopted in Ethiopia, as spouses), the main priority is to foster the eldest son's self-confidence, without reference to his racial identity: 'generally speaking, they're things that will help him cope with human stupidity when he's older, but not especially on that level, if you see what I mean'. Georges and Christine Giraudon (ages 52 and 53, account manager and project manager, one daughter adopted in Côte d'Ivoire, as spouses) also believe that such preparation, if any, is purely 'indirect', via very general values of tolerance and acceptance of difference. This universalist approach to the racial question is reflected in the way the parents talk about discrimination to their children. Several respondents compare racism with other forms of playground bullying or abuse. For example, when I asked if she intended to warn her two children aged 10 and 11, born in Vietnam, that they may one day be victims of racism, Valérie Legouis (age 49, human resources manager seeking employment, lone parent) replied that she 'tries', while also saying that 'it's a bit like' when the children are labelled as 'fat' or 'ugly' at school. For [START_REF] Samuels | Being raised by white people': Navigating racial difference among adopted multiracial adults[END_REF], this comparison between racial discrimination and other childish insults signals an incomplete acknowledgement of the problem of racism. It also echoes the teaching of responding with contempt to racial insults, 'without getting angry' (Valérie Legouis), in much the same way as parents in the survey by Smith and colleagues who treated racist incidents as merely anecdotal [START_REF] Smith | White on black: Can white parents teach black adoptive children how to understand and cope with racism[END_REF]. Similarly, Tiphaine Peyrat (age 49, project manager, one daughter adopted in Kazakhstan, lone parent) explained in her interview that she had advised her daughter, unhappy at being constantly asked about her origins and labelled as 'Chinese' at school, to simply say that she was an 'earthling'.

Instances of universalist socialisation, marked by a minimization of race or mere silence on the question, take several forms and are apparently not specific to the French context. The modes of socialisation I observed are similar to those of 'mainstream socialisation' which encourages children to develop the skills needed to navigate within the dominant culture rather than focusing on their birth culture or their minority status [START_REF] Boykin | Black child socialization: A conceptual frame-work[END_REF]Hughes, Rodriguez et al., 2006, 757), or of 'egalitarian' socialisation which aims 'to rear racially neutral children who notice people's individual qualities rather than their racial group membership' (Hughes, Bachman et al., 2006, 599).

Learning colourblindness also fosters what I identify as the promotion of assimilation. This assimilation is expressed on two levels: at national level, in the discourse of parents who claim to raise their children 'as French citizens', but also at the racial level, when the aim is to raise children 'as whites'. Here, nationality becomes conflated with race, whiteness and Frenchness being seen as the same thing, and synonymous with normality.

When asked if they maintain links with the children's birth culture, some adoptive parents claimed that it would be artificial to do so, and that they want to raise their children as French, with no reference to a second culture. This was the viewpoint of Benoît Mathurin (age 55, lawyer, three children adopted in France and Colombia, as spouse), who has cut off all ties with the children's birth cultures, considering that such ties would hinder their integration. Valérie Legouis also believes that when 'you are in France', it is French culture that should be transmitted. For her, the transmission of French culture is vital, and she has worked hard to instil in her children a sense of pride in France and its cultural heritage. In some cases, this desire to foster the children's integration and their allegiance to French society is reflected in the choice of a French forename. For Jehanne and Arnaud Asselin, for example, who adopted their son Jules in Mali, it was important to replace his original forename, Ahmed, with a 'more neutral' name that would serve as a 'basis for integration'-where the very connotation of the name Jules disappears in the conflation between majority and neutrality.

On a different register, some parents believe that socialising their children with an exclusively French set of references provides them with the armour they need by removing the justification for any mention of their otherness. Michèle and Bertrand Vaysse, who describe their son, adopted in Mali, as a real 'Frenchy', believe that educating him in French culture will give him the 'weapons' to deal with racism, in contrast to an 'immigrant' child:

And in any case, Raphaël doesn't have immigrant status, it's not the same after all. […] He's French, and he'll feel like a real Frenchman, you know. […] It's not the same as turning up in France, […] having a truly different origin and a different culture … Raphaël, he'll be living in our culture […] and he'll have the weapons to deal with that, because he'll have the right to say: 'I don't give a damn'.

(Michèle and Bertrand Vaysse, age 51 and 49, managers in the audiovisual industry, one son adopted in Mali, as spouses)

These parents argue that through their adoption, the children become 'legitimate' French citizens, and hence more French than immigrants. 10

Under this reasoning, legitimacy of nationality is not compatible with radical difference, be it formulated in cultural terms or more directly in terms of physical appearance. This distinction drawn between adopted and immigrant children, that [START_REF] Marre | We do not have immigrant children at this school, we just have children adopted from abroad': Flexible understandings of children's 'origins[END_REF] and [START_REF] Dorow | Transnational adoption: A cultural economy of race, gender, and kinship[END_REF] also observed among adoptive parents in Spain and the United States, is at least partly a socioeconomic distinction, with the adoptive parents refusing to liken their children to the descendants of immigrants, who often migrate for economic reasons and live in precarious circumstances. It is also a dis-tinction in terms of cultural assimilation, seen as more complete for adoptees than for immigrants, as clearly implied in the words of Michèle and Bertrand Vaysse. For adoptive parents, becoming a full member of the family and of the nation thus often go hand in hand. Underplaying the children's birth culture and adopting a mode of socialisation designed to assimilate them into their country of adoption is also a means for the parents to affirm their position as the children's only parents, with the frontiers of parenthood coinciding with the frontiers of the nation [START_REF] Dorow | Transnational adoption: A cultural economy of race, gender, and kinship[END_REF].

Last, for some parents, the assimilation rationale shifts from French socialisation to white socialisation. This shift occurs via a racialisation of Frenchness and its associated 'culture', as illustrated by Arnaud Asselin, who states that his son Jules 'will be black with a white culture', and describes him as 'métis' (mixed race): in Arnaud's mind, while Jules is phenotypically black, he is 'culturally' white in his ways of being and acting, and in his cultural references. This is a direct evocation of the racial dimension of the family socialisation process which, for Arnaud Asselin, becomes a factor of racial mixedness.

Moreover, adoptive parents believe that their children, having being raised by white parents, will also assume a certain whiteness that will help protect them from discrimination. Daniel Gimenez (age 49, teacher, one daughter adopted in Côte d'Ivoire, as spouse) shares this point of view, arguing that adopted children with white parents 'don't see themselves as black', and that this is an 'advantage' for confronting racism: Under this rationale, the children adopted by white parents enjoy a degree of whiteness and hence some of its associated privileges, including protection from racism. The question of preparing for racism is diluted and expunged through this socialisation to whiteness. [START_REF] Howell | Kinning: The creation of life trajectories in transnational adoptive families[END_REF] describes similar processes among international adoptive parents in Norway. According to Wade (2009, 189), the kinning process as described by Howell, whereby 'families put much effort into […] assimilating these children and making them into true Norwegians, individuals capable of talking and behaving like Norwegians' produces an erasure of race in favour of culture. In light of the results presented here and the racial assimilation arguments put forward by respondents, the interpretations of Howell and Wade can, I believe, be taken even further, with a more consubstantial reading of race and culture; race may not be 'erased' in the kinning process but rather transformed, with cultural assimilation leading to racial assimilation (Brun, 2019a). By socialising children in a 'white culture', its ways of being and its social expectations, their very racial belonging is cast into doubt and its boundaries blurred.

Frameworks and modes of socialisation: The determinants of parenting practices

The parents' approach to socialisation is shaped by their ways of seeing the world and its social structures, and their mode of racial socialisation is closely linked to their overall conception of racism, race relations and racial inequality in France. Their strategy will differ, depending on whether they see racism as a structural characteristic of French society that their children will one day have to confront, or as a characteristic of individual interactions linked to personal attitudes [START_REF] Crolley-Simic | Racial socialization practices of white mothers of international transracial adoptees[END_REF][START_REF] White-Johnson | Parental racial socialization profiles: Association with demographic factors, racial discrimination, child-hood socialization, and racial identity[END_REF]. These perceptions and underlying values are conveyed all the more strongly in the parents' discourse and their routine remarks, which send implicit messages to their children and provide opportunities for socialisation [START_REF] Percheron | La socialisation politique[END_REF]. Note, however, that the parents' opinions on race in general and racism in particular are not necessarily based on a consistent ideology. Certain colourblind attitudes or arguments may very well alternate with colour-conscious ones.

An affinity is thus drawn between the way racism and inequalities are perceived by parents and their child-rearing preferences. Parents who down-play the scale of racism in France or who have an essentially individualistic conception of the problem, as a sum of prejudices, will more readily adopt a colourblind perspective and, in some cases, they will avoid placing emphasis on the culture of the children's birth country. Conversely, those who have a more systematic understanding of racism will be more inclined to help their children learn their racial minority status. These different approaches to the racial problem in France are not randomly distributed, however. First, the fact that only a small minority of adoptive parents apply the mode of socialisation that I have called learning minority status reflects the institutionalised dominance of the colourblind perspective in France, where any talk of race is associated with racist intent. The colour-conscious viewpoint of respondents who defy this rule is linked to professional experience of racism (Béatrice Reynard), a rather radical political standpoint (Catherine Fournier, Flora Seblon), or a socialised understanding of racial categories influenced by the family circle (Corinne Crespel's husband is American, for example).

While the study did not systematically explore the respondents' political sympathies, the colourblind mode of racial socialisation appears to correspond both to people on what could be labelled as the 'universalist left', characterised by liberal values as well as an emphasis on universalism and a cosmopolitan ethos (Cosquer, forthcoming) Last, approaches to socialisation depend more generally on the context in which the children are raised; place of residence and parental sociability play an important role. [START_REF] Bonilla-Silva | Racism without racists: Color-blind racism and the persistence of racial inequality in the United States[END_REF] emphasises the importance of segregation, and hence of class and race homogamy, in the production of ways of acting and thinking internalised by whites in the United States. In doing so, he points up the need to consider the contexts of socialisation and their effects, paying attention to the structure of sociability in particular. Indeed, as noted by Berger and Luckmann (1986, 154), 'the child does not internalise the world of his significant others as one of many possible worlds. He internalises it as the world, the only existent and only conceivable world, the world tout court'. This world, as a social reality, internalised by children as the only possible one, exists in a specific time and place, and is structured by the individuals that move within it; as such, the place of residence and the composition of the parents' contact circle are central components.

Respondents who live in affluent Parisian districts or suburban towns raise their children in neighborhoods with little socioeconomic or racial diversity, and this can therefore impact the socialisation context in which children grow up. Residential and educational exclusivity leads to homogamous sociability, ensuring that the children internalise racially situated practices and codes. For example, one mother living in a racially homogeneous neighbourhood recounted that before he went to school, her son, adopted in Haiti, believed that all parents were white, because his mother's circles were very homogeneous and the only other non-white children around him were also adopted by white parents.

However, the rationales of racial socialisation do not depend solely on parental characteristics or preferences. For example, the only parents who mentioned fostering racial pride or citing role models in the children's racial group were those who adopted children racialised as black. 11 The others, while mentioning pride, focused exclusively on national cultures. Halifax and Labasque point out that while 21.2 per cent of internationally adopted children show an interest in their birth culture, the percentage varies widely by country of origin: fewer than 10 per cent of children born in Europe are interested, versus almost 30 per cent of children born in Haiti or on the African continent (Halifax & Labasque, 2013, 99). Likewise, only parents who have adopted a black child reported in interview that they were explicitly preparing them for exposure to racism and discrimination. This difference of approach reveals how racial hierarchies in French society are perceived by the adoptive parents interviewed. Several parents who adopted in South America or Asia claimed that racism in France mainly-or even exclusivelytargets black people, implying that other minorities in France are much less-or not at all-concerned by the problem. This idea, shared by several respondents, gives rise to modes of socialisation that differ by the child's country of origin. Exploring the socialisation practices of white parents thus sheds light on their perception and understanding of racial hierarchies in France.

Conclusion

While the racial socialisation of transracial adopted children has been widely documented in the United States, the question has rarely been explored in France. Yet even in a largely colourblind context, the study of parents of internationally adopted children reveals that racialised socialisation practices do indeed take place in those families that are bringing together people of different national origins and different racial positions. These practices mainly take two forms. The first is based on learning minority status, with parents anticipating the risk of exposure to racism and discrimination and seeking to instil a sense of pride (national and, in some cases, racial) in their children. The second, based on the learning and transmission of colourblindness, is characterised by a universalist approach to racial questions, silence on race, and the promotion of an assimilationist discourse, again in terms of nation and race.

I have addressed elsewhere the consequences of these two different modes of socialisation on the children and the development of their racial identification [START_REF] Brun | Trouble dans la race. Construction et négociations des frontières raciales dans deux types de familles mixtes en France[END_REF]. The typology presented here sheds light on the diversity of parenting approaches, and shows that silence about race must be seen as an integral component of racial socialisation. Here I concur with Bartoli and colleagues (2016), who argue that colourblindness is learnt and that it is not a hypothetically natural state, or a form of innocence that would be disrupted by socialisation. For these authors, 'not seeing race, in a heavily racialised society, is a skill that has to be carefully taught and cultivated in order to be developed ' (2016, 133). As such, it is essential to understand that the majority population is no less socialising in terms of race than the minority population is assumed to be.

France being a country where race remains taboo, it necessarily influences the parental approach to racial socialisation. For the parents interviewed, the subject is often addressed in a much more indirect and euphemistic manner than is described in the American or British literature on the racial socialisation of adoptees or mixed-raced children, and is more similar to the situa-tion described in Sweden (Hübinette & Tigervall, 2009a;[START_REF] Hübinette | When racism becomes individualised: Experiences of racialisation among adult adoptees and adoptive parents of Sweden[END_REF]. Above all, the colourblind worldview in which they live and in which they have them-selves been socialised is often seen as the only acceptable approach, and the only possible mode of socialisation. In this regard, this work aims to further the empirical investigation of racial socialisation in a national context which, as yet, remains under-documented.

Notes

1 The term 'transracial' applied to adoptions, coined in the United States in the 1970s, refers to adoptions of non-white children by white parents [START_REF] Fanshel | Far from the reservation. The transracial adoption of American Indian children[END_REF][START_REF] Grow | Black children, white parents: A study of transracial adoption[END_REF].

2 For those residing outside of metropolitan France, interviews were conducted via Skype.

3 Data provided by the International Adoption Mission (Mission de l'Adoption Internationale; MAI), the French central authority which reports to the Ministry of Foreign and European Affairs; and by the National Child Protection Observatory (Observatoire national de la protection de l'enfance; ONED). In 2006, 85% of all adoptions in France were international. See https://www.data. gouv.fr/fr/datasets/adoptionsinternationales-pays-dorigine-zone-geographique-tra nche-dages-et-procedures/#_. 4 MAI data; see note #3.

5 The inverted commas emphasise the fact that parental 'choice' in the adoption procedure is severely limited by the scarcity of adoptable children, the multiple restrictions imposed by sending countries and the conditions imposed by the French authorities.

6 The names of all respondents are anonymised.

7 Flora Seblon adopted her son as a single parent in 2007, before same-sex marriage and adoption were legalised in France. The child was later adopted by her partner.

8 Around one-third of the parents interviewed make efforts to familiarise their children with their birth culture, often with a concern to avoid 'wiping out' the children's past. Their initiatives take different forms, however, ranging from a largely cosmetic presence of the birth country to a more consequential and lasting investment.

9 Négritude is a theoretical and literary movement, created in the 1930s by francophone intellectuals, aimed at celebrating and cultivating black consciousness and black pride.

10 Given that they are French but born abroad, adopted children can formally be considered as immigrants.

11 This does not imply that all respondents who had adopted a child of African origin use the racial framework. Some of them only want to instil national pride, i.e. the pride of belonging to a particular country, rather than that of belonging to a racial minority.

  She has grown a white heart in a black body, in fact. And that's really what will happen; that's what happens after a while, I mean she identifies with her parents, and you can see it, and I even think it's an advantage for her. Because it means that if she's confronted by racism, she can tell herself that she isn't totally … […] That's why I say 'white heart, black body', or black skin, but her culture and her world, it's actually a world of whites. […] Personally, I think that an adopted child […] doesn't actually see himself as black. He sees himself […] like his parents in fact. So […] I'm not convinced that the first thing you should say to yourself is that he'll suffer from racism. For example, white racism. Because for him, it's his world.

  , and to those with a more conservative outlook. For example, while Benoît Mathurin, (age 55, lawyer) believes that having foreign friends can be 'a very nice thing', he nonetheless wants his children adopted in Colombia to become 'integrated' into French society, because 'we are in France'. Likewise, in her interview, Valérie Legouis (age 49, seeking employment in human resources) highlighted her patriotism and her pride in French heritage, from Louis XIV to Napoleon, and the importance of inculcating these values in her children adopted in Vietnam.


Fatiha Saïs
email: fatiha.sais@lri.fr

Nathalie Pernelle
email: nathalie.pernelle@lri.fr

Marie-Christine Rousset
email: christine.rousset@imag.fr

L2R: a Logical method for Reference Reconciliation

The reference reconciliation problem consists in deciding whether different identifiers refer to the same data, i.e., correspond to the same world entity. The L2R system exploits the semantics of a rich data model, which extends RDFS by a fragment of OWL-DL and SWRL rules. In L2R, the semantics of the schema is translated into a set of logical rules of reconciliation, which are then used to infer correct decisions both of reconciliation and no reconciliation. In contrast with other approaches, the L2R method has a precision of 100% by construction. First experiments show promising results for recall, and most importantly significant increases when rules are added.

Introduction

The reference reconciliation problem is one of the main problems encountered when different sources have to be integrated. It consists in deciding whether different identifiers refer to the same data, i.e., correspond to the same world entity (e.g. the same person or the same publication).

Schema heterogeneity is a major cause of the mismatch of the data descriptions between sources. Extensive research work has been done recently (see [START_REF] Rahm | A survey of approaches to automatic schema matching[END_REF][START_REF] Shvaiko | A survey of schemabased matching approaches[END_REF][START_REF] Noy | Semantic integration: a survey on ontologybased approaches[END_REF]) for surveys) to reconcile schemas and ontologies through mappings.

However, the homogeneity or reconciliation of the schemas do not prevent variations between the data descriptions. For example, two descriptions of persons with the same attributes Last Name, First Name, Address can vary on the values of those attributes while referring to the same person, for instance, if the First Name is given entirely in one tuple, while it is abbreviated in the second tuple.

Data cleaning which aims at detecting duplicates in databases is faced with the same problem. Most of the existing works (e.g., [START_REF] Galhardas | Declarative data cleaning: Language, model and algorithms[END_REF][START_REF] Bilenko | Adaptive duplicate detection using learnable string similarity measures[END_REF][START_REF] Ananthakrishna | Eliminating fuzzy duplicates in data warehouses[END_REF]) do comparisons between strings for computing the similarity between the values of the same attribute, and then combine them for computing the similarity between tuples. In [START_REF] Omar | Swoosh: A generic approach to entity resolution[END_REF] the matching between data descriptions is generic but is still based on local comparisons. Some recent works [START_REF] Kalashnikov | Exploiting relationships for domain-independent data cleaning[END_REF][START_REF] Dong | Reference reconciliation in complex information spaces[END_REF][START_REF] Singa | Object identification with attribute-mediated dependences[END_REF][START_REF] Bhattacharya | Entity Resolution in Graphs[END_REF] follow a global approach that exploits the dependencies possibly existing between reference reconciliations. Those dependencies often result from the semantics of the domain of interest. For example, the reconciliation between two courses described by their titles and the name of the professors in charge of them can entail the reconciliation between two descriptions of persons. This requires that some knowledge of the domain be made explicit, like the fact that a professor is a person, that a course is identified by its title and has only one professor in charge of it. In [START_REF] Dong | Reference reconciliation in complex information spaces[END_REF], such knowledge is taken into account but must be encoded in the weights of the edges of the dependency graph.

In this paper, we study the problem of reference reconciliation in the case where the data are described relatively to a rich schema expressed in RDFS (w3c Rec. b) extended by some primitives of OWL-DL (w3c Rec. a) and SWRL (w3c Sub. ). OWL-DL and SWRL are used to state axioms that enrich the semantics of the classes and properties declared in RDFS. It is then possible to express that two classes are disjoint or that some properties (or their inverse) are functional. We describe the L2R system which implements a logical method for reference reconciliation, based on rules of reconciliation that are automatically generated from the axioms of the schema. Those rules are a declarative translation of the dependencies between reconciliations resulting from the semantics of the schema. They enable to infer both sure reconciliations and no reconciliations. We therefore obtain a method with a precision of 100% and we show that the recall is significantly increased if the schema is enriched by adding axioms. L2R is based on the most recent proposals for the Semantic Web (RDF, OWL-DL and SWRL). Therefore, it can be used for reconciling data in most of the applications based on the Semantic Web technologies.

The paper is organized as follows. In Section 2, we define the data model and the problem of reference reconciliation that we consider. In Section 3, we describe the logical method that we have implemented in L2R. In Section 4, we summarize the results that we have obtained for the experimental evaluation of L2R on two data sets. Conclusions and perspectives are presented in Section 5.

Problem definition

We first describe the data model, that we have called RDFS+ because it extends RDFS with some OWL-DL primitives and SWRL rules. RDFS+ can be viewed as a fragment of the relational model (restricted to unary or binary relations) enriched with typing constraints, inclusion and exclusion between relations and functional dependencies.

The RDFS+ data model

The schema: A RDFS schema consists of a set of classes (unary relations) organized in a taxonomy and a set of typed properties (binary relations). These properties can also be organized in a taxonomy of properties. Two kinds of properties are distinguished in RDFS: the so-called relations the domain and the range of which are classes and the so-called attributes the domain of which is a class and the range of which is a set of basic values (Integer, date, String,...). We will use the following notation : -R(C, D) indicates that the domain of the relation R is the class C and that its range is the class D, -A(C, Literal) indicates that the domain of the attribute A is the class C and that its range is a set of alpha-numeric values.

For example, in the RDFS schema presented in figure 1 and corresponding to a cultural application, we have as relations located(Museum, City), contains(CulturalPlace, Painting), paintedBy(Painting, Artist) and as attributes museumName(Museum, Literal), yearOf-Birth(Artist, Date). • Axioms of functionality of properties P F (P ) is used to declare that the property P (relation or attribute) is a functional property. For example, P F (located) and P F (museumN ame) express respectively that a museum is located in one and only one city and that a museum has only one name. These axioms can be generalized to a set {P 1 , . . . , P n } of relations or attributes to state a combined constraint of functionality that we will denote P F (P 1 , . . . , P n ).

• Axioms of inverse functionality of properties P F I(P )

is used to declare that the property P (relation or attribute) is an inverse functional property. For example, P F I(Contains) expresses that a painting cannot belong to several cultural places. These axioms can be generalized to a set {P 1 , . . . , P n } of relations or attributes to state a combined constraint of inverse functionality that we will denote P F I(P 1 , . . . , P n ). For example, P F I(paintingN ame, paintedBy) expresses that one artist and one painting name cannot be associated to several paintings (i.e. both are needed to identify a painting). • Axioms for discriminant properties DISC(A) is used to declare that the attribute A is discriminant if it is known that each possible value of this attribute has a single form (a number or a code). For instance, the attributes yearOf-Birth and countryName can be declared as discriminant.

It is important to note that the axioms of disjunction and of simple functionality (i.e., of the form P F (P ) or P F I(P )) can be expressed in OWL-DL while the axioms stating combined constraints of functionality (i.e., of the form P F (P 1 , . . . , P n ) or P F I(P 1 , . . . , P n )) and those stating discriminant properties (i.e. DISC(P)) require the expressive power of SWRL.

The data: A datum has a reference which has the form of a URI (e.g. http://www.louvre.fr, NS-S1/painting243), and a description which is a set of RDF facts involving its reference. An RDF fact can be: -either a class-fact C(i), where C is a class and i is a reference, -or a relation-fact R(i 1 , i 2 ), where R is a relation and i 1 and i 2 are references, -or an attribute-fact A(i, v), where A is an attribute, i a reference and v a basic value (integer, string, date, ...).

We consider that the descriptions of data coming from different sources conform to the same RDFS+ schema. In order to distinguish the data coming from different sources, we use the source identifier as the prefix of the reference of the data coming from that source. For example, figure 2 provides examples of data coming from two RDF data sources S1 and S2 which conform to a same RDFS+ schema describing the cultural application previously mentioned.

The axioms on the data sources:

We consider two kinds of axioms accounting for the Unique Name Assumption (UNA) and the Local Unique Name Assumption (denoted LUNA). The UNA states that two data of the same data source having distinct references refer to two different real world entities (and thus cannot be reconciled). Such an assumption is valid when a data source is clean.

The LUNA is weaker than the UNA, and states that all the references related to a same reference by a relation refer Source S1 :

CulturalPlace(S1 m1); MiddleAgeMuseum(S1 m3); Painting(S1 p1); Painting(S1 p2);Artist(S1 a1); museumName(S1 m1,"musee du LOUVRE"); museumName(S1 m2, "musee des arts premiers"); . . . to real world entities that are pairwise distinct. For example, from the facts authored(p, a 1 ), ..., authored(p, a n ) coming from the same data source, we can infer that the references a 1 , . . . , a n correspond to distinct authors of the paper referred to by p.

The reference reconciliation problem

Let S 1 and S 2 be two data sources which conform to the same RDFS+ schema. Let I 1 and I 2 be the two reference sets that correspond respectively to the data of S 1 and S 2 . Let Reconcile 1 be a binary predicate. Reconcile(X, Y) means that the two references denoted by X and Y refer to the same world entity.

The reference reconciliation problem between S 1 and S 2 consists in partitioning the set I 1 × I 2 of reference pairs into two subsets REC and NREC such that for each reference pair (i 1 , i 2 ) ∈ REC Reconcile(i 1 , i 2 ) and such that for each pair

(i 1 , i 2 ) ∈ N REC ¬Reconcile(i 1 , i 2 ).
A reconciliation method is complete if it provides a result (Reconcile(i 1 , i 2 ) or ¬Reconcile(i 1 , i 2 )) for each pair

(i 1 , i 2 ) ∈ I 1 × I 2 .
The precision of a reconciliation method is the ratio of correct reconciliations and no reconciliations among those found by the method. The recall of a reconciliation method is the ratio of correct reconciliations and no reconciliations found by the method among the whole expected set of correct reconciliations and no reconciliations.

The reconciliation method L2R described in the next section is not complete since it does not guarantee to infer reconciliations or no reconciliations for all the pairs of I 1 × I 2 . Its distinguishing features are that it is global and logicbased: every schema axiom is automatically translated into logical rules that express dependencies between reconciliations. The advantage of such a logical approach is that it guarantees a 100% precision. Therefore our experiments are focused on estimating its recall.

Reference Reconciliation method

The method is based on the inference of facts of reconciliation (Reconcile(i, j)) and of no reconciliation (¬Reconcile(i ′ , j ′ )) from a set of facts and a set of rules 1 Reconcile and not Reconcile can also be expressed in OWL by using sameAs and differentFrom predicates.

which transpose the semantics of the data sources and of the schema into logical dependencies between reference reconciliations. Facts of synonymy (SynV als(v 1 , v 2 )) and of no synonymy (¬SynV als(u 1 , u 2 )) between basic values (strings, dates) are also inferred. The binary predicate Syn-Vals is analogous to the predicate Reconcile but applied on basic values.

We first describe the generation of the reconciliation rules, then the generation of the facts and finally the reasoning which is performed on the set of rules and facts to infer reconciliation decisions.

Generation of the set of reconciliation rules

They are automatically generated from the axioms that are declared on the data sources and on their common schema.

Translation of the axioms on the data sources We introduce the unary predicates src1 and src2 in order to label each reference according to its original source (srci(X) means that the reference X is coming from the source Si).

The UNA assumption, if it is stated on the sources S1 and S2, is translated automatically by the following four rules :

R1 : src1(X)∧src1(Y )∧(X = Y ) ⇒ ¬Reconcile(X, Y ) R2 : src2(X)∧src2(Y )∧(X = Y ) ⇒ ¬Reconcile(X, Y ) R3 : src1(X) ∧ src1(Z) ∧ src2(Y ) ∧ Reconcile(X, Y ) ⇒ ¬Reconcile(Z, Y ) R4 : src1(X) ∧ src2(Y ) ∧ src2(Z) ∧ Reconcile(X, Y ) ⇒ ¬Reconcile(X, Z)
The first two rules express the fact that two references coming from the same source cannot be reconciled. The last ones mean that one reference coming from a source S2 (resp. S1) can be reconciled with at most one reference coming from a source S1(resp. S2).

For each relation R, the LUNA assumption is translated automatically by the following rules denoted respectively R11(R) and R12(R):

R(Z, X) ∧ R(Z, Y ) ∧ (X = Y ) ⇒ ¬Reconcile(X, Y ) R(X, Z) ∧ R(Y, Z) ∧ (X = Y ) ⇒ ¬Reconcile(X, Y )
Translation of the schema axioms For each pair of classes C and D involved in a DISJOIN T (C, D) statement declared in the schema, or such that their disjunction is inferred by inheritance, the following rule is generated:

R5(C, D) : C(X) ∧ D(Y ) ⇒ ¬Reconcile(X, Y )
For each relation R declared as functional by the axiom P F (R), the following rule R6.1(R) is generated :

Reconcile(X, Y )∧R(X, Z)∧R(Y, W ) ⇒ Reconcile(Z, W )
For each attribute A declared as functional by the axiom P F (A), the following rule R6.2(A) is generated :

Reconcile(X, Y )∧A(X, Z)∧A(Y, W ) ⇒ SynV als(Z, W )
The binary predicate SynVals replaces the predicate Reconcile, applied on basic values. For each relation R declared as inverse functional by the axiom P F I(R), the following rule R7.1(R) is generated : Reconcile(X, Y )∧R(Z, X)∧R(W, Y ) ⇒ Reconcile(Z, W ) For each attribute A declared as inverse functional by the axiom P F I(A), the following rule R7.2(A) is generated : SynV als(X, Y )∧A(Z, X)∧A(W, Y ) ⇒ Reconcile(Z, W ) Likewise, analogous rules are generated for translating axioms P F (P 1 , . . . , P n ) of combined functionality and P F I(P 1 , . . . , P n ) of combined inverse functionality. For instance, P F (P 1 , . . . , P n ), where all the P i 's are relations, is translated into the rule:

R7.1(P 1 , . . . , P n ) :

i∈[1..n] [P i (Z, X i ) ∧ P i (W, Y i )∧ Reconcile(X i , Y i )] ⇒ Reconcile(Z, W )
If some P i 's are attributes, the corresponding Reconcile(X i , Y i ) must be replaced by SynV als(X i , Y i ). Similarly, P F I(P 1 , . . . , P n ), where all the P i 's are relations, is translated into the rule:

R7.2(P 1 , . . . , P n ) :

i∈[1..n] [P i (X i , Z) ∧ P i (Y i , W )∧ Reconcile(X i , Y i )] ⇒ Reconcile(Z, W
) Finally, for each attribute A declared as discriminant by the axiom DISC(A) the following rule R8(A) is generated : ¬SynV als(X, Y )∧A(Z, X)∧A(W, Y ) ⇒ ¬Reconcile(Z, W ) Transitivity rule : this rule is generated only if the UNA axiom is not stated on the data sources.

R9 : Reconcile(X, Y )∧Reconcile(Y, Z) ⇒ Reconcile(X, Z)

Generation of the set of facts

The set of RDF facts corresponding to the description of the data in the two sources S 1 and S 2 is augmented with the generation of:

• new class-facts, relation-facts and attribute-facts obtained by inheritance, i.e., by exploiting the subsumption statements between classes and properties that are stated into the RDFS schema: for example if the fact Contemporary-Museum(i) is present in one of the sources, the class-facts M useum(i) and CulturalP lace(i) are added to the description of that source; • facts of the form src1(i) and src2(j) for each reference i ∈ I 1 and each reference j ∈ I 2 , • synonymy facts of the form SynV als(v 1 , v 2 ) for each pair (v 1 , v 2 ) of basic values that are identical (up to some punctuation or case variations): for instance, the fact Syn-Vals("La Joconde", "la joconde") is added because these two values differ only by two capital letters, • non synonymy facts of the form ¬SynV als(v 1 , v 2 ) for each pair (v 1 , v 2 ) of distinct basic values associated with so-called discriminant attributes. For instance, ¬SynV als( ′′ 2004 ′′ , ′′ 2001 ′′ ), ¬SynV als( ′′ F RAN CE ′′ , ′′ P ORT U GAL ′′ ) are added if yearOfBirth and countryName are declared discriminant.

Reasoning

The reasoning applies to the union R ∪ F of the set of rules and the set of facts generated as explained before. It must infer all the facts of reconciliation, no reconciliation, synonymy, no synonymy that are logically entailed by R ∪ S, based on the standard first-order logical semantics.

It is important to notice that the reconciliation rules though having negative conclusions still correspond to Horn clauses, for which there exists reasoning methods that are complete for the inference of prime implicates, like for instance SLD resolution [START_REF] Chang | Symbolic Logic and Mechanical Theorem Proving[END_REF].

The reasoning algorithm that we have implemented in L2R is a three-steps application of SLD resolution [START_REF] Chang | Symbolic Logic and Mechanical Theorem Proving[END_REF] to the Horn clausal form of the rules and to the facts that are unit ground clauses.

Propositionalization step: all the possible resolutions of the ground facts in F with the Horn clauses corresponding to the rules in R\{R9} are computed. It consists in propagating the ground facts into the rules except the transitivity rule R9. The result is a set P of fully instantiated Horn clauses in which the only remaining literals are of the form Reconcile(i, j), ¬Reconcile(i ′ , j ′ ), SynV als(u, v), or ¬SynV als(u ′ , v ′ ), and each atom Reconcile(i, j) or SynV als(u, v) is seen as a propositional variable.

Propositional inference step: the propositional SLD resolution is applied to the set P of the propositional Horn clauses resulting from the first step.

Transitivity step: This step applies only if the rule R9 is in R, i.e., only if the UNA axiom is not stated on the data sources. The first-order SLD resolution is applied to the ground facts obtained at the previous step and to the clausal form of R9.

It is easy to show that for any literal l of the form Reconcile(i, j), ¬Reconcile(i ′ , j ′ ), SynV als(u, v), or ¬SynV als(u ′ , v ′ ): R ∪ F |= l iff P |= l Since the SLD resolution on Horn clauses is complete, and since R ∪ F and P are equivalent for the derivation of ground literals, this algorithm guarantees to derive all the facts of the form Reconcile(i, j), ¬Reconcile(i ′ , j ′ ), SynV als(u, v), or ¬SynV als(u ′ , v ′ ) that can be logically entailed from the set of rules and the set of facts.

Other reasoners, like for instance description logic reasoners, could be used for the derivation of reconciliation facts. However, description logics are not specially appropriate to express some of the reconciliation rules that we consider, which require explicit variable bindings. In addition, up to our knowledge, the existing description logic reasoners are not guaranteed to be complete for the computation of prime implicates.

Experiments

The L2R rule-based method has been implemented and tested on data sets related to two different domains: the tourism domain and the scientific publications.

Presentation of the data sets(HOTELS and CORA)

The first real data set HOTELS, provided by an industrial partner, corresponds to a set of seven data sources which leads to a pairwise data integration problem of 21 pairs of data sources. These data sources contain 28,934 references to hotels located in Europe. The UNA is stated for each source.

The hotel descriptions in the different sources are very heterogeneous. First, the properties that are instantiated are different from one to another. Second, the basic values are multilingual, contain abbreviations, and so on.

The second data set CORA2 (used by [START_REF] Dong | Reference reconciliation in complex information spaces[END_REF]) is a collection of 1295 citations of 112 different research papers in computer science. In this data set, the objective of the reference reconciliation is the cleaning of a given data source (i.e. duplicates elimination). The reference reconciliation problem applies then to I × I where I is the set of references of the data source S to be cleaned. For this data set, the UNA is not stated and the RDF facts describe references which belong to three different classes (Article, Conference, Person).

The RDFS+ schemas : HOTELS conforms to a RDFS schema of tourism domain, which is provided by the industrial partner. We have added a set of disjunction axioms (e.g. DISJOINT(Hotel, Service)), a set of functional property axioms (e.g. PF(establishmentName)) and a set of inverse functional property axioms (e.g. PFI(establishmentName, associatedAddress)).

For the CORA data set, we have designed a simple RDFS schema on the scientific publication domain, which we have enriched with disjunction axioms (e.g. DIS-JOINT(Article, Conference)), a set of functional property axioms (e.g. PF(published), PF(confName)) and a set of inverse functional property axioms (e.g. PFI(title, year,type), PFI(confName, confYear)).

Results

Since the set of reconciliations and the set of no reconciliations are obtained by a logical rule-based algorithm the precision is of 100% by construction. Then, the measure that it is meaningful to evaluate in our experiments is the recall. For the CORA data set, the expected results for reference reconciliation are provided. Therefore, the recall can be easily obtained by computing the ratio of the reconciliations and no reconciliations obtained by L2R among those that are provided.

For the HOTELS data set, we have manually detected the correct reconciliations and no reconciliations between the references of two data sources containing respectively 404 and 1392 references to hotels. For the other pairs of data sources, we provide quantitative results, i.e. the number of reconciliations and no reconciliations.

In the following, we summarize the results obtained on the HOTELS data set and then those obtained on the CORA data set. We emphasize the impact on the recall of increasing the expressiveness of the schema by adding axioms. In the figure 3, we show the recall that we have obtained on the two sources on which we have manually detected the reconciliation and no reconcilation pairs. We distinguish the recall computed only on the set of reconciled references (REC) and only on not reconciled references (NREC).

As it is shown in the column named "RDFS+ (HOTELS)" of the figure 3, we have obtained a recall of 8.3%. If we only consider the reconciliations subset (REC) the recall is 54%. The REC subset corresponds to the reconciliations inferred by exploiting the inverse functional axiom PFI(establishmentName, associatedAddress). It is important to emphasize that those reconciliations are inferred in spite of the irregularities in the data descriptions: not valued addresses and a lot of variability in the values, in particular in the addresses : "parc des fees" vs. "parc des fees, (nearby Royan)". In addition, in one of the data sources, several languages are used for the basic values: "Chatatoa" versus "Chahatoenia" in Basque language.

If we only consider the no reconciliations subset (NREC) the recall is 8.2%. Actually, the only rules that are likely to infer no reconciliations are those translating the UNA assumption. Now, if we enrich the schema just by declaring pairwise disjoint specializations of the Hotel class (by distinguishing hotels by their countries), we obtain an impressive increasing of the recall on NREC, from 8.2% to 75.9%, as it is shown in the "RDFS+ (HOTELS) & DA" column.

Results on CORA data set

We focus on the results obtained for the Article and Conference classes, which contain respectively 1295 references and 1292 references.

As presented in the column named "RDFS+ (CORA)" of the figure 3, the recall obtained on the CORA data set is 50.7%. This can be refined in a recall of 52.7% computed on the REC subset and a recall of 50.6% computed on NREC subset. The set of inferred reconciliations (REC subset) for references to articles is obtained by exploiting the axiom PFI(Title, Year) of combined inverse functionality on the properties title and year. For the conferences, 35.8% of the reconciliations are obtained by exploiting the axiom PFI(confName, confYear) of combined inverse functionality on the attributes conf N ame and conf Y ear, and 64.1% are obtained by propagating the reconciliations of references to articles, using the axiom PF(published) of functionality of the relation published.

The set of inferred no reconciliations (NREC subset) are obtained by exploiting the axiom of disjunction between the Article and Conference classes. For this data set, the RDFS+ schema can be easily enriched by the declaration that the property confYear is discriminant. When this discriminant property is exploited, the recall on the REC subset remains unchanged (52.7%) but the recall on NREC subset grows to 94.9%, as it is shown in the "RDFS+ (CORA) & DP" column. This significant improvement is due to chaining of different rules of reconciliations: the no reconciliations on references to conferences for which the values of the confYear are different entail in turn no reconciliations of the associated articles by exploiting the axiom PF(published).

This recall is comparable to (while a little bit lower than) the recall on the same data set obtained by supervised methods like e.g., [START_REF] Dong | Reference reconciliation in complex information spaces[END_REF]. The point is that L2R is not supervised and guarantees a 100% precision.

For the references of the class Person, since there is no axiom concerning the properties associated to that class, only the LUNA assumption can infer no reconciliations. For 3521 Person references, 4298 no reconciliations have been inferred by using the rules corresponding to LUNA application to the author relation.

Conclusion

L2R is a logical method for the reference reconciliation problem. One of the advantages of such an approach is that it provides reconciliations and no reconciliations that are sure. This distinguishes L2R from other existing works. This is an important point since, as it has been emphasized in [START_REF] Winkler | Overview of record linkage and current research directions[END_REF], unsupervised approaches which deal with the reference reconciliation problem have a lot of difficulties to estimate in advance the precision of their system when it is applied to a new set of data. The experiments show promising results for recall, and most importantly its significant increasing when rules are added. This shows the interest and the power of the generic and flexible approach of L2R since it is quite easy to add rules to express constraints on the domain of interest.

Inferring no reconciliation can be related to the so-called blocking methods introduced in [START_REF] Newcombe | Record linkage: making maximum use of the discriminating power of identifying information[END_REF] and used in recent approaches such as [START_REF] Baxter | A comparison of fast blocking methods for record linkage[END_REF] for reducing the reconcilation space. Note also that our definition of LUNA is used by [START_REF] Dong | Reference reconciliation in complex information spaces[END_REF] to eliminate inconsistent reconciliations after the reconciliation step. In our approach, the different kinds of knowledge used for reducing the reconciliation space are handled in a declarative way.

The main perspective that we plan is to complement the L2R logical method (which does not guarantee to provide a result for every pair of references) with a numerical method. This numerical step will apply to pairs of references for which the logical step has not produced any result of reconciliation or of no reconciliation. It will compute scores of similarities between references based on the combination of similarities between related sets of values and references. This step will take into account the L2R results by assigning a maximum similarity score to the inferred reconciliations and synonyms. We plan to exploit the results of the logical step to learn the weighting coefficients involved in the combination of the different similarity scores.

Figure 1 :

 1 Figure 1: Example of a RDFS schema

  m1); Museum(S2 m2);Painting(S2 p1); Painting(S2 p2); Artist(S2 a1); located(S2 m1,S2 c1); museumName(S2 m1,"Le LOUVRE"); contains(S2 m1,S2 p2); . . .

Figure 2 :

 2 Figure 2: Example of RDF data

another version of CORA is provided by McCallum, (http://www.cs.umass.edu/ mccallum/data/cora-refs.tar.gz)