Arabization and Islamization in the Making of the Sudanese "Postcolonial" State (1946-1964) Cultural Representations, Political Strategies and School Practices

The ethnic and linguistic diversity of Sudan and South Sudan is an established fact, although the contours of "legitimate" ethnolinguistic categorizations have been disputed in the region since the early 20th century by administrators, missionaries, local leaders, intellectuals, politicians, social activists, anthropologists and linguists. Censuses and statistics have played a pivotal role in the construction of taxonomies of "Arab groups" subdivided along tribal lines, e.g. Jaʿālī, Juhayna, Shaygiyya, and so-called "non-Arab groups" defined by language, e.g. Nubian, Beja, Fur, Masalit, Zaghawa, Dinka, Nuer, Shilluk, Bari, Lotuko, Zande (Miller 2018). Beyond their historical plasticity and social relativeness, such categories and broader ones like "Arab" or "African" are politically sensitive. Indeed, they have contributed to ethnicize the wars plaguing Sudan since the middle of the 20th century (Johnson 2016). Recent developments have again brought to the fore conflicting social identities and unequal access to political, economic and symbolic resources. These issues largely underpin Sudan's scission into two states in 2011, the civil war that broke out in South Sudan in 2013 and the ongoing conflicts and tensions in Darfur, South Kordofan, Blue Nile and Red Sea states. They are also crucial in the revolutionary process that has unfolded in Sudan since December 2018, toppling the "salvation" (ingādh) regime in April 2019 (see Deshayes in this issue). Dynamics of power and ethnocultural belonging are not new in the region; they have shaped the construction of Sudan as a modern territory at least since the 19th century, be it through exogenous regimes (Ottoman-Egyptian rule 1820-1885; Anglo-Egyptian Condominium 1899-1955) or endogenous polities (the Mahdist state 1885-1898; postcolonial Sudan 1956-2011). Yet the 2010s have stirred a sense of historical acceleration (Koselleck 2011) in the Sudans, which is not unrelated to the various Arab uprisings of 2011 (Tunisia, Egypt, Libya, Yemen) and 2019 (Algeria, Sudan, Lebanon, Iraq). The overthrow of President Omar al-Bashir's thirty-year long authoritarian rule, the setting up of a mixed civilian-military council and the appointment of a transitional government under the economist Abdalla Hamdok have opened up opportunities for redefining political ideologies in Sudan. For certain Sudanese actors, this process entails rethinking the meaning of

categories such as "Arab," "Islamic," "African" and "Sudanese," as well as reaffirming or contesting connections between them [START_REF] Jāmiʿ | Qadāyā al-hawiyya wa-l-qawmiyyāt fī al-Sūdān[END_REF]). 1 This article offers historical depth to this debate by examining how such (auto)identifications were formulated and used in another "accelerating time," namely the decolonization era. The transformation of Sudan from an Anglo-Egyptian Condominium into a postcolonial state was all but a linear, predetermined or complete process. Rather, the period stretching from the 1946 British decision to lead Sudan towards self-government through the 1956 proclamation of independence and until the 1964 popular uprising that ended Ibrahim Abboud's military regime was full of political hopes, doubts and disillusions (Seri-Hersch 2018: 45-63). An equally important aim of this article is to contribute to the study of concrete articulations between Arabization (taʿrīb in Arabic) and Islamization (aslama) in historically situated Sudanese contexts. Indeed, the two phenomena have been very often closely-but rather uncritically-associated in a wide array of academic texts referring either to the long-term historical process that has made Sudan into a largely Arabic-speaking and Muslim society in the modern era [START_REF] Macmichael | A History of the Arabs in the Sudan[END_REF][START_REF] Macmichael | A History of the Arabs in the Sudan[END_REF]; [START_REF] Hasan | The Arabs and the Sudan from the Seventh to the Early Sixteenth Century[END_REF]Abd al-Rahim 1970;[START_REF] Grandin | Politiques d'enseignement religieux et culture arabo-islamique au Soudan[END_REF] or to a specific set of Sudanese state policies meant to Arabize and Islamize Southern populations after 1956 [START_REF] Nyombe | Survival or Extinction: The Fate of the Local Languages of the Southern Sudan[END_REF][START_REF] Poggo | General Ibrahim Abboud's Military Administration in the Sudan, 1958-1964: Implementation of the Programs of Islamization and Arabization in the Southern Sudan[END_REF]Sharkey 2012).

The taken-for-granted conflation between language, ethnicity and religion not only relies on long-lived "Orientalist" readings of Sudanese history [START_REF] Spaulding | The Orientalist Paradigm in the Historiography of the Late Colonial Sudan[END_REF]; it has also influenced political and media discourses on Sudan, while strengthening the ideological tools of al-Bashir's "Islamist" regime from 1989 until 2019 (Abdelhay et al. 2011: 479-480;[START_REF] Salomon | For Love of the Prophet: An Ethnography of Sudan's Islamic State[END_REF].

Over the last twenty years, several sociolinguists, anthropologists and historians have engaged in empirically-based studies that unpack the enmeshment of linguistic practices, religious affiliations, state policies, economic processes and ethnic claims in colonial and postcolonial Sudan. These works significantly contribute to our understanding of Sudanese societies and politics because they denaturalize the relations between Arabic, Arabness and Islamness, demonstrating how social practices vary according to specific contexts and issues.

For instance, it has been shown that Juba Arabic has been historically and is still used by non-Muslim Southern Sudanese people in South Sudan and Khartoum. This pidgincreole served not only as a lingua franca in certain multilingual areas and towns from the late 19th century onwards; it became the mother tongue of part of Juba's population from the 1940s and the marker of a Southern, non-Arab supratribal identity from the 1970s [START_REF]FAL)[END_REF][START_REF] Leonardi | South Sudanese Arabic and the Negotiation of the Local State, c. 1840-2011[END_REF]Miller 2014;[START_REF] Manfredi | Juba Arabic (Árabi Júba): A 'Less Indigenous' Language of South Sudan[END_REF]. Other studies have highlighted the actual role of European and North American Christian missionaries in promoting Arabic varieties in Southern Sudan, although these same missions officially fought against the spread of Arabic-seen as an Islamization factor-by cultivating English and "indigenous" Southern Sudanese languages such as Dinka, Nuer and Shilluk [START_REF] Miller | Southern Sudanese Arabic and the Churches[END_REF]Sharkey 2011). After independence in 1956, Arabization policies carried out by the successive Khartoum governments were unsuccessful in fostering a broadly shared Arab identity in Sudanese society; on the contrary, they triggered the development of "African" (implying culturally pluralistic) identities among populations in Southern Sudan, the Nuba Mountains and Darfur, even if Arabic as a spoken language progressed in these areas [START_REF] Sharkey | Arab Identity and Ideology in the Sudan: The Politics of Language, Ethnicity, and Race[END_REF]. Ethnographic work has also shown that identification with Islam and the adoption of "Arab" practices among Lafofa people in the Nuba Mountains in the 1980s were part of economic strategies rather than strictly religious processes of conversion [START_REF] Manger | Religion, Identities, and Politics: Defining Muslim Discourses in the Nuba Mountains of the Sudan[END_REF].

The following study contributes to this scholarship in two ways: first, by reappraising the chronology of Arabization and Islamization policies in Southern Sudan, locating their inception in late colonial times rather than in the post-independence era. Second, it examines to what extent, how and why the Arabic language and the Islamic religion were enmeshed in cultural discourses, political strategies and school practices at the critical time of British imperial retreat and Northern Sudanese empowerment (1946)(1947)(1948)(1949)(1950)(1951)(1952)(1953)(1954)(1955)(1956)(1957)(1958)(1959)(1960)(1961)(1962)(1963)(1964). In this regard, the attainment of independence in 1956 was not a clear-cut rupture, but rather one stage in the larger process of political and cultural "Northernization" at work from the 1940s. The analysis draws on Sudanese and British intellectual/scholarly writings, political speeches, administrative proceedings, educational plans and reports, schoolbooks for elementary teachers and Southern Sudanese press articles, coupled with a wealth of academic studies.

It will bring to light a set of actors, dynamics and social experience that resulted in a strong conflation of language, ethnicity and religion in the making of "postcolonial" Sudan.

The Late Colonial Drive Towards an Arab and Islamic Sudan

During most of the colonial era , the British-dominated government of Sudan ruled separately the Northern and Southern parts of the country. This well-studied "Southern Policy" (Abd al-Rahim 1966;[START_REF] Sanderson | Education, Religion and Politics in Southern Sudan: 1899-1964[END_REF][START_REF] Collins R | Shadows in the Grass: Britain in the Southern Sudan, 1918-1956[END_REF][START_REF] Mayo | The British Southern Policy in Sudan: An Inquiry intro the Closed District Ordinances (1914-1946)[END_REF] was rooted in British attempts to prevent the spread of the North's predominantly Arabic and Islamic culture into the South, "protect" the Southerners from Northern slave traders and concentrate the government's limited financial resources in the North, which was perceived as more "civilized" than the South. The separation policy was formalized through three ordinances in 1922 and 1925 that considerably restricted the movement of goods and people between Northern and Southern Sudan. It also affected how the British authorities in Khartoum and Juba dealt with language and religion. Whereas Arabic was selected as the main administrative language in Northern Sudan, English was preferred for the South. This dichotomy was in part reproduced in the distinct educational systems that were established in the colonial era (Seri-Hersch 2017): Arabic and English were used as teaching languages in the Northern government school system, while local languages (Dinka, Nuer, Shilluk, Bari, Lotuko, Zande) and English dominated the Southern missionary school system.

The 1928 Rejaf Conference was a landmark in the history of linguistic policies in Southern Sudan, insofar as it selected "indigenous" languages (labelled as such from that time) as media of instruction rather than Arabic or English [START_REF] Abdelhay | The Colonial Linguistics of Governance in Sudan: The Rejaf Language Conference, 1928[END_REF]).2 Christian missionaries, who included British Anglicans, American Presbyterians and Italian Catholics, were allowed to develop their activities only in the South, being barred from proselytizing among the predominantly Muslim Northern Sudanese [START_REF] Sanderson | Education, Religion and Politics in Southern Sudan: 1899-1964[END_REF].

The British policy of separate administration was abandoned in 1946, at a time of growing Anglo-Egyptian rivalries over the control of Sudan. By "reuniting" the Northern and Southern Sudan-two regions that had been formally integrated into the "Anglo-Egyptian Sudan" in 1899 but had hitherto never existed as one administrative unit-the British sought to coopt Northern Sudanese elites and weaken the Sudanese partisans of the "unity of the Nile valley" project, namely an Egyptian-Sudanese political union under Egyptian leadership. The British strategy to win over Northern Sudanese opinion against Britain's Egyptian ideological rival was twofold. First, British authorities in Khartoum and London officially defined Sudanese self-determination as their goal, stressing the ultimate aim of Sudanese independence. Second, they proceeded with the administrative and educational unification of Northern and Southern Sudan, answering an old Northern claim that had been voiced increasingly loudly since the early 1940s. The new institutions set up in 1948 reflected these policy changes: the Executive Council (EC) and the Legislative Assembly (LA) were meant to represent the whole country,3 although their prerogatives were seriously limited by the British Governor-General, who appointed the EC and kept the right to veto the laws designed by the LA. In the same year, a Ministry of Education was created with ʿAbd al-Raḥmān ʿAlī Ṭāhā, a Northern Sudanese educator and Umma party-affiliated politician, as its first head. It was under his tenure as Minister of Education (1948Education ( -1953) ) that the "unification" of school curricula and educational systems in Sudan was launched (Seri-Hersch 2018: 56-61, 93-94).

In practice, unification did not entail the blending of existing Northern and Southern educational structures and methods. Rather, it meant the Northernization of Southern teaching via the introduction of the Arabic language and the adoption of Northern curricula and textbooks in Southern schools. 4 This is not surprising given the nature of the Sudanization process-namely the gradual replacement of British with Sudanese officials-, which was accelerated from 1946 onwards: the overwhelming majority of posts were taken up by Northern Sudanese men, as exemplified in 1954, when only 6 out of 800 Sudanized posts went to Southern Sudanese (Collins 2008: 65), although the Southerners represented one third of Sudan's total population of ca. 10 million people at the time. 5 Hence, the Arabic-speaking, Muslim elites that came to dominate state institutions sought to shape Sudan as an Arab and Islamic nation-state almost a decade before the attainment of political independence in 1956.

Arabizing and Islamizing the South

Several concrete measures were implemented to carry out the Arabization of Southern Sudanese people in the late colonial era. In August 1949, the EC passed a resolution defining Arabic as the vehicular language of Sudan (Sanderson & Sanderson 1981: 298). A few months later, ʿAlī Ṭāhā announced before the LA that Arabic as a main subject matter would be introduced in all schools in the South (Beshir 1968: 68). By 1954, Arabic was used as a teaching language in the 22 government elementary schools operating in the South (which were still fewer than the 62 mission schools) and as a subject matter in all types of elementary, intermediate and secondary schools (Sanderson & Sanderson 1981: 304, 310).

The entrance exam to Rumbek secondary school included an Arabic exam as from 1953 (Sanderson & Sanderson 1981: 310;Sandell 1982: 70).

The quick pace of Arabization owed much to the efforts of Sirr al-Khatm al-Khalīfa, the Province Education Officer of Equatoria Province in Juba (1950)(1951)(1952)(1953)(1954)(1955), who was later appointed Chief Inspector (1956) and Assistant Director of Education in Southern Sudan (1957)(1958)(1959)(1960), before serving as Prime Minister of Sudan (1964)(1965) in the aftermath of the October Revolution that overthrew Abboud's military regime. In spite of some difficulties caused by the historical legacy of slavery, which tainted Northern-Southern relationships with arrogance and distrust,6 Arabization policies made significant progress in the first half of the 1950s. This was also due to the fact that the missionary societies all accepted to cooperate with the Ministry of Education in introducing Arabic into the schools under their supervision (Sandell 1982: 67).7 Indeed, the Ministry turned to a surprising variety of actors in order to implement Arabization in Southern Sudan. In 1952, some American Christian missionaries, who had previous experience in translating the Bible into Sudanese Arabic, were asked to prepare two simple textbooks to help teach Southern pupils colloquial Arabic. Northern Sudanese educators may have then envisaged written colloquial Arabic as a step towards learning standard Arabic, although this view was not undisputed among missionaries and Southern Sudanese students (Sharkey 2011: 42). Following another line of action, the Ministry of Education hired an Egyptian linguist from Cairo University, Khalīl Muḥammad ʿAsākir, to transcribe the main Southern Sudanese languages in the Arabic script. This operation was thought as a first step towards the spread of Arabic in the South. Readers in Dinka, Bari, Zande, Lotuko and Moro written in the Roman script were transliterated into Arabic (Abdelhay et al. 2015: 267). Yet ʿAsākir was confronted with two major obstacles, namely the difficulty to adapt the Arabic alphabet to sounds that did not exist in Arabic-a difficulty that had also arisen when transcribing Southern vernaculars in the Latin script-and the lack of teachers able to teach vernacular languages in that alphabet (al-Sayyid 1990: 55-56;Sharkey 2008: 34).

Arabization policies largely benefited from the resources of the state-sponsored Publications Bureau in Juba (founded in 1948), whose Arabic Section was set up in 1950 under the supervision of ʿAwaḍ Sātī, a teacher who was at the time the Chief Editor of the Publications Bureau in Khartoum and would later be appointed Director of Education (1954Education ( -1956) ) before becoming the first Sudanese ambassador in the United Kingdom in June 1956.

The Arabic Section in Juba published Arabic readers, textbooks in Arabic (some of which were translated works), a weekly magazine called Sambala after a village near Juba, as well as an illustrated Arabic encyclopedia (Cookson et al. 1964: 196;Sanderson & Sanderson 1981: 336;ʿAlī Ṭāhā 2004: 233). Among the 24 textbooks published by the Juba Bureau during the 1956-1957 school year, 19 were in Arabic. Four were in English and one in Moro. Their printed quantity ranged from 50 to 2,550 copies, reaching much higher numbers in the case of two Arabic books printed by the Khartoum Bureau (15,900 and 17,000 copies), which helped the Juba Bureau when most of the team temporarily relocated in the capital (August 1955-September 1956) because of the eruption of the civil war in the South. 8The Northernization of Southern education was taken a step further with the nationalization of missionary and private schools in 1957, one year after independence.

Northern Sudanese civil servants replaced missionaries as heads of elementary schools, introducing state curricula as early as 1958 in the Upper Nile province, later in more distant Equatoria (Seri-Hersch 2017). Amidst the first Sudanese civil war (1955)(1956)(1957)(1958)(1959)(1960)(1961)(1962)(1963)(1964)(1965)(1966)(1967)(1968)(1969)(1970)(1971)(1972), two educational models coexisted-or rather strove to survive-in Southern Sudan until the mid-1970s. Some schools, notably those in Anyanya-controlled areas, continued using vernacular languages and English as teaching media while teaching Arabic as a subject. Other schools conformed to governmental directives, offering a totally Arabized curriculum and relegating English to a mere subject. The state model prevailed over time: from 1966 onwards, no government school used Southern "indigenous" languages as media of instruction anymore.

Hence, Khartoum's Northern Sudanese elites succeeded in imposing Arabic as a teaching language in numerous schools, especially in Upper Nile and Bahr al-Ghazal provinces (Sandell 1982: 79-80).9

Islamization measures were undertaken as soon as the Southern Policy was abrogated.

After travel restrictions between the two regions were lifted in 1947, many Southerners sought to work in the North; they were often forced to convert to Islam to find a job (ʿAlī Ṭāhā 2004: 243). The decade preceding independence witnessed a significant flow of Northern merchants into the South, where Quranic schools and mosques were quickly opened (Nyombe 1997: 107). Despite a 1952 law limiting religious education to pupils that had been officially registered as Christians or Muslims, it was found that some government schools in the South automatically taught the Islamic religion to "animist" pupils (Sanderson & Sanderson 1981: 327;Aḥmad 1983: 23) Returning from a trip to Southern Sudan, Northern journalists wrote newspaper pieces containing similar accusations against Christian missionaries. In January 1953, ʿAlī Ṭāhā decided to inspect all schoolbooks and materials "used, seen or read" by pupils in missionary schools in order to check their contents (Sanderson & Sanderson 1981: 328). 10The Islamization of Sudanese society and state was also pursued by political and legal means. The Sudanese declaration of independence (January 1st, 1956) mentioned Arabic as the sole official language and Islam as the state religion (Sharkey 2008: 34-35). In September 1956, the Umma-People's Democratic Party coalition government appointed a committee to draft a new Constitution, which was to replace the "secular" temporary Constitution derived from the 1953 Self-Government Statute (Bin Matt 2006: 6). Two months later, the Chief Judge (qāḍī) of Sudan, Ḥasan Muddathir, addressed a memorandum to the Constituent Assembly, in which he recommended the adoption of an Islamic Constitution:

In an Islamic country like the Sudan, the social organization of which has been built upon Arab customs and Islamic ways and of which the majority are Moslems, it is essential that the general principles of the Constitution of such a country should be derived from the principles of Islam (Deng 1995: 518, n. 4).

At the same time, the Umma party and the Khatmiyya order issued a joint statement on the necessity of making Sudan into an Islamic parliamentary republic, with the sharīʿa as its exclusive source of legislation. Yet the political vision of an Islamic state, which would be further elaborated by Sudanese "Islamists" under the leadership of Hasan al-Turabi from the 1960s up to the 1990s (Berridge 2017), did not go beyond rhetoric at this stage: the constitutional process was brutally interrupted by the military coup of General Ibrahim Abboud in November 1958 (Fluehr-Lobban 1990: 617). 11 Bringing important nuances to the existing literature [START_REF] Nyombe | Survival or Extinction: The Fate of the Local Languages of the Southern Sudan[END_REF][START_REF] Poggo | General Ibrahim Abboud's Military Administration in the Sudan, 1958-1964: Implementation of the Programs of Islamization and Arabization in the Southern Sudan[END_REF]Sharkey 2012), the above development demonstrates that Arabization and Islamization policies began to be implemented as early as one decade before the Abboud era (1958)(1959)(1960)(1961)(1962)(1963)(1964), when Sudan was still under British rule and amid many uncertainties about its political future.

Indeed, the unification of the North and the South in 1947 had not meant the end of the ideological struggle between Sudanese independentists and unionists, supported by their respective British and Egyptian allies. The 1952 revolution by the Free Officers in Egypt brought to power a regime that for the first time recognized the Sudanese right to selfdetermination, opening the way to a new Anglo-Egyptian agreement (1953) on Sudanese selfgovernment and the grant of self-determination after a three-year transitional period. Yet, until 1955, no one knew whether Sudan would become an independent state or a mere province within a broader Egyptian-Sudanese polity; perhaps ironically, the pro-unionist al-Azharī government eventually opted for Sudanese full independence in March 1955. 12 In the following sections, we explore how Arabization and Islamization were specifically articulated through discourses and practices at that time of British disengagement and Northern Sudanese takeover.

Cultural Representations: The Convergence of Northern Sudanese and

Orientalist Discourses

Various social actors living in Sudan in the 1940s and 1950s shared a similar vision of the Arabic language and the Islamic religion as two close-knit elements. The connection was strong to the point that it entailed a seemingly mechanical or immediate association between the processes of Arabization and Islamization in political speeches and intellectual writings. A few examples will be developed to show that Northern Sudanese and Orientalist (mainly British) discourses often converged in this regard. One year after its creation in 1938, the Graduates Congress, which had been inspired by the Indian National Congress and served as an intellectual and political forum for educated Sudanese (Niblock 1987: 187), addressed a 11 The first Sudanese "permanent" Constitution was promulgated one year after the Addis Ababa Agreement (1973) and remained in force until the popular uprising that overthrew President Jaafar Nimeiry (1985). 12 For a fuller discussion, see ABD AL-RAHIM (1969: 221-223) and HANES (1995: 166-167).

"Note on Education" to the (British) Sudan Government. In its general educational recommendations, the Congress wrote the following:

In numerous aspects of our life we have much in common with the Arab countries of Islamic Orient [sic] which is due to our akin descent. We therefore consider that education in this country should take an Islamic Oriental character and not a pagan African one, or in other words that the Arabic Language and Religious Instructions should receive the greatest possible care in all stages of education (Beshir 1969: 237).

The almost ontological connection between Arabic and Islam was even more blatantly stated by Muḥammad Aḥmad Maḥjūb, who was an engineer, a lawyer and a nationalist activist before joining the Umma party in 1953. In a book entitled Al-ḥaraka al-fikriyya fī al-Sūdān: ilā ayna yajibu an tattajiha? ("The Intellectual Movement in Sudan: In What Direction Does it Have to Go?"), published in 1941, he wrote:

In every place where Islam spread, Arabic literature and Arabic culture inevitably spread too. So did the Book of God the Bountiful, the Sunna of God's Messenger and the Noble Tradition, all these in the Arabic language. […] Sudan's fate was that the Arabic language spread in its quarters first to propagate Islam among its people, second because Arab blood is dominant among its inhabitants.

[…] The influence of the Islamic religion and the Arab culture in this country is most visible in the works of men of letters from the previous generation (Maḥjūb 1941: 15-16).

In Maḥjūb's outlook, there was a bidirectional interaction between Islamization and Arabization: one dynamic had historically fed the other and vice-versa, until the two were inextricably linked in the modern era. 13 Such an enmeshment was also present in the conference that ʿAwaḍ Sātī, then the Sudanese ambassador in London, gave to the Royal Empire Society on the topic of education in Sudan. 14 Interestingly, the conflation of Arabness and Islamness was also common in the writings of British administrators, missionaries and academics who had lived in Sudan in the Condominium era. It was thus shared beyond the colonial divide. On the "orientalist" side [START_REF] Spaulding | The Orientalist Paradigm in the Historiography of the Late Colonial Sudan[END_REF], the foundations of such a discourse were laid by the British administrator Harold A. MacMichael, who served in the Sudan Political Service (1905-1934, as Civil Secretary 1925-1934) before obtaining high positions elsewhere in the British Empire: he was appointed Governor of Tanganyika (1934Tanganyika ( -1938)), High Commissioner in Palestine (1938Palestine ( -1944)), and Special Representative of the British Government in Malaya (1945). 15 First published in 1922, his influential book A History of the Arabs in the Sudan (MacMichael 1967) put at the center of the stage the medieval Islamic invasions that had 13 On Maḥjūb's pan-Arabist linguistic ideology in the 1950s and 1960s, see ABDELHAY ET AL. (2011: 474-477). 14 SATTI A., 1957, "Education in the Sudan: A Talk Given by His Excellency Sayed Awad Satti, Sudanese Ambassador in London, to the Jersey Branch of the Royal Empire Society on Friday, 11 th January, 1957," Durham University Library, Sudan Archive, SAD 658/4/20-33, UK. 15 Durham University Library, n.d., "Harold Alfred MacMichael," Durham University Library Special Collections Catalogue, <http://reed.dur.ac.uk/xtf/view?docId=ark/32150_s1vd66vz949.xml>. brought to Sudan a myriad of "Arab tribes." MacMichael offered a racial reading of (predominantly Northern) Sudanese history based on tribal genealogies and, to a lesser degree, linguistic features. One of the enduring legacies of his writings was the assumption that two idealized racial types, Arab and non-Arab, had interacted over the centuries to produce modern Sudanese society. But the Arabs' adherence to Islam gave the latter "moral ascendancy over the more backward Sudanese" (MacMichael 1934, quoted in Spaulding & Kapteijns 1991: 143).

As he headed the Church Missionary Society in Sudan in the 1940s, John S. Trimingham wrote a book that echoed MacMichael's racial interpretation of Sudanese history. However, the protestant missionary elaborated more fully on the connection between Arabization and Islamization: according to him, the two processes had not only gone hand in hand from medieval times until the 20th century; they totally merged in the cultural changes that were ongoing in the White Nile regions and the Nuba Mountains: "The official tendency to regard these as two processes is misleading. It is a cultural process and every pagan area that becomes permanently arabicized becomes permanently islamized" (Trimingham 1949: 245 n. 1). Yet Trimingham simultaneously noticed a wide array of different social configurations in the Nuba Mountains. Whereas certain groups such as Nuba populations in North Kordofan had been completely Arabized without being Islamized, others were perceived as "semi-Islamized" without being Arabized. Such was the case of people living in the hills around the towns of Dilling, Kadugli, Talodi, Dalami and Rashad (ibid.: 245-246). These conclusions resonated with the findings of the Galicia-born British anthropologist Siegfried Nadel, who had been approached by the British authorities to conduct fieldwork in the Nuba Mountains in 1938[START_REF] Maḥjūb | Al-ḥaraka al-fikriyya fī al-Sūdān: ilā ayna yajibu an tattajiha?[END_REF][START_REF] Nadel | The Nuba: An Anthropological Study of the Hill Tribes in Kordofan[END_REF].

Dissociating Arabness and Islamness as a Political Strategy

In spite of these dominant cultural representations, Arabness and Islamness were sometimes overtly dissociated by Northern Sudanese, Egyptian and British public figures. Disconnecting the Arabic language from Islam usually served political strategies or educational agendas.

For instance, at the conference that brought together 6 British officials, 17 Southern personalities and 5 Northern politicians in Juba (12-13 June 1947) to discuss Sudanese unification, the judge-and later deputy-Muḥammad Ṣāliḥ al-Shingeitī defended the Arabization of Southern education on practical and economic grounds:

[He] felt that the available teachers should be equally distributed between North and South, and even more generously to the South to help them catch up. […] [He] thought that [a single education policy] meant firstly that the standards of equivalent schools should be roughly equal, and secondly that a boy leaving a Southern Intermediate School should be able to go straight to a Northern Secondary School. 16 Two years and a half later, the Minister of Education ʿAlī Ṭāhā developed similar arguments to try and convince the LA 13 Southern deputies and British officials posted in Southern Sudan (most of whom were reluctant to unification with the North) to adhere to Arabization policies. After a six-week tour in the South, during which he had visited government and missionary schools, met Southern deputies and tribal chiefs, and spoken with British and Sudanese officials, ʿAlī Ṭāhā gave a speech at the LA in November 1949.

He insisted on the necessity of promoting one national language understood by all the Sudanese, stressing that only Arabic could fulfill this function. He presented the Arabization policy as an opportunity offered to all young Sudanese, boys and girls, to learn "the general/public language of the country" (lughat al-bilād al-ʿāmma). Knowing how to speak, read and write in Arabic provided crucial access to the job market in both the public and the private sectors (Beshir 1968: 68;ʿAlī Ṭāhā 2004: 223, 227). Defining the mastering of Arabic primarily as a professional skill, ʿAlī Ṭāhā also attempted to reassure his interlocutors about the fate of Southern local languages. He expressed the Ministry's commitment to pursue the teaching of vernacular languages in the lower school grades provided that they would be written in the Arabic script (al-Sayyid 1990: 55). 17 This laid the ground for hiring the Egyptian linguist ʿAsākir a few years afterwards.

As the Arabization of Southern education was well under way, an international commission mandated by the Sudanese government in November 1954 to enquire on secondary education provided the Ministry's policy with additional expert legitimacy. 1947.aspx>: 24. 17 The great importance attributed to the script, both in this case (Southern languages in the Arabic script) and at the Rejaf Language Conference in 1928 (which authorized the use of Arabic in Southern Sudan only in the Roman script), testifies to the highly ideological nature of alphabetical choices, which often prevailed over practical considerations.

Education, University of Ain Shams, Egypt), W. Abbott and L. C. Wilcher (Principal, University College of Khartoum). 18 After meeting in Sudan in January and February 1955, the commission prepared a 150-page report, in which its members strongly recommended the use of Arabic as a teaching language in all Sudanese schools and at all school levels. There was no reference to Islam or Arabic culture. Rather, a series of didactic and practical arguments were put forward to support Arabization in the South. A first general claim was that pupils should learn in their own language, rather than in English. The commission noted that a lingua franca had developed "long ago" in the South, to the effect that a "sort of corrupt Arabic" 19 was already in use there. 20 It also stressed that Arabic-speaking teachers from the North would be more skilled to teach Arabic to Southern pupils than Italian missionaries teaching them English (a common practice in Comboni schools). Moreover, various textbooks and teaching materials in Arabic already existed, which was not the case for Southern vernaculars. The Indian, British and Egyptian educators, none of whom knew any Southern language (Sanderson & Sanderson 1981: 337;Collins 1983: 248), discarded them by affirming that "the vocabularies of these languages are reported to be very limited, so much so that most of them do not have more than about 300 words". 21 Finally, they emphasized the need of the Southerners to communicate with their Northern compatriots and get jobs in a country where Arabic was the national official language, 22 implicitly repeating ʿAlī Ṭāhā's main argument.

Until the early 1950s, very few Southern Sudanese openly associated Arabization with an

Islamizing project. Southern leaders expressing themselves in the political arena seemed to view the Arabization of Southern education rather favourably, even if some voiced some concern. At the Juba Conference in 1947, Buth Diu, a local government official who would later cofound the Southern Party in 1951-1952, called for the quick introduction of Arabic into Southern schools so that the Southerners could "catch up" with the North. The pastor Andrea Apaya did not oppose the introduction of Arabic but expressed doubts about the ability of elementary boys to assimilate English and Arabic, two "difficult" languages.

The only Southern participant that raised the religious issue was Chief Lolik Lado, although he did not specifically mention Islam; finding that Catholics and Protestants "did not readily co-operate," he feared that the introduction of Arabic would add "a new complication". 23Debates at the LA in 1949-1950 reflect more divided Southern positions on Arabization.

The deputy Stanislaus Abdalla Paysama, who had cofounded the Southern Sudan Welfare Committee in 1946 and would later work with Buth Diu to establish the Southern Party [START_REF] Kuyok | South Sudan: The Notable Firsts[END_REF], supported the learning of Arabic by Southern people, stressing the necessary collaboration between the Ministry of Education and Christian missions to find suitable teachers. Siricio Iro, who had served as an administrator (sub-mamur) in several Southern districts in the second half of the 1940s (ibid.), voiced concern about the professional future of Southern officials who did not master the Arabic language. Buth Diu's opinion had become ambivalent compared to his position back in 1947. On the one hand, he stressed the historical role of Arabic as a lingua franca in the South and the interest of the Southerners in mastering the dominant language of Sudanese politics and economy. On the other hand, he mentioned the fears of some of his colleagues about the possible vanishing of local languages and an upcoming confrontation with Muslim proselytizing teachers sent from Northern Sudan (ʿAlī Ṭāhā 2004: 228). 24 Hence, the Southern deputies did not formulate a collective opposition to the Arabization of Southern education (Collins 1983: 437), even if some began to link it with Islamization.

School Practices at the Time of Educational Northernization

As Sudan was moving from an Anglo-Egyptian Condominium towards an independent state, there was an interesting discrepancy between the "profession-oriented" discourse of Northern Sudanese and foreign educators, who tended to dissociate the Arabic language from Islam, and the actual contents of teaching materials and school curricula. The examples discussed below pertain to boys' elementary education: this level affected the overwhelming majority among the small proportion of Sudanese children and youth receiving any formal education between 1946 and 1964. Despite the rapid expansion of the state school system from 1948 onwards (Seri-Hersch 2017), in 1961, the 335,089 elementary pupils represented only 24,4 % of all Sudanese children of elementary school age. Still, this school population constituted 80,5 % of the Sudanese population enrolled in any kind of schooling from kindergarten to higher education. Boys were 2,5 as numerous as girls in elementary education. 25 Among the 200 schoolbooks produced by Sudan's Institute of Education in Bakht er Ruda between 1939and 1955(Seri-Hersch 2018: 102-103), history and geography books for elementary teachers and pupils (7-10 years old) combined the use of the Arabic language with an Islamic perspective on the world. The different actors of the educational process (textbook authors, teachers and pupils) were invariably presumed to be Muslim in the text of the three Bakr was to show third-grade pupils that "the death of the Prophet (God bless him) was a woeful tragedy meant to test the people's faith in Islam"; most of them had been successful "thanks to God" (Haywood & Ṣāliḥ 1950: 45). In relation to the Crusades, the same textbook referred to the Muslim pilgrimage (ḥajj) as a shared practice between the orator (the teacher) and his audience (the pupils):

The cause of the war [between Muslims and Christians] is that the land that is holy for Christians, to which they go on pilgrimage in the same way as we make our pilgrimage to Mecca, was conquered and ruled by Muslims (ibid.: 96).

It is well attested that elementary teachers working in the government school system were Sudanese-rather than British, Egyptian or Syrian nationals-throughout the colonial era (Seri-Hersch 2018: 126). But it is equally clear that after the educational unification between the North and the South, not all of them were Muslims, nor native Arabic speakers, even if Muslim teachers largely predominated in the elementary sector. 26 Third-grade geography teaching also targeted an Arabic-speaking and Muslim audience of Sudanese boys. The course had first been devised in 1940-1941, before the educational unification of the country. It consisted of nine imaginary visits to families living in various parts of Sudan. The Northern Sudanese pupils were taken on a long journey that started in Khartoum. Only one visit occurred in Southern Sudan, to a Zande family in Yambio 25 Ministry of Education, Sudan, 1962, Educational Statistics: Academic Year 1961/1962 (Khartoum: Publications Bureau): 10. 26 In 1955-1956, there were 458 elementary schools in Northern Sudan and only 44 in the South (Ministry of Education, Sudan, 1956, "Annual Report: from July 1955 to June 1956," Durham University Library, UK: 9). In the same year, the first population census of Sudan recorded that 39 % of the Sudanese spoke Arabic as their mother tongue and that an additional 12 % were also able to speak it, determining a total of 51 % Arabicspeaking Sudanese (AGUDA 1973: 177 n. 1). (Equatoria). Differences between the pupils' culture, presumed to be Arab and Islamic, and the Zande culture, were emphasized. The young Zande boy Mongu Zamberi and his relatives spoke an unknown language, which the teacher offered to "translate" to his pupils. 27 They bore few clothes and engaged in strange funerary practices. The geography text reiterated the non-Muslim identity of Mongu's family to explain why "they" liked to bury their relatives near the house and made offerings to their ancestors' spirits. 28 After the abandonment of the Southern policy, this course, which was edited in Arabic as a book as early as 1941, was extended to all Sudanese elementary schools. Published in 1957, a revised version replaced the initial cultural distance with a frontal depreciation of Zande culture. The teacher was supposed to tell his pupils:

Obviously, you cannot understand anything of what the Zande talk about, but they can communicate with you in a faulty Arabic (lugha ʿarabiyya rakīka). We hope that they will soon improve so that they are able to speak with you in correct Arabic (ʿarabiyya salīma)" (Wizārat al-Tarbiya wa-l-Taʿlīm 1969: 119).

The idea that non-Arabic speaking Sudanese people should learn Arabic, and not the other way around, underlay the set of Arabization policies implemented from 1949 onwards. This program of cultural homogenization, which appeared to be widely shared among riverine Northern Sudanese elites (Sanderson & Sanderson 1981: 293, 297;Beasley 1992: 388), 29 also included religion. In the revised geography schoolbook, which was reprinted in 1961 and 1969, a predictive sentence was added on the expected disappearance of Zande funeral rituals "thanks to the diffusion of education and the spread of the Christian and Muslim religions" (Wizārat al-Tarbiya wa-l-Taʿlīm 1969: 123). 30 The growing importance of the Islamic religion as a subject matter in the elementary curriculum also reflects the state's Islamization policies. In 1951, "Koran and Religion" was the third most studied subject after "Arabic" and "Arithmetic" (Table 1). 29 One notable exception was ʿAbd al-Khāliq Maḥjūb, the Secretary of the Sudanese Communist Party (SCP) from 1949 until 1971, who advocated the free development of all Sudanese languages and cultures, condemning the imposition of Arabic on minorities (ʿALĪ ṬĀHĀ 2004: 226-227). Regarding the SCP's flexible attitude towards Islam and Christianity, see ISMAEL (2012: 19, 22-23). 30 The contribution of Christian missions to "civilizing" efforts in Southern Sudan was recognized despite widespread Northern Sudanese hostility towards missionaries in the 1950s and 1960s. (Atem 1964: 8). As recounted by M. A. Atem, Arabization served as a means to achieve Islamization, which was the government's ultimate aim. This logic seems indeed to have guided much of Abboud's policies in Southern Sudan [START_REF] Poggo | General Ibrahim Abboud's Military Administration in the Sudan, 1958-1964: Implementation of the Programs of Islamization and Arabization in the Southern Sudan[END_REF]).

Yet the opposite perception also existed among the Southern Sudanese. The diffusion of Muslim rituals was sometimes considered as a deliberate tool to impose "Arab" culture. Atem himself mentioned the cultural influence expected from sons of Northern Arab traders in Southern schools. By wearing a "jalabia" and an "imam," by praying to "Allah" or reciting Quranic verses, these children were supposed to set "a typical example" to "African"

[Southern] children (Atem 1964: 7). Another writer insisted on the instrumental nature of Islamization as serving a large-scale social engineering project geared towards Arabness:

The policy of successive Arab Governments since self-government towards the South was that of assimilation of the Africans in the Southern Sudan, into the Arab group. This policy is popularly known as 'one country, one language and one religion' […] If at all, Christianity and Missionaries, is now an issue in the North-South conflict, that is so, because of the Arab Government policy, which uses Islamic religion, as a means of assimilating the four million Africans" (Anonymous 1964: 24, 26). This article has contributed to unpack the historical process through which Arabness and Islamness came to be strongly conflated and politicized in contemporary Sudan. While being rooted in a more distant past tainted by slavery relations [START_REF] Idris | Conflict and Politics of Identity in Sudan[END_REF], such dynamics owe much to late colonial politics of British imperialism in the Nile Valley and Northern Sudanese empowerment. They persisted well after independence in 1956, fuelling the North-South civil war (1955-1972; 1983-2005) and serving as a matrix for the "Islamist" policies of al-Bashir's regime after 1989. The increasingly close association between the Arabic language, a putative Arab ethnicity and the Islamic religion was constructed through intellectual discourses and school practices in the 1940s and 1950s, although it was sometimes denied or nuanced by politicians and education professionals. The everyday experience of Southern Sudanese students, workers, and officials both in the South and in Khartoum [START_REF] Willis | The Southern Problem: Representing Sudan's Southern Province to c. 1970[END_REF][START_REF] Hayer | Education, Migration and Nationalism: Mapping the School Days of the First Generation of Southern Sudanese Nationalist Leaders, c. 1948-1972[END_REF]) led them to view Arabness and Islamness as inextricably connected and associated with a politically dominant, aggressive North. Thus, cultural homogenization as it was promoted by state agents from 1946 until 1964 was alternately perceived as a legitimate policy of national unification or as a form of Arab-Islamic imperialism that merely succeeded British Christian colonialism (King 1975: 312-313;Deng 1995: 93;O'Fahey 1996: 262). In this sense, for many politically, economically and culturally marginalized Sudanese groups and regions-including majority Muslim areas in the North [START_REF] Idris | Conflict and Politics of Identity in Sudan[END_REF][START_REF] El Tom | Darfur People: Too Black for the Arab-Islamic Project of Sudan, Part Two[END_REF][START_REF] De | The Politics of Resources, Resistance and Peripheries in Sudan[END_REF])-, post-1956 Sudan was not a "postcolonial" state, but rather a structural heir to the colonial state's bifurcated power [START_REF] Mamdani | Citizen and Subject: Contemporary Africa and the Legacy of Late Colonialism[END_REF] Mots-clés : Soudan, arabisation, citoyenneté, décolonisation, enseignement, État, islamisation, langue, politique, religion

  . At the same time, a virulent anti-missionary campaign was voiced by Northern Sudanese politicians and the Arabic-speaking press in Khartoum. In a speech at the LA in March 1950, Muḥammad Aḥmad Maḥjūb (Umma) asserted that Christian missionaries spread a hostile vision of Islam and stirred feelings of hate between Northerners and Southerners, working against Sudanese unification. He enjoined the Minister of Education to stop cooperating with them in the South (ʿAlī Ṭāhā 2004: 242-243).

  The commission was chaired by Khwaja Ghulam Saiyidain, Secretary at the Indian Ministry of Education. Its members included L. E. Charlesworth (Headmistress of Sutton High School for Girls in Britain), Muḥammad Farīd Abū Ḥadīd (Advisor to the Egyptian Ministry of Education in Cairo), Charles R. Morris (Vice-Chancellor, University of Leeds, Britain), ʿAbd al ʿAzīz al-Sayyid Ibrāhīm (Director-General of Egyptian Primary Education and Professor of 16 "Proceedings of the Juba Conference on the Political Development of the Southern Sudan. June 1947," Gurtong: Bringing South Sudanese Together, 28 February 2006, <http://www.gurtong.net/ECM/Editorial/tabid/124/ctl/ArticleView/mid/519/articleId/2205/Juba-Conference-

  history handbooks jointly produced by British and Northern Sudanese educators between 1948 and 1950, no matter if they dealt with a "universal" history of human inventions and techniques (Shuʿbat al-Tārīkh bi-Bakht al-Ruḍā 1970), stories from various Islamic and non-Islamic lands in medieval and modern times (Haywood & Ṣāliḥ 1950), or Sudanese history (Haywood & Ṣāliḥ 1958). For instance, the stated goal of a lesson on the Muslim caliph Abu

  . Whereas the independence of South Sudan in 2011 reoriented Southern politics towards internal Dinka-Nuer ethnicized strife, the 2019 toppling of al-Bashir in Sudan might well invite new answers to an old problem: what should be the cultural definition of the Sudanese nation (if any), and how is it linked to questions about the nature of the Sudanese political regime, the meaning of citizenship and the distribution of educational, political and economic resources across the country? Institut de recherches et d'études sur les mondes arabes et musulmans (IREMAM), CNRS/Aix-Marseille Université. BIBLIOGRAPHY ABD AL-RAHIM M., 1966, "The Development of British Policy in the Southern Sudan, 1899-1947," Middle Eastern Studies 2 (3): 227-250. -1969, Imperialism and Nationalism in the Sudan: A Study in Constitutional and Political Development, 1899-1956 (Oxford: Clarendon Press). -1970, "Arabism, Africanism and Self-Identification in the Sudan," Journal of Modern African Studies 8 (2): 233-249. ABDELHAY A., MAKONI B., MAKONI S. & MUGADDAM A. R., 2011, "The Sociolinguistics of Nationalism in the Sudan: The Politicisation of Arabic and the Arabicisation of Politics," Current Issues in Language Planning 12: 457-501. ABDELHAY A., ABU MANGA AL-A. & MILLER C., 2015, "Language Policy and Planning in Sudan: From Local Vernaculars to National Languages," in B. CASCIARRI, M. ASSAL & F. IRETON (eds.), Multidimensional Change in Sudan (1989-2011): Reshaping Livelihoods, Conflicts, and Identities (Oxford: Berghahn): 263-280. WIZĀRAT AL-TARBIYA WA-L-TAʿLĪM, 1969 [1941], Subul kisb al-ʿaysh fī al-Sūdān: mabādī jughrāfiyat al-Sūdān li-l-madāris al-awwaliyya (Khartoum: Maktab al-Nashr). ABSTRACT Scholars have depicted the Arabization and Islamization of Sudan either as two parallel, centuries-long processes or as a set of interrelated state policies in the postcolonial era. This article contributes new chronological and empirical insights into the growing conflation of Arabic, Arabness and Islam in twentieth-century Sudan. First, it locates state efforts at Arabizing and Islamizing the South one decade before independence (1956) within the context of British imperial retreat and Northern Sudanese empowerment. Second, it examines how language and religion were increasingly enmeshed in cultural representations and school practices, even if the two were strategically distinguished in political discourses. The article assesses Southern Sudanese experience of forceful Arabization and Islamization, suggesting that cultural definitions of the nation and the access to educational, political and economic resources remain at the heart of the current citizenship crisis in Sudan and South Sudan. Keywords: Sudan, Arabization, Citizenship, Decolonization, Education, Islamization, Language, Politics, Religion, State Arabisation et islamisation dans la fabrique de l'État « postcolonial » soudanais (1946-1964) : représentations culturelles, stratégies politiques et pratiques scolaires RESUME Les historiens du Soudan ont décrit l'arabisation et l'islamisation du pays comme deux processus parallèles sur la longue durée ou comme des politiques étatiques étroitement liées à l'ère postcoloniale. Cet article apporte un nouvel éclairage chronologique et empirique sur l'intrication croissante de l'arabe, de l'arabité et de l'islam dans le Soudan du XX e siècle. Il situe les politiques d'arabisation et d'islamisation du Sud une décennie avant l'indépendance (1956), dans le contexte du retrait impérial britannique et de la montée en puissance des élites nord-soudanaises. L'analyse montre que si les représentations culturelles et les pratiques scolaires alimentèrent la confusion entre langue et religion, elles coexistaient avec des stratégies politiques visant à dissocier arabe et islam. L'article évalue le vécu sud-soudanais de l'arabisation et de l'islamisation imposées, suggérant que les définitions culturelles de la nation et l'accès aux ressources éducatives, politiques et économiques demeurent au coeur de la crise actuelle de la citoyenneté au Soudan et au Soudan du Sud.

TABLE 1 :

 1 NUMBER OF WEEKLY PERIODS ALLOTTED TO THE THREE MAJOR SUBJECTS IN SUDANESE BOYS'

	ELEMENTARY EDUCATION
	27 Sudan Government Education Department, 1940, "Ways of Living in the Sudan: An Introduction to the
	Geography of the Sudan for Elementary Schools," Durham University Library, Sudan Archive, SAD 666/5/1-
	114, UK: 54.
	28 Ibid.: 55.

  In 1965, the Minister of Education Al-Sayyid Badawī Muṣṭafā decided to increase the time devoted to the study of Islam at all school levels. Each of the fourth elementary grades henceforth included 6 weekly periods for religion(Al-Amīn 2007: 164-167). The connection between language and religion was also reinforced through private initiatives, such as the Arabic literacy campaigns organized in Omdurman in the late 1940s and early 1950s by the Sudanese branch of the Muslim Brothers, which especially targeted Southern converts to Islam(Berridge 2019: 592).Assistant Director of Education in the South), who received a complaint from Peter Anai, was to send him to the Islamic college (maʿhad ʿilmī) in Juba, where he had to register under the Muslim name Sirr al-Khatm Anai. Only under this condition could he go back to Loka the following year and then continue to secondary education at Rumbek, still under his Muslim name

	Subject	1st Year	2nd Year	3rd Year	4th Year
	Arabic	6	8	8	6
	Arithmetic	5	6	6	6
	Koran and Religion	4	5	4	4
	Weekly periods (all subjects)	20	29	30	31
	Percentage of religious studies	20 %	17 %	13 %	13 %
	Source: Ministry of Education, Sudan, 1951, Handbook to Elementary Education for Boys' Schools and Boys'
	Clubs in the Sudan, London: Longmans, Green & Co: 3.
	Southern Sudanese Experience and the Conflation of Language, Ethnicity and
	Religion
	In the 1940s and early 1950s, Sudanese and foreign discourses on the link between Arabic
	and Islam were not univocal, even among Southern Sudanese leaders. However, Southern
	views became much more critical after experimenting fifteen years of Arabization and
	Islamization policies, which by 1964 resulted in the conflation of language, ethnicity and
	religion. Southern Sudanese wrote about their experience in Voice of Southern Sudan, the
	London-based newsletter of the Sudan African National Union (SANU), a political party
	established in Kampala (Uganda) in 1962 that advocated Southern autonomy in a Sudanese
	federal state. For instance, a student explained how conversion to Islam was necessary to
	access the Southern educational system. Pupils' names were central in the process: some
	children were right away registered under Arab names in place of their Christian name. Others
	had to change their name in order to pursue their studies. Such was the case of Peter Anai, a
	bright student at Loka Intermediate School who was also a religious Christian.

The headmaster dismissed him from the school after failing to convince him to convert to Islam, "the National Religion." The solution found by Sirr al-Khatm al-Khalīfa (then

Some Christian missionaries did use Arabic but in the Roman script, as was the case of the Catholic mission in Wau in 1929. That Arabic was different from both Juba Arabic and Northern Sudanese Arabic (MILLER 2009).

The LA was composed of 75 members: 10 nominated by the Governor-General, 52 Northerners (10 directly elected in Khartoum and Omdurman and

indirectly elected by Northern provincial electoral colleges), and 13 Southerners (nominated by the three Southern provincial councils). SeeCOLLINS (2008: 58).4 The Republic of the Sudan, 1957, This is Our Way to Build a Strong Nation: Education (Khartoum: Information Centre of the Ministry of Social Affairs).5 For more details on educational gaps between the Northern and Southern Sudan, which had been broadened by the British "Southern Policy," and which partly account for Northern over-representation in the Sudanization process, seeBESHIR (1969) and[START_REF] Seri- | Education in Colonial Sudan, 1900-1957[END_REF].

As recalled by al-Khalīfa himself in a 1981 interview with the scholar Liza Sandell(Sandell 1982: 66).

See also Ministry of Education, Sudan, 1950, Proposals for the Expansion and Improvement of the Educational System in the Southern Provinces, 1951-56 (Khartoum: McCorquodale & Co).

Ministry of Education, Sudan, 1958, Annual Report, 1956-57 (Khartoum: n.p.): 67-68.

The 1964 October Revolution, which was mainly led by Northern protagonists, initially offered some hopes for Northern-Southern reconciliation; the al-Khalīfa government included two Southern representatives, among whom Clement Mboro, who was appointed Minister of Interior(BERRIDGE 2015: 169-171). Yet the return to parliamentary politics(1964)(1965)(1966)(1967)(1968)(1969) did not imply any significant change in the state's Arabization policies in Southern Sudan.

The hostility of Northern Sudanese elites towards Christian missionaries was not new(KING 1975: 300), but it was expressed more vigorously after the country's unification. The limited human and financial resources of the Ministry of Education explain the ongoing collaboration between the state and missionaries in the South(SANDERSON & SANDERSON 1981: 298-299), until all Christian missionaries were expelled from Sudan in 1964.

The Republic of the Sudan,

1957, Report of the International Commission on Secondary Education in theSudan, appointed by the Sudan Government, February 1955 (Khartoum: Publications Bureau): Foreword.19 This pejorative expression probably referred to Juba Arabic, which linguists have defined as a pidgincreole rather than as an Arabic variety[START_REF] Manfredi | Juba Arabic (Árabi Júba): A 'Less Indigenous' Language of South Sudan[END_REF].20 The Republic of the Sudan, 1957, Report of the International Commission on Secondary Education in the Sudan, appointed by the SudanGovernment, February 1955, op. cit.: 51. 21 Ibid.22 Ibid.: 51-52.

"Proceedings of the Juba Conference on the Political Development of the Southern Sudan. June 1947," op. cit.:

 24 ʿAlī Ṭāhā relies on the proceedings of the First Legislative Assembly, Second Session, n° 10, 12 November 1950, which are conserved at the Sudanese National Records Office (NRO) in Khartoum. Diu certainly referred to Juba Arabic when speaking about the South's lingua franca.


Stefano A Cerri
email: sacerri@didaelkts.itphilippe.lemoisson@cirad.fr

Philippe Lemoisson

Sovereignty by personalization of information search: A collective wisdom may influence my knowledge

Keywords: Learning as a Side Effect of Interactions, Collaborative and Group Learning, Personalized and Adaptive Learning Environments, Recommender Systems for Learning. ITS2021, 010, v2

With the experiment that we outline in this paper, we have had the ambition to pave the way for addressing the problem of supporting, enhancing and measuring collective AND informal learning, in particular serendipity. We want to support a new type of free navigation on Web resources (Documents, Topics, Events and Agents -human and artificial -) that is driven by the learner's current needs and the preferences of the community of trust chosen by the learner, not by external actors. The experiment exploits the ViewpointS Web Application (VWA) prototype, that restructures a private version of a subset of the Web according to personalized choices in order to determine distances/proximities among resources. The process allows to enable, empower and measure the influence of members of the community of trust of the learner, on the learner's choices when navigating in search of THE resources corresponding to THE immediate need, goal, strategy, wish. In the following, we will outline: 1. the rationale of our efforts and 2. the user's reactions during the phase of -formal and informal-learning the functions and use of the prototypical software environment VWA, i.e.: a proof of concept for VWA.

Introduction

Since a number of years, we work on a model, an approach, a paradigm called ViewpointS [START_REF] Cerri | Tracing and enhancing serendipitous learning with ViewpointS[END_REF][START_REF] Lemoisson | ViewpointS: When Social Ranking Meets the Semantic Web[END_REF][START_REF] Lemoisson | ViewpointS Web Application to Assess Collective Knowledge Building[END_REF][START_REF] Lemoisson | ViewPointS: capturing formal data and informal contributions into an evolutionary knowledge graph[END_REF][START_REF] Lemoisson | ViewpointS: A Collective Brain[END_REF][START_REF] Cerri | Serendipitous Learning Fostered by Brain State Assessment and Collective Wisdom[END_REF]. Recently, we also developed a system, called VWA (ViewpointS Web Application) than embodies the principles of the ViewpointS paradigm.

After a preliminary study concerned with the collaborative construction of ontologies [START_REF] Lemoisson | Interactive Knowledge Construction in the Collaborative Building of an Encyclopedia[END_REF], we have decided that simpler principles may better serve the process of structuring Information in order to usefully retrieve it when knowledge is needed, in particular through interactions with peers.

We have assumed that the Web consists of four types of resources: Agents (human and artificial, i.e.: event-driven software programs), documents, topics and events. As examples: two authors may be more or less « professionally distant »; but also an author is more proximal to his/her own papers (documents) as to someone else's; to his/her topics of interest; a sub-topic is more proximal to its super-topic as two totally distinguished topics; similarly: a Conference -an event -is more proximal to its topics as to other ones. You may compute proximities / distances in various ways building a kind of « spatial, geographic representation » of the world, governed by distances in a graph.

In our approach, these distances are directly influenced by the community of trust, rather than by other "logical, algorithmic" rules, such as those adopted in numerous previous works typical of various kinds of recommender systems based on the Semantic Web [START_REF] Alaa | Personalized Recommendation for Online Retail Applications Based on Ontology Evolution[END_REF][START_REF] Musto | Context-aware graph-based recommendations exploiting Personalized PageRank[END_REF][START_REF] Obeid | Ontology-based recommender system in higher education[END_REF][START_REF] Kotkov | A survey of serendipity in recommender systems[END_REF][START_REF] Pandey | Recommending Serendipitous Items using Transfer Learning[END_REF]. This community of trust is what we consider the origin of collective wisdom, contributing to the personalization of the graph and thus the corpus of resources accessed by the user. We have basically adopted the recommendation [START_REF] Verbert | Context-Aware Recommender Systems for Learning: A Survey and Future Challenges[END_REF] "that the combination of visualization and recommendation techniques to empower users with actionable knowledge to become an active and responsible part-taker in the recommending process, instead of being the typical passive provider of just personal preferences and social connections" is a necessary, even if perhaps not sufficient, condition for the personalization of informational processes. We have interpreted this vision as an encouraging mandate towards the integration of collective human and artificial intelligence. Further, we have also capitalized (see e.g.: [START_REF] Cerri | Tracing and enhancing serendipitous learning with ViewpointS[END_REF][START_REF] Cerri | Serendipitous Learning Fostered by Brain State Assessment and Collective Wisdom[END_REF]) from the [START_REF] Lops | Content-based Recommender Systems: State of the Art and Trends[END_REF] that "new user-centric directions for evaluating new emerging aspects in recommender systems, such as serendipity of recommendations, are required. "

For us, this approach may represent a disruptive change of paradigm in many relevant processes of construction and access to Information (and therefore Knowledge) including the most relevant side effect: human informal learning. It is for us a strong assumption that "proximity" is a property known to facilitate learning [START_REF] Zpd | [END_REF] under the condition that proximity of resources depends on the dynamic behavior of the community of trust chosen by the learner. We are at the same time aware that the challenge we have adopted years ago is not yet demonstrated.

We have started to experiment VWA with a small but significant number of users. In this experiment we may distinguish two aspects: the user's (or learner's) reactions to the "new tool" during an indispensable initial phase of training and the effects of the new tool concerning understanding, discovering, learning using the new tool: informal learning [START_REF] Breuker | Learning as a Side Effect[END_REF] and social learning in a knowledge domain. Social learning consists of a kind of collective intelligence, where "collective intelligence suggests that in certain settings, a group is better able to solve difficult problems than an individual working alone" (see, for instance [START_REF] Tucker | Crowdsourcing in medical research: concepts and applications[END_REF] in the crucial domain of medicine, or -even more generally: [START_REF] Muthukrishna | Innovation in the collective brain[END_REF]). Notice that informal learning, even if it has no explicit learning objective, requires anyhow to solve the difficult problem that one should finally learn.

While the generic effects of VWA on informal and collective learning are described in another paper [START_REF] Lemoisson | Collective and Informal Learning in the ViewpointS interactive medium[END_REF], the learner's reactions to the new tool (components, functions and use) are shortly described in this contribution.

An instance of context that seems to us relevant is offered by the compilation of a state of the art on some new, cross disciplinary research domain (e.g.: in translational research): it is evident that each researcher has his/her own preferences for collaborative filtering of too many and differently useful items, and that the best advisors are the human members of the trusted community of peers that (s)he has chosen.

Three degrees of personalization supporting sovereignty

In this section we outline the applicability of our approach to the goal as stated in the title, leaving details of the architecture and the algorithms to other contributions that have been quoted in the introduction.

The ViewpointS model relies on two concepts: resources and viewpoints. The resources are 'Human Agents', 'Documents', 'Topics', and 'Events'. 'Topics' may be keywords or short expressions aimed at describing other resources. Each viewpoint is a connection between two resources established by a 'Human Agent' (or alternatively by an 'Artificial Agent'). Both resources and viewpoints can be either extracted from the Web, or directly created by Human Agents. The viewpoints can be of five types; in this experiment, we concentrate on the two most important types: 'factual' and 'subjective'. A factual viewpoint means that the semantics linking the two resources can be checked by others, e.g.: when a 'Human Agent' is the author of a 'Document' or when a 'Human Agent' participates to an 'Event'. A subjective viewpoint means that the link indicates an emotion, an opinion or a belief of the emitter of the viewpoint, e.g.: when a 'Human Agent' likes a 'Document' or believes a 'Document' is relevant with respect to a 'Topic'. The bipartite graph consisting of resources connected by viewpoints is called Knowledge Graph (KG).

Since this graph is too complex to be interpreted by humans, it is locally transformed in the neighborhood of a target resource, whenever a user is searching information, into a Knowledge Map (KM). This transformation is automatic and goes through the following process: i) the user chooses a perspective by choosing the respective strengths of the 'factual' versus the 'subjective' viewpoints (the rule may be more complex), ii) the viewpoints connecting the pairs of resources are valued and aggregated into 'synapses' reflecting proximities and iii) the labels indicating distances (inverse from the synapses strengths) appear on the KM edges between resources. The KG->KM transformation is dynamic: whenever a member of the community updates the KG, the various KMs computed for the other members are impacted. In the current experiment, the only Agents that produce resources and viewpoints are the Human Agents. This is a temporary simplification: artificial Agents may fruitfully produce many more useful resources and viewpoints in subsequent applications of VWA by activating softbots instructed to reason on Web resources. This aspect of our model enables us to declare that our approach is synergic and complementary with other ones available in the literature. The main differences with other models of access to Information (e.g.: Google) are: i. the whole set of resources available on the Web is exploited in order to build a subset of "relevant and trusted" resources, organized in a bipartite graph called Knowledge Graph (KG). Notice that Agents (Human or Artificial) are first class resources in ViewpointS, in the same way as Documents or Topics or Events. The process of selection of resources by qualified Agents offers a first degree of personalization; ii. the User (or Learner) does not navigate on the KG, rather on a transformed graph, called Knowledge Map (KM) that is built dynamically -by means of a MapReduce transformation-according to a set of preferences (called a "perspective") chosen by the Learner; viewpoints are weighted according to the preferences and then aggregated in binary links called "synapses" (adopting the metaphor of the brain [START_REF] Lemoisson | ViewpointS: A Collective Brain[END_REF]). The choice of preferences by Users offers a second degree of personalization; iii. the Learner may share with a community of trust (a group) the same KG in such a way that other Agents may contribute (dynamically) with new resources and/or new viewpoints, leading to the strengthening or weakening of synapses. The "collective behavior/wisdom" offers a third degree of personalization which engages the collective rather than the individuals.

VWA(ViewpointS Web Application): the SandBox experiment

The process of learning "how to use" a new tool is not simple, for several reasons.

The main problem is that if the tool is really new, it represents functionalities that are previously neither conceived nor acquired or mastered by the learner. Therefore, in order to expose our subjects to the "concepts" of the Information processes envisaged by the ViewpointS model, we designed and exploited a "SandBox" where we have invited our subjects to follow us in a first introduction on "concepts and essential procedures".

In the "SandBox" tutorial experiment we have tried to teach Users-Learners to feed Data (e.g.: documents and topics) to VWA and to structure the Information necessary for VWA in order to answer a query (i.e.: to add viewpoints). The challenges were multiple: i) to keep Users within a pro-active learning process, ii) to introduce Users progressively to the various features and functionalities of the prototype while leaving them discovering it at their own pace, iii) to record and assess their positive but also their negative reactions to the learning environment, and particularly to verify their acceptance and preferences with respect to the main innovation of VWA.

Any User entering VWA immediately becomes a resource of the type 'Human Agent" and, as such, will appear both in the tabular view and the graphical view of the KM as a blue node. All the learning resources are hosted by the KG "SandBox". The three learning modules respectively named "topo uno", "topo dos" and "topo tres" are resources of type 'Event'; they aggregate resources of type 'Document': either videos or textual pedagogical documents. The three learning modules which introduce the ViewpointS paradigm are sketched hereafter: Learning module n°1: discovering the environment. Users are firstly invited to listen to a 4'30" clip presenting the ViewpointS model, then to follow a clip teaching them how to connect themselves to a learning module; Learning module n°2: the basics for proactivity. Users are taught how to create a new resource, how to connect two resources (a viewpoint), and finally how to connect a preview, i.e.: an image intended to give a hint before opening the resource; Learning module n°3: understanding the underlying processes. Users are explained the importance of the "perspective", they go through the notions of "SP-distance" and "Kdistance"; they learn how to emit reactive viewpoints and finally discover how "shortcut viewpoints" enhance serendipity [see, e.g.: 1,6].

The educational paths followed by the Users are hosted by the KG "SandBox" as well. As soon as a User has read (or listened to) the documents linked to a module, (s)he is asked to establish a connection, i.e. to emit a factual viewpoint, between him/her and the corresponding module. This appears in Fig. 2 which is the view of the KG "SandBox" taken at the end of the process: the 36 participants (blue nodes) are connected to the three modules (orange nodes) which aggregate a Glossary and the 9 pedagogical documents (green nodes). The pedagogy of the VWA SandBox intertwines therefore three learning modes: i) learning through documents, i.e.: "classical" knowledge acquisition through resources, ii) learning by doing, i.e.: creating resources and viewpoints and iii) participating to collective learning by reshaping the KMs browsed by the others.

Among the 55 initial volunteers, 36 people actually took the time to go through the three modules, as illustrated in Fig. 2, despite the heavy time schedules and constraints of the autumn 2020. This could be interpreted as a relative success with respect to the challenge of keeping users within a pro-active learning process.

Fig. 3 illustrates this proactivity; in the middle of the KM, we can see Users (Human Agents) subjectively connected to the 'Documents' they have appreciated. Note that the chosen perspective ('subjective' only) is orthogonal to the perspective of Fig. 2 ('factual' only) so that the map illustrates opinions about the content rather than participation in the modules. Assessment of the learning modules. Almost all participants acknowledged clarity of the pedagogical documents and easiness in the progression. Assessment of the VWA environment. The participants had been firstly invited to contribute with free comments to a specific 'Topic' named "Feedbacks about the SandBox experiment". These comments pointed out several points concerning the environment: a. some users were disappointed not to be able to suppress viewpoints they had created; b. most users observed difficulties in exploiting the KM as soon as it became dense; c. several users asked for a "global view" of the whole KG, c. several users asked for special means to find back the resources created by themselves; d. one user asked for a special feature allowing the batch import of documents; e. one user asked for a shortcut grouping the actions of creating a new resource AND connecting it to an existing one; f. several users asked for a special feature facilitating contextualized comments on existing resources. In addition to those free comments, the participants were asked to rate from 1 (worst) to 5 (best) the two alternative views on the KM (tabular and graphical). This survey led to the following: tabular view: mean rating= 2,2 ; standard deviation = 0,80; graphical view: mean rating= 4,1 ; standard deviation = 0,53.

Conclusion

We make reference to [20] in order to qualify our SandBox experiment as a proof of concept of several rather radical changes in the collective construction and retrieval of knowledge. Referring to the goal of this paper indicated by its title, we believe to have proved several concepts: 1. Users exploit the graph representation with relative ease and increasing interest; 2. the proximity introduced by "synapses" in the KM is a useful means for aggregating resources and influencing the Users' navigation; 3. the three levels of personalization favor not only the trust of Users, but also their protection from external undesired influences (sovereignty); 4. the exploitation of collective wisdom by a trusted community allows to privilege shared values, interests, goals and knowledge; 5. learning the use of VWA in the SandBox has been a relative success, even if many suggested improvements of the current VWA platform will require to engage significant energy in the months to come.

Fig. 1 .

 1 Fig.1. The ViewpointS paradigm: 1. resources and viewpoints are stored in the KG (upper left), 2. a user chooses a perspective (down left) and searches for a resource (e.g.: "topo uno"), 3. a KM is computed in the neighborhood of "topo uno" and 4. this KM is displayed both in a table view (center) and in graphical view (right).

Fig. 1

 1 Fig.1 illustrates a KM computed around the neighborhood of the resource "topo uno". The distances labeling the edges of the KM in the right part are SP-distances (shortest path distances). In the central part, the tabular view recapitulates the SP-

Fig. 2 .

 2 Fig. 2.A view on the three learning modules in the SandBox (resource type = "Event"; colour = orange), the 10 documents linked to them (resource type = "Numeric Document"; colour = green), and the 36 active Users (resource type = "Human Agent; colour = blue). The chosen perspective selects the factual connections and discards the subjective ones.

Fig. 3 .

 3 Fig. 3. A view illustrating the proactivity of the participants. The chosen perspective selects the subjective connections and discards the factual ones.

ITS2021, 010, v2 (final): 'Sovereignty by personalization of information search: collective . . .


Andreas Herzig
email: herzig@irit.fr

Ivan Varzinczak

On modularity of theories

Keywords:

Introduction

In many cases knowledge is represented by logical theories containing multiple modalities α 1 , α 2 , . . . Then it is often the case that we have modularity, in the sense that our theory T can be partitioned in a union of theories

T = T ∅ ∪ T α 1 ∪ T α 2 ∪ . . .

such that

• T ∅ contains no modal operators, and

• the only modality of T α i is α i .

We call these subtheories modules. Examples of such theories can be found in reasoning about actions, where each T α i contains descriptions of the atomic action α i in terms of preconditions and effects, and T ∅ is the set of static laws (alias domain constraints, alias integrity constraints), i.e. those formulas that hold in every possible state of a dynamic system. For example, T marry = {¬married → marry , [marry]married}, and T ∅ = 1 {¬(married ∧ bachelor)}. Another example is when mental attitudes such as knowledge, beliefs or goals of several independent agents are represented: then each T α i contains the respective mental attitude of agent α i . [START_REF] Doherty | Explaining explanation closure[END_REF] Let the underlying multimodal logic be independently axiomatized (i.e. the logic is a fusion and there is no interaction between the modal operators), and suppose we want to know whether T |= ϕ, i.e. whether a formula ϕ follows from the theory T . Then it is natural to expect that we only have to consider those elements of T which concern the modal operators occurring in ϕ. For instance the proof of some consequences of action α 1 should not involve laws for other actions α 2 ; querying the belief base of agent α 1 should not require bothering with that of agent α 2 . Moreover, intensional information in any T α i should not influence information about the laws of the world encoded in T ∅ .

Similar modular design principles can be found in structural and objectoriented programming. We have advocated and investigated the case of reasoning about actions in [3].

Preliminaries

Let MOD = {α 1 , α 2 , . . .} be the set of modalities. Formulas are constructed in the standard way from these and the set of atomic formulas ATM. They are denoted by ϕ, ψ, . . .. Formulas without modal operators (propositional formulas) are denoted by PFOR = {A, B, C, . . .}.

Let mod (ϕ) return the set of modalities occurring in formula ϕ, and let mod (T ) = ψ∈T mod (ψ). For instance mod

([α 1 ](p → [α 2 ]q)) = {α 1 , α 2 }. If M ⊆ MOD is a set of modalities then we define T M = {ϕ ∈ T : mod (ϕ) ∩ M = ∅}
Hence T ∅ is a set of formulas without modal operators. Another example is

T {marry,divorce} = ¬married → marry , [marry]married, married → divorce , [divorce]¬married
We write T α instead of T {α} .

We suppose from now on that T is partitioned, in the sense that {T ∅ } ∪ {T α i : α i ∈ MOD} is a partition of T . We thus exclude T α i containing more than one modal operator.

Models of the logic under concern are of the form M = W, R, V , where W is a set of possible worlds, R : MOD -→ W ×W associates an accessibility relation to every modality, and V : W -→ 2 ATM associates a valuation to every possible world.

Satisfaction of a formula ϕ in world

w of model M (M, w |= ϕ) and truth of a formula ϕ in M (noted M |= ϕ) are defined as usual. Truth of a set of formulas T in M (noted M |= T ) is defined by: M |= T iff M |= ψ for every ψ ∈ T . T has global consequence ϕ (noted T |= ϕ) iff M |= T implies M |= ϕ.
We suppose that the logic under concern is compact.

Modularity

Under the hypothesis that {T ∅ } ∪ {T α i : α i ∈ MOD} partitions T , we are interested in the following principle of modularity:

Definition 3.1 A theory T is modular if for every formula ϕ, T |= ϕ implies T mod(ϕ) |= ϕ
Modularity means that when investigating whether ϕ is a consequence of T , the only formulas of T that are relevant are those whose modal operators occur in ϕ. This is reminiscent of interpolation, which more or less2 says: Definition 3.2 A theory T has the interpolation property if for every formula ϕ, if T |= ϕ then there is a theory T ϕ such that

• mod (T ϕ ) ⊆ mod (T ) ∩ mod (ϕ) • T |= ψ for every ψ ∈ T ϕ • T ϕ |= ϕ
Our definition of modularity is a strengthening of interpolation because it requires T ϕ to be a subset of T . Contrarily to interpolation, modularity does not generally hold. For example, let

T = {p ∨ [α]⊥, p ∨ ¬[α]⊥} Then T ∅ = ∅, and T α = T . Now T |= p, but clearly T ∅ |= p.
Being modular is a useful feature of theories: beyond being a reasonable principle of design that helps avoiding mistakes, it clearly restricts the search space, and thus makes reasoning easier. To witness, if T is modular then consistency of T amounts to consistency (in classical logic) of the propositional part T ∅ .

Propositional modularity

How can we know whether a given theory T is modular? The following criterion is simpler:

Definition 4.1 A theory T is propositionally modular if for every proposi- tional formula A, T |= A implies T ∅ |= A
And it will suffice to guarantee modularity: Theorem 4.1 Let T be a partitioned theory. If T is propositionally modular then T is modular.

Proof: Let T be propositionally modular. Suppose T mod(ϕ) |= ϕ. Hence there is a model M = W, R, V such that M |= T mod(ϕ) , and there is some w in M such that M, w |= ϕ. We prove that T |= ϕ by constructing from M a model M such that M |= T and M , w |= ϕ.

First, as we have supposed that our logic is compact, propositional modularity implies that for every propositional valuation val ⊆ 2 ATM which is a model of T ∅ there is a possible worlds model M val = W val , R val , V val such that M val |= T , and there is some w in M val such that V val (w) = val. In other words, for every propositional model of T ∅ there is a model of T containing that propositional model. Second, taking the disjoint union of all these models we obtain a 'big model' M big such that M big |= T , and for every propositional model val ⊆ 2 ATM of T ∅ there is a possible world w in M big such that V (w) = val. Now we can use the big model to adjust those accessibility relations R(α) of M whose α does not appear in ϕ, in a way such that the resulting model satisfies the rest of the theory T \ T mod(ϕ) : let M = W , R , V such that

• W = {u v : u ∈ W, v ∈ W big , and V (u) = V big (v)} • if α ∈ mod (ϕ) then u v R (α)u v iff uRu • if α ∈ mod (ϕ) then u v R (α)u v iff vRv • V (u v ) = V (u) = V big (v)
W is nonempty because M is 'big enough' and contains every possible propositional model of T ∅ . Then for the sublanguage constructed from mod (ϕ) it can be proved by structural induction that for every formula ψ of the sublanguage and every u ∈ W and v ∈ W big , M, u |= ψ iff M , u v |= ψ. The same can be proved for the sublanguage constructed from MOD \ mod (ϕ). As T ∅ and each of our modules T α are in at least one of these sublanguages (in both sublanguages in the case of T ∅ ), we have thus proved that M |= T , and M , w v |= ϕ for every v.

Action theories

In the rest of the paper we investigate how it can be automatically checked whether a given theory T is modular or not. We do this for a particular kind of theories that are commonly used in reasoning about actions. For such theories we also show how the parts of the theory that are responsible for the violation of modularity can be identified. First of all we say what an action theory is.

Every action theory contains a representation of action effects. We call effect laws formulas relating an action to its effects. Executability laws in turn stipulate the context where an action is guaranteed to be executable. Finally, static laws are formulas that do not mention actions and express constraints that must hold in every possible state. These are our four ingredients that we introduce more formally in the sequel.

Static laws

Frameworks which allow for indirect effects make use of logical formulas that link invariant propositions about the world. Such formulas characterize the set of possible states. They do not refer to actions, and we suppose they are formulas of classical propositional logic A, B, . . . ∈ PFOR.

A static law3 is a formula A ∈ PFOR that is consistent. An example is Walking → Alive, saying that if a turkey is walking, then it must be alive [10].

Effect laws Here MOD is the set of all actions. To speak about action effects we use the syntax of propositional dynamic logic (PDL) [2]. The formula [α]A expresses that A is true after every possible execution of α.

An effect law [START_REF] Kracht | Properties of independently axiomatizable bimodal logics[END_REF] for α is of the form A → [α]C, where A, C ∈ PFOR. The consequent C is the effect which obtains when α is executed in a state where the antecedent A holds. An example is Loaded → [shoot]¬Alive, saying that whenever the gun is loaded, after shooting the turkey is dead. Another one is [tease]Walking: in every circumstance, the result of teasing is that the turkey starts walking.

A particular case of effect laws are inexecutability laws of the form A → [α]⊥. For example ¬HasGun → [shoot]⊥ expresses that shoot cannot be executed if the agent has no gun.

Executability laws With only static and effect laws one cannot guarantee that shoot is executable if the agent has a gun. [START_REF] Kracht | Simulation and transfer results in modal logic: A survey[END_REF] In dynamic logic the dual α A, defined as ¬[α]¬A, can be used to express executability. α thus reads "the execution of action α is possible".

An executability law [START_REF] Lin | Embracing causality in specifying the indirect effects of actions[END_REF] for α is of the form A → α , where A ∈ PFOR.

For instance HasGun → shoot says that shooting can be executed whenever the agent has a gun, and tease says that the turkey can always be teased.

Action theories S ⊆ PFOR denotes the set of all static laws of a domain. For a given action α ∈ MOD, E α is the set of its effect laws, and X α is the set of its executability laws. We define E = α∈MOD E α , and X = α∈MOD X α . An action theory is a tuple of the form S, E, X . We suppose that S, E and X are finite.

Checking modularity of action theories

How can we check whether a given action theory T = S, E, X is modular? Assuming T is finite, the algorithm below does the job: Algorithm 6.1 (Modularity check) input: S, E, X output: a set of implicit static laws S I S I := ∅ for all α do for all J ⊆ E α do

A J := {A i : A i → [α]C i ∈ J} C J := {C i : A i → [α]C i ∈ J} if S ∪ {A J } ⊥ and S ∪ {C J } ⊥ then for all B → α ∈ X do if A J ∧ B ⊥ then S I := S I ∪ {¬(A J ∧ B)} Theorem 6.1 An action theory S, E, X is modular iff S I = ∅.
The proof of this theorem relies on a sort of interpolation theorem for multimodal logic, which basically says that if Φ |= Ψ and Φ and Ψ have no action symbol in common, then there is a classical formula A such that Φ |= A and A |= Ψ. [START_REF] Mccain | A causal theory of ramifications and qualifications[END_REF] Remark 6.1 In [3] a monotonic solution to the frame problem has been integrated in such an algorithm. This makes the algorithm a bit more complex as it involves computing of prime implicates. For the sake of simplicity this has not been done here.

Discussion and conclusion

In the perspective of independently axiomatized multimodal logics we have investigated several criteria of modularity for simple theories. We have demonstrated the usefulness of modularity in reasoning about actions, where we have given an algorithmic checking for modularity of a given action theory.

We can have our criterion of modularity refined by taking into account polarity. Let mod ± (ϕ) be the set of modalities of MOD occurring in ϕ together with their polarity. For instance mod ± ([α 1 ]([α 2 ]p → q)) = {+α 1 , -α 2 }. mod ± (T ) is defined accordingly. If M is a set of modalities with polarity then we define: T M = {ϕ ∈ T : mod ± (ϕ) ∩ M = ∅}. For the restricted case of action theories this has been proved in [3].

Definition 7 . 1

 71 A theory T is ±-modular if for every formula ϕ,T |= ϕ implies T mod ± (ϕ) |= ϕThere are other theories that are modular but not ±-modular, e.g.T = {¬[α]p, [α]p ∨ [α]¬p} Indeed, T |= [α]¬p, but T +α |= [α]¬p.

Here we should assume more generally that [α i ] is the only outermost modal operator of T αi ; we think that this case could be analyzed in a way that is similar to ours. Things get just more complicated.

We here present a version in terms of global consequence, as opposed to local consequence or material implication versions that can be found in the literature[START_REF] Kracht | Properties of independently axiomatizable bimodal logics[END_REF][START_REF] Kracht | Simulation and transfer results in modal logic: A survey[END_REF]. We were unable to find such global versions in the literature.

Static laws are often called domain constraints, but the different laws for actions that we shall introduce in the sequel could in principle also be called like that.

Effect laws are often called action laws, but we prefer not to use that term here because it would also apply to executability laws that are to be introduced in the sequel.

Some authors[START_REF] Schubert | Monotonic solution of the frame problem in the situation calculus: an efficient method for worlds with fully specified actions[END_REF][START_REF] Doherty | Explaining explanation closure[END_REF][START_REF] Mccain | A causal theory of ramifications and qualifications[END_REF][START_REF] Thielscher | Computing ramifications by postprocessing[END_REF] more or less tacitly consider that executability laws should not be made explicit, but rather inferred by the reasoning mechanism. Others[START_REF] Lin | Embracing causality in specifying the indirect effects of actions[END_REF][START_REF] Zhang | EPDL: A logic for causal reasoning[END_REF] have executability laws as first class objects one can reason about. It seems a matter of debate whether one can always do without, but we think that in several domains one wants to explicitly state under which conditions a given action is guaranteed to be executable, e.g. that a robot should never get stuck and should always be able to execute a move action. In any case, allowing for executability laws gives us more flexibility and expressive power.

Some approaches (most prominently Reiter's) use biconditionals A ↔ α , called precondition axioms. This is equivalent to ¬A ↔ [α]⊥, which illustrates that they thus merge information about inexecutability with information about executability.

The detailed proof can be found in http://www.irit.fr/ACTIVITES/LILaC/Pers/ Herzig/P/AiML04.html

* Supported by a fellowship from the government of the Federative Republic of Brazil. Grant: CAPES BEX 1389/01-7.