Michael Von Cotta-Schönberg

Silvio Enea

; Piccolomini

Sylvius Aeneas

Silvius Aeneas

Piccolomini

Michael V Cotta-Schönberg

Report of an Imperial Mission to Rome, 1455, by Enea

In April 1455, Cardinal Alfons de Borja was elected pope. Soon afterwards the embassies from the the Christian princes and city states began to arrive in Rome to make the traditional declaration of obedience to the new pope. In August, the embassy of Emperor Friedrich III arrived, consisting of Bishop Enea Silvio Piccolomini of Trieste, imperial councilor and top diplomat, and Johann Hinderbach, another

Table of volumes in Reports on Five Diplomatic Missions, 1447-1455, by Enea Silvio Piccolomini

On 8 April 1455, Cardinal Alfons de Borja 2 was elected pope and took the name of Calixtus III.

News of the death of his predecessor, Pope Nicolaus V, 3 reached the imperial court some weeks later, during a diet held in the presence of Emperor Friederich III 4 at the imperial residence in Wiener Neustadt 5 . One of the main objectives of the diet was to make concrete preparations for a crusade against the Turks, the pope being responsible for assembling a fleet to support a land army under German leadership. The news of the pope's death put an end to the diet and, indeed, to the German war effort.

Immediately, important parties at the imperial court, first among them the Archbishop of Trier, 6 began to argue that the Germans should take advantage of the occasion to obtain the same distance and ecclesiastical independence from the Papacy that the French had previously achieved by means of the Pragmatic Sanction of Bourges in 1438. 7 The emperor, however, on the advice of Bishop Piccolomini of Siena, his senior diplomat and advisor on church affairs and Italian affairs, decided to continue his alliance with the papacy which he considered essential to support the waning authority of the imperial office, especially in relation to the German princes.

He, therefore, despatched an embassy consisting of Piccolomini and other courtiers to Rome to present the traditional declaration of obedience of the Holy Roman Empire to the new pope. It was the second time that Piccolomini performed such a task, having also presented the imperial declaration of obedience to Pope Eugenius IV. 8 The declaration was made as part of an oration, the "Solent plerique" [27], delivered by Piccolomini during a public consistory in Rome on 13 August 1455.

Later, as pope, he wrote about these events in his Commentarii:

1 CO, I, 29; Piccolomini's orations "Solent plerique" [26] and "Modestius" [27] 7 A church law in France, incorporating a number of decrees from the Council of Basel, tending generally to limit the pope's influence in national church affairs, and particularly with regard to the appointment of bishops 8 See Piccolomini's oration "Non habet me dubium" [11] When the news of this was reported in Austria, there were many who tried to persuade the emperor that now was the time to exert pressure on the Apostolic See and thus reduce its power in Germany. The compacts settled with Eugenius IV had been violated, they argued; therefore they should make no submission to the new pope unless he granted the petitions of the German nation. Long regarded as a servant, Germany deserved at last to be free. This was the policy promoted tenaciously by Archbishop Jacob of Trier, who expected to profit from the dispute. Aeneas, however, argued that the emperor would gain nothing from an assault on the pope's authority, especially if it were done for the sake of popular opinion, which is inherently fickle. The reins of government must never be handed to the people for they, as he knew, hated the rule of princes. Between princes, friendship was sometimes possible, but between the people and a king the hatred was undying. The pope and the emperor needed each other's support, and it was folly to injure the man you hoped would help you. The start of a new pontificate was a time to win the favour of the pope by showing him kindness; if one started by lashing out, it would be difficult to then find a path to his good will. Frederick must make submission, as his ancestors had done, and negotiate an honourable treaty with the new pope; once that was agreed, the Germans would follow the emperor's lead. Aeneas' advice prevailed and he himself was despatched together with ... Johann Hinderbach, to see his plan through. ... At their arrival a public consistory was convened in which Aeneas, after making his submission in the time-honored way, delivered an oration which praised the emperor and the empire and at the same time called for a crusade against the Turks. Afterwards, copies of this speech circulated widely. 1 In Rome, the German ambassadors attempted in vain to negotiate a number of issues and problems in the relations between Germany and the papacy before making the declaration of obedience. But the pope refused to enter into such negotiations before obedience had been declared since he would not under any circumstances accept a conditional obedience. The ambassadors had to accept this: the negotiations were postponed, and when they were resumed, after the declaration of obedience, the German petitions were roundly refused by the pope! 2

Themes

Obedience to the pope

Piccolomini came to Rome twice on imperial missions to present the emperor's declaration of obedience to the pope. The first time was in 1447, as mentioned, when the emperor was finally ready to recognize the pope in Rome, Eugenius IV, and to reject the antipope elected in 1439 by the rump council in Basel, Felix V. 1 On that occasion, the imperial recognition of the pope only happened after protracted preparations and even last-minute negotiations and important Roman concessions to the emperor, opening the way to the declaration of obedience to the dying pope.2

At that time, the papacy was still weakened by the 70-year long exile in Avignon, followed by the Great Western Schism, with two and even three reigning popes, and later followed by the antipapalist Council in Basel, which had opened in 1432 and was only ended, though as a rump council, in 1449. In this situation, it was quite natural for the secular powers to negotiate their obedience to the pope, making it conditional on concessions and favours.

The pontificate of Pope Nicolaus V3 , uncontested from 1449 to his death in 1455, strengthened the papacy to the extent that his successor, Calixtus III, absolutely refused to accept conditional declarations of obedience from the secular powers,4 implicitly daring the princely ambassadors to return to their masters without declaring obedience5 :

He let us know that he would gladly hear us, but that we should not want to make any agreements with him before the declaration of obedience because in no way would he accept a conditional obedience. We thought that this message was harsh. [Sect. 9]

We should know, however, that because of the declaration of obedience he was to receive, he could make no promises. For he knew that the obedience was owed to him, and he would rather die than receive it conditionally. He said that also the legates of the King of Aragon as well as ambassadors from other kings had been with him and wanted to negotiate their obedience, but they were rebuffed. [Sect. 10] Even the imperial ambassadors dared not risk the scandal arising from not declaring obedience, as Piccolomini wrote to the emperor:

His words left us perplexed us, but when we realized that it could not be done otherwise and that it would cause a scandal if we left without making the declaration of obedience, we decided to make this declaration and afterwards pursue the matter of the petitions, since it could not be done otherwise. [Sect. 1] Thus, Piccolomini's report to the emperor is a testimony of the Renaissance papacy's remarkable recovery after generations of abject weakness.

Papal control over ecclesiastical appointments

Another sign of growing papal confidence and strength vis-à-vis the secular powers is pope Calixtus' polite, but adamant resistance to imperial control over ecclesiastical appointments. In practice, accommodations might be found, but there was little flexibility on the principle of papal control over such appointments.

The papal stance was strengthened by the -exaggerated -news from France that the clergy there were positively inclined towards the pope and possibly willing to be accomodating in the matter of the Pragmatic Sanction of 1438. This measure had greatly reduced papal influence in French ecclesiastical affairs and appointments and much diminished the flow of French money to the papal curia:

In

Papal finances

Control over ecclesiastic appointments had for centuries been a major issue in the Church's fight for ecclesiastical freedom from secular power, and as such, it was a matter of basic ideology.

It was also extremely important for the financing of the central government of the Church and the upkeep of pope and cardinals. Various methods and mechanisms were used, but basically, they all resulted in the transfer of money to Rome, to such an extent that they would later contribute greatly to the secular powers' support of the Reformation in Germany.

The system of annates 2 is a case in point. Annates were a form of taxation of the incomes of an ecclesiastical benefice, to be paid by any new incumbent (bishop, abbot etc.). In the 15 th century, it regularly amounted to half of the annual revenue of the benefice. This is the case referred to by Piccolomini in his report to the emperor:

Because of the opposition of the cardinals, we were completely unable the obtain the remission of annates for the Abbot of Saint Lambrecht. [Sect. 17]

The reason why the emperor favoured Johannes Schachner's intrusion into the abbacy that Ratmannsdorfer had obtained very shortly before is unknown. It may have been related to the emperor's policy of influencing the appointments to important ecclesiastical offices and lucrative benefices.

The reason for the cardinals being generally opposed to the remission of annates was evidently that an important part of their own incomes came from the annates received by the Apostolic Chamber.

As for the pope's claim that his predecessor had left no money whatsoever, this is hard to believe. Pope Nicolaus had improved the papal finances, especially in connection with the Jubilee Year in 1450, but he had also spent much money on his building program in Rome. Still, it defies belief that there should not be even a single coin left, so either somebody had removed or stolen the cash left at his death, or Pope Calixtus grossly exaggerated the situation in order to avoid having to pay the emperor the money due to him, by virtue of an agreement with Pope Eugenius in 1447.

Crusade

The crusade against the Turks was a major theme in Piccolomini's oration of obedience to Pope Calixtus, 1 and indeed, it was a major concern both for Piccolomini and the pope. The emperor and the German princes, however, were not interested in a crusade, so this issue was not really part of the negotiations of the imperial diplomats with the pope.

The report does mention, however, a number of facts connected with the crusade worth mentioning.

Firstly, the pope was intensely occupied with the crusade and almost thought of nothing else. He even believed that he would not die before the Christians had retaken Constantinople, though that hope was evidently destined to fail.

Secondly, the pope would soon be sending Cardinal Carvajal to Germany with the object of mobilizing and leading a land army against the Turks (to be complemented by a papally organized fleet). Knowing the failure of the imperial diets in 1454 and 1455 with regard to the crusade, the cardinal did not intend to hold more such meetings but would be urging the princes and cities individually to keep their promises of assistance to the crusade undertaking.

Thirdly, it was reported from Naples that King Alfonso V, when gravely ill, had promised to prepare a large fleet against the Turks and even to fight in person. Sceptics, however, doubted that much would come of this, wrote Piccolomini -and they would be proven right.

Fourthly, the Duke of Burgundy, the most and probably the only important European prince to genuinely support a crusade, had reported to the pope that on the appointed day he would arrive with an army of no less than 16,000 soldiers and even fight in person.

Fifthly, encouraged by these news the pope had held a splendid ceremony in Saint Peter's where he had given the cross, the sign of a crusader, to two cardinal legates.

Finally, Piccolomini reported to the emperor that the Archbishop of Trier had complained to the pope of not having information from neither pope nor emperor concerning the crusade. The archbishop's complaint would certainly not have been caused by his eagerness for a crusade, but rather by his worries that the pope with the emperor's support would somehow be able to get a crusade moving. Piccolomini advised the emperor to forestall further such -hypocritical -criticism by informing the German princes and cities of his diplomats' actions in this matter in Venice, Ferrara, Florence, Siena, and at the Papal Court, and also about the coming of a papal legate with the task of raising an army against the Turks. Moreover, the emperor should urge the princes to fulfil their promise of providing soldiers to the crusade. Such a letter would not be welcome to the princes, but a least the Holy Roman Emperor would have demonstrated to the world his impeccable Christian zeal for the crusade and the protection of the Faith.

Conduct of diplomacy

Appointment of ambassadors

Two ambassadors were appointed to go on the mission to Rome to present the emperor's declaration of obedience to the new pope. One was Enea Silvio Piccolomini, Bishop of Siena, highranking member of the imperial court, prince of the Empire, and former papal envoy to Central Europe. The other was Johann Hinderbach, an imperial advisor, later Prince-Bishop of Trento.

Ambassadorial mandate

Piccolomini does not mention the mandate as such, but he repeatedly refers to the ambassadors' instructions concerning the affairs to be negotiated with the curia: Money owed to the emperor by the pope, reservations of ecclesiastical offices, tithes, and other affairs.

Ceremonies at arrival

At their arrival, the ambassadors were met, honourably, by the legates of all the princes present in Rome, all the bishops, and the households of the cardinals and the pope. Some days later, they were received by the pope in a public audience (consistory).

Ambassadorial oration

During the public audience, Piccolomini delivered the obligatory oration, the "Solent plerique". 1 This oration had special significance because it included the formal declaration of the emperor's obedience to the pope. The pope answered the oration in person.

Strategy of negotiation

The ambassadors had planned to negotiate the various affairs entrusted to them in a private audience with the pope before presenting the declaration of the obedience, thus intending to put pressure on the pope to grant their petitions. The pope, however, himself a most accomplished and experienced negotiator, very well understood and adamantly rejected this strategy. In no way, would he negotiate the affairs before the declaration of obedience, and in no way would he accept a conditional obedience. So, this strategy failed miserably. Interestingly, the episode was a learning experience for Piccolomini who when he became pope himself three years later would take the same stance as Calixtus with ambassadors trying to use the declaration of obedience to bargain for advantages.

Technique of negotiation

Interlocutors

The ambassadors presumably negotiated with cardinals and high curial officials concerning the affairs entrusted to them, some of them quite mundane. However, the pope chose to negotiate the important matters directly with the ambassadors, in private meetings. This was really not an advantage for the ambassadors since the normal frank exchange between lower-level negotiators would not be possible with such an august personage. Also, their task was made difficult by the pope's superior negotiating style, a mixture of uncontradictable authority (the pope imposed silence upon the ambassadors concerning two important matters, and bade them be content with his decisions), crass exaggeration (the pope claimed that his predecessor had left not even one coin in the treasury), and pious theatrics: And raising his eyes to Heaven, as if speaking directly with God, he implored Divine Piety to remove him rather than to allow any scandal to arise through him. What could the ambassadors possibly say to that?

Written procedure

The petitions from the imperial court were naturally handed over in writing to the pope who passed them on to the Bishop of Zamora for consideration. But concerning the important matters, there would be no meetings with minutes taken and sealed by all, as had happened during the imperial mission to Rome in 1447.1

Diplomatic report

As was the custom, Piccolomini wrote up a report to the emperor after the end of the mission. Two other diplomatic reports of his in the same format are extant as well as two reports on diplomatic missions that went beyond the normal format of the diplomatic report.

The present report comprises a description of the situation at the host court and in Italy, generally, an account of the ceremonies of arrival (a matter of the emperor's honour), a detailed account of the negotiations, a rather embarrassed conclusion on the meagre results of the embassy, and an account of the journey back.

At the end of the report, Piccolomini informs the emperor of a recent letter from the Archbishop of Trier to the pope concerning the crusade, and sent back his recommendation to the emperor on how to react to this letter.

Date, recipient and format

In the manuscripts, the report is dated on the Feast of the Nativity of the Holy Virgin, i.e., 7 September 1456.

The addresse is the emperor.

The format is a report from an ambassador to his prince concerning a diplomatic mission on the prince's behalf.

Text

The report to the emperor is -mostly -contained as letter nr. 94 in an "official" collection of Piccolomini's letters from the period of his episcopate ("in episcopatu"), probably produced under his personal supervision as pope.

Manuscripts

The collection of letters "in episcopatu" are contained, among others, in the following manuscripts: As an individual text, the report is included in the following manuscript:

 Firenze /
 Roma / Biblioteca Apostolica Vaticana Chis. J.V.175, 1 ff. 111v-120v (Z)

Editions

The collection of letters "in episcopatu" appears not to have been printed as such.

The report to the emperor was printed by Cugnoni, on the basis of the Chis. J.V.175 manuscript:

 Aenea Silvii Piccolomini Senensis: Opera inedita. Cur. Josephus Cugnoni. Roma, 1883, pp. 122-126

Present edition

The edition is based on all five manuscripts listed above.

Pagination is after the Plut. 54.19. 2 Situation at the papal court

Bibliography

Appointment of papal legates

[2] The day before we entered Rome, the Roman Pontiff appointed four legates, the Cardinal of Avignon 2 to France, the Cardinal of San Pietro 3 to England, the Cardinal of Esztergom 4 to Hungary, Hungary, and the Cardinal of Sant'Angelo to the whole of Germany. 5 The last one was also given the task to lead a land army against the Turks. When travelling, we wrote to you about the legates, naming some about whom we had erroneous information from people coming from the City. 6 It is no wonder that we could not obtain correct information outside the City since we had such difficulty in getting it when we were inside the walls. [3] The Cardinal of Sant'Angelo will first travel to Your Mansuetude to consult with you about the protection of religion. As far as we can ascertain, his intention is not to summon or conduct a conference on the matter for he does not expect anything good to come from that. 1 Instead, he plans to address -by letter or by envoy -the princes and the cities 2 on an individual basis and to demand of them to aid the Church in the present crisis with the number of soldiers [previously] charged to them. If they cannot send these, then they should send as many men as they want to, as long as they do not completely fail the Catholic Faith.

Pope's crusading zeal

[4] This matter is close to Our Most Holy Lord's 3 heart, and day and night he only thinks about how to destroy the Turks. He even says in private and in public that he is convinced he will not die before Constantinople has been regained. All are awed by this Father's great faith, and since he has foreseen other things that actually happened, 4 they also trust him in this matter, believing him to talk in a prophetic spirit. 1 Bearing in mind the failure of the diets of Regensburg, Frankfurt and Wiener Neustadt in 1454 and 1455 2 "communitates" 3 I.e., the pope 4 He had actually predicted that he would become pope, something everyone considered to be quite unlikely

Jacopo Piccinino and King Alfonso V

[5] A major impediment to his plans, however, is Jacopo Piccinino, who has invaded the Sienese territory with a large force of calvary and infantry. He greatly hopes to conquer this imperial city and has already decided to call himself Duke of Siena. 1 When the pope tried to block his endeavours and sent large troops against him, the King of Aragon became much upset. He came to Jacopo's assistance and is still helping him, to the great harm of Siena and the Roman Church. But a short while ago, the king caught a fever, and his survival was in doubt. Then he vowed to God that if he regained his health, he would go to war against the Turks. When, soon afterwards, he regained his health, he summoned his princes and nobles to a meeting, where he made a public announcement of his vow. He also told them that he intended to prepare the largest and strongest possible fleet against Mehmed, to personally lead it, and to fight for the protection of the Faith and -if necessary -to die. 2 He also decided to take the cross on the [Feast of the] Nativity of the Holy Virgin Mary, 3 and many nobles made the same vow. He then informed Our Most Holy Lord about his decision and promised to negotiate a settlement between the Sienese and Jacopo Piccinino 4 so that Jacopo would restore everything to the Sienese that he had taken and ask the pope for forgiveness. Some, however, greatly doubt the promises of this king, especially since they say that he is not yet fully recovered.

Duke of Burgundy

[6] In his letters, the Duke of Burgundy, 5 however, daily confirms that if only he is in good health, he will under all circumstances be ready with his people on the appointed day, and he declares that he will certainly not bring less than 16,000 armed men with him.

[7] Thus reassured, the Supreme Pontiff this morning celebrated mass in Saint Peter's. Then with great devotion and many tears he gave the cross to two cardinals, viz. the Cardinal of Avignon 6 and and the Cardinal of Sant'Angelo, 7 and decided that these cardinals should depart for their provinces 8 as soon as possible. [8] Interea de Francia felicia 1 nova allata 2 sunt. Nam rex gentis illius oratores constituit, qui oboedientiam intra dies paucos allaturi sunt. Cardinalis autem Rothomagensis ex eo regno curiam repetens litteras praemisit, quibus significat praelatos regni 3 Franciae inclinatissimos esse domino nostro pragmaticamque illam sanctionem, quam inter se tenebant, ex apostolicae sedis arbitrio moderari velle. Atque hic est modo curiae status.

[9] Veniendum nunc est ad res nobis commissas, quas etiam breviter referemus. Intrantibus nobis urbem obviam venere legati omnium principum, qui hic erant, omnes episcopi et omnium cardinalium comites 4 et denique familia papae. De sero autem misimus ad sanctissimum dominum dominum nostrum dicentes, quod ante publicam audientiam vellemus secrete 5 alloqui suam 6 sanctitatem. Ipse vero nobis significavit, quia 7 libenti animo nos audiret 8 , sed caveremus, ne pacta pacta cum eo propter oboedientiam facere vellemus, quia nullo pacto conditionalem oboedientiam susciperet. Dura nobis significatio visa est. Accessimus tamen sanctitatem suam die sequenti, et quae videbantur de sinceritate tuae majestatis erga suam beatitudinem exposuimus. Deinde cum omni modestia, qua potuimus, petitiones tuas annectere 9 curavimus: de pecunia debita, de reservationibus ecclesiarum, de decima, de nominationibus 10 , de collationibus beneficiorum, de primariis precibus, et de aliis pluribus causis, quibus ad longum enarratis sua sanctitas multa in laudem tuam retulit asserens eidem 11 sese magnopere affectum.

1 foelia X 2 alta Z 3 regi Z 4 familiae Z 5 secreta U 6 alloqui suam : suam alloqui Y 7 omit. Y 8 auditurum Y 9 ammittere X 10 ecclesiarum de … nominationibus omit. X 11 ita X

France

[8] In the meantime, good news arrived from France. The king of that people 1 has appointed ambassadors to bring [his declaration of] obedience very soon. But the Cardinal of Rouen, 2 returning from the kingdom to the curia, has sent a letter ahead stating that the prelates of the Kingdom of France are very sympathetic towards Our Lord 3 and desire to modify the Pragmatic Sanction, to which they adhere as a group, on the basis of the wishes of the Apostolic See.

This is the situation at the curia.

Affairs of the Empire

[9] We must now come to the affairs entrusted to us, which we shall report on, though briefly.

Pope's refusal to negotiate before the declaration of obedience

When we entered the city, we were met by the legates of all the princes present in Rome, all the bishops, and the households of the cardinals and the pope. 4 In the evening, we sent a message to Our Most Holy Lord saying that we desired to meet His Holiness before the public audience and speak with him on certain confidential matters. He let us know that he would gladly hear us, but that we should not want to make any agreements with him before the declaration of obedience because in no way would he accept a conditional obedience. We thought that this message was harsh. Still, we met with His Holiness on the following day and assured him of Your Majesty's sincere [devotion] towards His Beatitude. Then, as respectfully as we could, we, at length, presented your petitions concerning the money owed [to you], the reservations of churches, the tithes, the appointments, the granting of benefices, the first requests and several other matters. 5 Afterwards, the pope said much in your praise, declaring that he had great affection for you. [10] Ad petitiones autem dixit, quia 1 post praestitam oboedientiam responderet 2 , nec dubitare deberemus 3 , quin omnia factura esset sua sanctitas 4 , possibilia saltem et honesta. Sed certi esse deberemus, quod ipse propter oboedientiam suscipiendam nullo modo quidquam 5 promitteret. Sciret enim illam sibi debitam 6 esse et mori mallet quam sub conditione recipere. Fuisse quoque apud se regis Aragonum legatos ait et aliorum principum oratores, qui cum pacisci super oboedientia 7 vellent, repulsam habuere. Itaque nollet sua sanctitas {66r} ante praestitam oboedientiam quidquam promittere, sed certa esse deberet imperialis mansuetudo, quia si umquam sedit aliquis in sede Petri imperatoriae majestati favens, ipse 8 ille esset, qui omni studio conari vellet tuae sublimitati complacere.

[11] His ita dictis fuimus admodum anxii, sed cum videremus aliter fieri non posse et, quod scandalum esset, hinc recedere oboedientia non praestita, deliberavimus oboedientiam ipsam praestare ac deinde petitiones prosequi, cum secus fieri non posset.

[12] Tenuit papa post biduum consistorium publicum 9 10 , in quo sicut de more est, sermonem habuimus et oboedientiam praestitimus. Ibi de laudibus tuis papa multa 11 disseruit, et quoniam de rebus Turcorum mentionem fecimus, juxta 12 conclusionem habitam 13 in dieta 14 coram serenitate tua habita [START_REF]{66v} expedito omnes litteras opportunas et omnes favores impartiri, quibus tua majestas promissam sibi decimam colligere possit[END_REF] , multum [START_REF]ad gratias. Itaque putamus adhuc aliquid de nominationibus obtinere[END_REF] [10] Concerning the petitions, he said that he would respond after the declaration of obedience and that we should not doubt that His Holiness would do everything [for you], as far as possible and honourable. We should know, however, that he could make no promises before the declaration of obedience he was to receive. For he knew that the obedience was owed to him, and he would rather die than receive it conditionally. He said that also the legates of the King of Aragon1 as well as ambassadors from other princes had met with him and wanted to negotiate their obedience but were rebuffed. Thus, His Holiness did not want to promise anything before the declaration of obedience, but Your Imperial Mansuetude could be sure that if ever somebody occupied Saint Peter's See who favoured the Imperial Majesty, it was him, and that he would endeavour with all his might to accommodate Your Highness.

[11] His words left us perplexed, but when we realized that it could not be done otherwise and that it would cause a scandal if we left without making the declaration of obedience, we decided to make this declaration and afterwards pursue the matter of the petitions since it could not be done otherwise.

Declaration of obedience

[12] Two days afterwards, the pope held a public consistory in which we gave the traditional oration and made the declaration of obedience.2 Afterwards, the pope said much in your praise, and since we had spoken on the Turkish matters, on the basis of the decisions made in the diet3 held in the presence of Your Serenity, he greatly commended yours and the nation's intentions and assured that he would do all he could to bring about the destruction of the Turks.

[13] Sequentibus diebus dedimus in scriptis omnes petitiones tuas et iteratis vicibus cum sanctissimo domino nostro fuimus, qui post deliberationem habitam super 1

Emperor's petitions

Money owed to the emperor

[13] The following days, we handed over your petitions in writing and met with Our Most Holy Lord several times. After deliberating on the matter of the money [owed to you], 1 he answered that he would gladly satisfy your wish, but that it was absolutely impossible for him to do so now, or even to send just a small amount, for the truth was that he had found not one single coin left by his predecessor, though he had found some worked silver, cloth, books, and furnishings. 2 But he himself had had to spend more than 100,000 golden ducats on subduing Jacopo Piccinino, that he had borrowed from merchants. Moreover, he now had to spend much money for the expenses of the legates, money which he did not yet know from where to get. He, therefore, asked Your Majesty not to blame him if he was unable to honour the debt, now.

Reservations of ecclesiastical offices

[14] Concerning the reservations of episcopal appointments, he would certainly accommodate you when churches and monasteries in your dominions fell vacant. 3 But Your Serenity would have to take care not to nominate unworthy persons since that would be a sin on your part. He himself would always accommodate you even if he knew that he would be sinning. 4 He declined, however, however, to issue a letter on this matter, saying that it would be unbecoming for the Apostolic See to do so. But he will reserve the churches, monasteries and deaneries, we have petitioned for, to the disposition of the Apostolic See, so that it can dispose of them as you require when they become vacant.

1 25.000 or 18.000 ducats (Voigt, III, p. 162), out of the total sum promised by Pope Eugenius III to the emperor in 1447 in connection with his recognition of the Roman pope and the rejection of the antipope, Felix V (Toews, p. 266) 2 Pope Nicolaus V had indeed left a very difficult financial situation to his successor, but it defies belief that there would not have been a single coin left. So either Calixtus exaggerated his financial distress, or there might have been some dubious manipulations with the money left by Nicolaus after his death and before the accession of Calixtus 3 Voigt, III, p. 162: Ferner war in jenen Privataudienzen von den hundert Benefizien die Rede, deren Vergabung dem Kaiser in seinen Erblanden reserviert bleiben sollte 4 A quite remarkable statement for a pope to an emperor quas mihi lutea Roma reservavit, et timeo, ne nimis hic detinear. Ego Johannes interim, quae restant agenda, promoveo, nec aliud desiderium nostrum est, quam ut 1 hinc celeriter absolvamur, absolvamur, quo facto alter majestatem tuam, alter ad ecclesiam suam redibit.

[20] Concerning the first petitions 2 , the pope promised to make appropriate provisions, as we requested.

[21] Concerning these matters, we said much to the pope and heard much from him, especially about the pecuniary matter and the tithes as well as about the confirmation of your right of nomination to a number of churches, which we requested. Concerning the pecuniary matter, the pope finally said that we should not insist further since we were requesting something impossible and trying in vain to press oil from a hard rock where there was none. But since the Cardinal of Saint'Angelo 3 was going to Your Majesty with plenary powers in the matter of tithes and indulgences, he would charge him with allocating to Your Serene Majesty a part -and if possible a major part -of the money coming from them, but only in such a way that no scandal might arise. He bade us be content with this. Thus, we must report back to you a discharge of our tasks 4 without results and with little honour.

[22] Concerning the tithes and the promises of churches, the pope implored us -by the heart 5 of Our Lord Jesus Christ -not to insist further since he could not in conscience do what we requested. He declared that he had received the papacy not for destruction, but for edification, 6 and that his whole intention was only to reform the Universal Church. And raising his eyes to Heaven, as if speaking directly with God, he implored Divine Piety to remove him rather than to allow any scandal to arise through him. Then he imposed complete silence upon us on these two matters. But we are hoping to obtain some letters from His Beatitude providing for the tithes, maybe not such as we wish, but then at least such as we can obtain, so that this matter will not be a complete failure.

[23] The various other petitions entrusted to us by Your Serenity we wrote down in a document which we presented to His Beatitude, who gave it for examination to the Bishop of Zamora, 7 head of the chancellery. We are not expecting any answer on these matters while his report on them is pending.

[24] This is what we have achieved until now. We have been unable to obtain more. We have shown diligent care but to no avail. In the meantime, I, Bishop of Siena, have fallen sick with a fever caused by the filth of Rome, and I fear that I shall be detained here for some time. In the1 omit. X 2 Primarii preces. Voigt, III, p. 163: Die "ersten Bitten" des Kaisers schien er indess nicht für ärgerlich zu halten 3 Juan Carvajal 4 "quitantias" 5 "per viscera" 6 2. Corinthians, 10, 8; 13, 10 7 Juan de Mella (1397-1467): Curial. Bishop of Zamora 1440-1465. Appointed cardinal in 1458 meantime, I, Johann, pursue the remaining matters. Our only wish is to finish here quickly, and then one of us will return to Your Majesty, and the other to his Church. 1

;

  Pastor I, pp. 675-676; Toews, pp. 265-267; Voigt, III, pp. 157-163 2 Calixtus III [Alfons de Borja] (1378-1458): Pope from 1455 to his death in 1458. The first Borgia pope 3 Nicolaus V (Tommaso Parentucelli) (1397-1455): Pope from 6 March 1447 to his death 4 Friedrich III (Habsburg) (1415-1493): Duke of Austria (as Friedrich V) from 1424. Elected King of Germany and Holy Roman Emperor in 1440, crowned emperor in Rome in 1452 5 It was the third in a series of German diets dealing, among other things, with the military response to the Fall of Constantinople in May 1453. The first was the Diet of Regensburg, May 1454, and the second the Diet of Frankfurt, October 1454. The Diet of Wiener Neustadt began in February 1455 and ended in April 6 Sierck, Jakob von (1398-1456): Archbishop of Trier and Prince Elector from 1439 to his death and imperial chancellor of Friedrich III from 1441

AND TRANSLATION Epistola LXXXXIIII de oboedientia Calisto praestita, de Jacobo Picinino, de rege Aragonum et de plerisque aliis privatis rebus

  Geschichte der Päpste im Zeitalter der Renaissance. 16 vols. Freiburg i.B., 1886-1933 Pius II: Commentarii rerum memorabilium quae suis temporibus contigerunt. [1464]  Commentarii rervm memorabilivm que svis temporibus contigervnt. Ed. A. van Heck. 2 vols. Città del Vaticano, 1984. (Studi e testi; 312-313)  Pius II: Commentaries. Ed. and transl. by M. Meserve and M. Simonetta. Vols. 1 ff. Cambridge, MA, 2003 ff. (The I Tatti Renaissance Library) Pridie quam urbem ingrederemur, designavit Romanus pontifex legatos quattuor ex ordine, cardinalium 6 , Avinionensem in Galliam, sancti Petri in Angliam, Strigoniensem in Hungariam, sancti angeli per universam Germaniam 7 . Huic enim 8 cura commissa est terrestris exercitus contra Turcos educendi. Nos ex itinere de legatis scribentes, tibi nonnullos alios nominavimus ab aliis decepti, qui ex urbe veniebant, nec mirum si extra urbem 9 veri cognitionem habere nequivimus, quando et et intra moenia positi vix tandem veri periculum fecimus.

	II. TEXT [1] {64v} Aeneas 1 , episcopus Senensis, et Johannes Inderbachius 2 serenissimo imperatori Friderico 3
	salutem plurimam dicit. Ingressi Romam, serenissime atque 4 invictissime Caesar, nihil adhuc
	majestati tuae rescripsimus. Fuerunt enim res pendulae usque nunc et incertae penitus. Modo,
	quia responsum aliquod habemus, non tamen omnino resolutum, visum est et statum hujus curiae
	et quae per nos gesta sunt hactenus mansuetudini tuae 5 reserare, deinceps, quae sequentur, non
	negligemus. Res in hunc modum se habent:
	Pius II: Orationes. [1436-1464] 1856-63 7. Sigla and abbreviations U = Firenze / Biblioteca Medicea-Laurentiniana / Plut. 54.19 V = Roma / Biblioteca Apostolica Vaticana / Ott. lat. 347 X = Roma / Biblioteca Apostolica Vaticana / Urb. Lat. 401 Y = Roma / Biblioteca Apostolica Vaticana / Vat. lat. 1787 Z = Roma / Biblioteca Apostolica Vaticana / Chis. J.V.175 [2] 1 Eneas U, Y 2 Inderbach Z 3 III. add. Z 4 ac U 5 mansuetudini tuae : tuae mansuetudini Z 6 cardinalem U	Berlin,

1 Manuscript written, not very accurately, by Jo. Gabinium Triviensem, 1465. Listed by Cugnoni, p. 13 Pastor, Ludwig:  Collected Orations of Pope Pius II. Edited and translated by Michael von Cotta-Schønberg. 12 vols. 2019-2020 o "Non habet me dubium" (9 January 1447, Rome) [11] o "In hoc florentissimo" (25 February 1455, Wiener Neustadt) [23] o "Si mihi" (25 March 1455, Wiener Neustadt) [24] o "Optasset" (23 April 1455, Wiener Neustadt) [25] o "Solent plerique" (13 August 1455, Rome) [26] o "Modestius" (6 June 1456, Naples) [27] Toews, John B.: Emperor Frederick III and his Relations with the Papacy from 1440 to 1493. University of Colorado, Ph.D., 1962 Voigt, Georg: Enea Silvio de' Piccolomini als Papst Pius der Zweite und sein Zeitalter. 3 vols. 7 sancti angeli … Germaniam omit. U 8 omit. Y 9 veniebant nec … urbem omit. X Letter

94 on the declaration of obedience to Calixtus, on Jacopo Piccinino, on the King of Aragon, and and on several other, private, matters

  Since we arrived in Rome, Most Serene and Unvanquished Caesar, we have not written to Your Majesty since, until now, matters have been fluid and uncertain. But now that we have an answer, though not quite final, we have decided to report to Your Mansuetude on the situation at this court1 and on what we have achieved until now -without neglecting what will happen later. This is how the matter stands:

	1. Introduction
	[1] Aeneas, Bishop of Siena, and Johann Hinderbach send many greetings to the Most Serene
	Emperor, Friedrich.

  Cardinalis ergo sancti Angeli ad tuam mansuetudinem iter imprimis faciet ac de tutanda religione cum eadem consilium capiet. Ejus sententia est, quantum intelligimus, nullum conventum indicere aut prosequi -{65r} nihil enim ex his bene sperat -sed gerit in animo per litteras ac nuntios principes ac communitates singillatim 1 requirere, ut pro designato sibi militum numero ecclesiasticae necessitati subveniant. Quod si nequeant praescriptas copias mittere, quas possint 2 quasque volunt, saltem gentes mittant, catholicam fidem omnino non deserant.[4] Res est sanctissimo domino nostro admodum cordi neque dies noctesque aliud meditatur, nisi quo pacto Turcos perdere possit, et ait secrete et palam certam se fidem tenere, quia non morietur ante recuperatam Constantinopolim. Mirantur omnes tantam hujus patris fiduciam, et quoniam res alias praedixit antequam 3 fierent, in hac quoque fidem ei non abnuunt prophetico spiritu ea dici putantes.

	1 I.e. the papal curia 2 Alain de Coëtivy (1407-1474): Bishop of Avignon. Cardinal in 1447
	1 sigillatim X 2 possunt Z 3 quam U

3

Nikolaus of Kues (1401-1464): Appointed cardinal in 1448, and Prince Bishop of Brixen in 1450

4

Dénes Szécsi (ca. 1410-1465): Archbishop of Esztergom from 1440 to his death. Appointed cardinal 1439 5 Cardinal Juan Carvajal (ca. 1400-1469): Appointed cardinal in 1446

6

The two ambassadors had apparently written to the emperor on the way to Rome

[3]

  [5] Praestat tamen non modicum impedimentum desiderio suo Jacobus Picininus, qui cum magna manu militum equestrium ac pedestrium agrum Senensem ingressus non parvam spem habuit urbem illam imperialem sibi subjicere jamque se ducem Senarum 1 constituerat appellare, cujus conatus cum papa refringere conaretur missis adversus eum non parvis copiis, indignatus est parumper rex Aragonum, qui Jacobum defendere nixus est et in hanc usque diem defendit non sine magno Senensium ac Romanae ecclesiae damno. Proximis tamen diebus cum febricitasset rex ac salus sua venisset in dubium, Deo vovit, si sanitatem recuperaret, omnino se contra Turchos arma sumpturum, nec multo post resumpta bona 2 valitudine principibus ac optimatibus suis in contionem vocatis, quae voverat palam fecit publiceque contestatus est 3 , quam possit magnam et potentem adversus Maumethum 4 classem se instituere 5 velle eamque per se ducere ac pro tuenda fide propria in persona militare et 6 -si necesse fuerit -mori, statuens in die nativitatis sacratissmae sacratissmae virginis Mariae crucem assumere, cum quo multi nobiles votum fecere, misitque 7 ad sanctissimum dominum nostrum 8 deliberationem suam, et deinde concordiam inter Senenses et Jacobum Piccininum tractaturum se promisit, ita ut reddat Jacobus Senensibus omnia, quae abstulit, et a papa veniam petat. Sunt tamen aliqui, qui non parum dubitant de 9 promissionibus hujus regis, et praesertim cum ejus valitudinem non omnino solidam dicant.

	1 senatum Y 2 omit. Z 3 omit. Z 4 Maumetem X; Maumethem Z 5 instruere Z 6 ac Y 7 misit U 8 omit. V 9 omit. Z 10 Borgundiae V, X 11 in dies Y 12 omit. X 13 omit. X 14 arriperent U; arripient X, Z

[6] Dux autem Burgundiae 10 suis litteris dietim 11 affirmat in tempore debito absque ulla exceptione, si modo sanus fuerit, cum suis gentibus paratum se fore et affirmatur, quia infra XVI milia hominum armatorum secum {65v} nequaquam adducet.

[7] His rebus confortatus summus pontifex hoc mane rem divinam in sancto Petro fecit. Deinde cum maxima devotione multisque lacrimis duos cardinales, Avinionensem scilicet et 12 sancti angeli, aliquos episcopos et 13 plures nobiles cruce signavit statuens, ut quam primum cardinales ipsi in suas provincias iter arripiant 14 .

  commendavit propositum[START_REF]Remissionem annatae propter abbatem sancti Lamberti renitentibus 3 cardinalibus nulla ratione potuimus obtinere, sed domino Ulrico Riedrer 4 concessa est plena remissio[END_REF] tuum et nationis 18 , et confirmavit sese omnia facturum, quae ad exterminium Turcorum tendunt.

	1 omit. Y 2 responsurum Y 3 debemus X 4 dubitare deberemus … sanctitas : dubitandum facturam suam sanctitatem Y 5 quidcumque U 6 sibi debitam : debitam sibi Z 7 obedientiam X 8 que add. U 9 omit. X 10 consistorium publicum : publicum consistorium V 11 omit. Z 12 iusta X 13 omit. Y 14 in dieta omit. X 15 habitam X, Y 16 omit. X 17 prepositum Z 18 et nationis omit. X

  facto pecuniarum respondit, quod libenter vellet desiderio tuo satisfacere, sed impossibile esset ei 2 nunc quovis modo vel minimam pecuniam mittere, quia veritas esset, quod de suo praedecessore neque unum 3 nummum invenisset, quamvis argentum celatum et pannos et libros et ornamenta domus quamplurima reperisset. Ipse autem ad comprimendum Jacobum Picininum supra centum milia aureorum exposuisset, quae mutuo ex mercatoribus recepisset, et nunc legatis 4 pro sumptibus faciendis 5 non parum argenti traditurus esset, quod adhuc nesciret, unde recipere. Rogabat igitur majestatem tuam, ne sibi imputaret, si modo huic debito pecuniario satisfacere non posset.[14] De reservationibus ecclesiarum respondit, quod vacantibus ecclesiis et monasteriis tuorum dominiorum indubitanter tibi complaceret. Videret tamen 6 tua serenitas, ne personam indignam nominaret, quia peccatum tuum esset.7 Ipse autem, etiam si certe sciret se peccare, tibi semper morem gereret. Litteras autem super his dare negabat, apostolicae sedi indecorum esse dicens. Placet sibi tamen ecclesias et monasteria ac praeposituras, pro quibus supplicavimus, apostolicae sedis dispositioni reservare, ut cum vacaverint, ad tuam requisitionem de illis disponere possit.

	1 de U 2 omit. Z 3 minimum X 4 legatus X 5 omit. X 6 omit. Y 7 omit. U

CO, I,

(Meserve, I, pp. 143-147) 2 Voigt, III, pp. 160-163; Pastor, I, p. 511-512

The Duke of Savoy, Amédée VIII (1383-1451)

See Piccolomini's oration "Non habet med dubium"[11] from January 1447

Nicolaus V [Tommaso Parentucelli]: Bishop of Bologna. Cardinal 1446. Elected pope in 1447

Pastor, I, p. 673: Eine besonders glänzende Abordnung sandte König Alfonso von Neapel; deren Versuch über die Gehorsamsleistung zuerst verhandeln zu wollen, war indes schlecht geeignet, das bisherige gute Verhältnis zwischen dem neapolitanischen König und Alonso de Borja zu erhalten. Der Papst wies die ungebührliche Forderung Alfonsos ebenso entschieden zurück wie später eine ähnliche Zumutung von seiten der Gesandten Kaiser Friedrichs III

Voigt, III, p. 159: … der alte Papst … sass … fester auf dem apostolischen Stuhle, den kein Concil und kein Gegenpapst ihm mehr streitig machten

See Piccolomini's oration "Solent plerique"[26]

Piccolomini: Oration "Solent plerique"

See 1 st report in the present series

Alfonso V

See Piccolomini's oration "Solent plerique"[26]

The Diet of Wiener Neustadt, 1454, see Piccolomini's orations "In hoc florentissimo" [23], "Si mihi" [24], "Optasset" [25], all from 1454

Piccolomini had been released from his service to the emperor, likely so that he could pursue his ecclesiastical career in Rome, including his obtaining the cardinalate, which would also be in the emperor's interest

Concerning the tithes 1 he considered that there was absolutely no reason to issue new letters letters as long as the present collection of tithes last, levied for the purpose of protecting the Church against the Turks. But when that business is finished, he promises to issue new letters and to grant all the favours making it possible for Your Majesty to collect the tithes you have been promised.

Other affairs

[16] Concerning the granting of benefices, 2 he would promise nothing. Concerning the appointments, he said that he not yet decided to grant expectative favours, but when he opened that gate, he would be more generous to Your Majesty than to any other prince. And he did intend to later open up for such favours. So we think that we might still obtain something concerning the appointments.

[17] Because of the opposition of the cardinals, we were completely unable the obtain the remission of annates 3 for the Abbot of Saint Lambrecht, 4 but Lord Ulrich Riederer 5 was given a full full remission.

[18] The petition for his Lordship of Tiberias 6 for confirmation of the grant of the abbey of Ossiach in commendam, made by me, Bishop of Siena, has been approved, but the letter cannot be expedited because a great sum of money is needed for the annates and the minuta servitia. 7 [19] Concerning the matter of the Dean of Berchtesgaden, 8 we have been unable to achieve anything as yet because His Lordship of Salzburg 9 has his people here at the curia who oppose the matter strongly and have the support of the Cardinal of San Marco. 1 But we are stilling working on on the matter and may achieve something.

[20] Super primariis precibus pollicitus est papa opportune providere, quemadmodum supplicavimus.

[21] Multa super his rebus et diximus papae et audivimus ab eo, et maxime super re pecuniaria ac decimarum necnon super confirmatione, quam petebamus ecclesiarum ad tuam nominationem conferendarum. Denique super re pecuniaria respondit papa, ne ultra instaremus, quia impossibilem rem peteremus 2 et frustra conaremur de saxo durissimo, ubi non est, oleum extrahere. Sed quia venturus esset cardinalis sancti angeli ad majestatem tuam cum plena potestate super facto decimarum et indulgentiarum, ei committere vellet, ut 3 de pecuniis, quae inde provenient, tuae serenitati aliquam partem tribuat, et -quanta 4 fieri posset -majorem, ita tamen ne scandalum oriatur, atque in hoc voluit nos esse contentos. Et ita quietantias sine fructu et cum modico honore reportabimus.

[22] Super decima vero et ecclesiarum promissione obtestatus est nos per viscera domini nostri Jesu Christi, ne ultra instaremus 5 , quia non 6 posset salva conscientia sua, quod peteremus efficere, efficere, asserens se papatum non in destructionem, sed in aedificationem recepisse 7 , et quod intentionis suae nihil aliud esse 8 quam universalem ecclesiam reformare, et respiciens caelum quasi cum Deo loquens divinam pietatem deprecatus est, ut se potius de medio auferat 9 quam scandalum aliquod per eum {67r} fieri permittat. Itaque super his duabus rebus nobis omnino silentium imposuit. Speramus tamen 10 aliquas litteras ex sua beatitudine obtinere per quas, si non ut volumus, saltem ut possumus, decimae consulatur, ne penitus ruat.

[23] Alias diversas supplicationes per tuam serenitatem nobis commissas in rotulo quodam praesentavimus suae beatitudini, quae eas episcopo Zamorensi cancellariam regenti examinandas dedit, nec dum facta relatio est, expectamus 11 super illis responsionem.

[24] Haec egimus in hanc usque diem, nec plura obtinere potuimus. Adhibuimus 12 exactam diligentiam, sed nihil profuit. Interea ego, episcopus Senensis, aegrotare coepi propter febres,


Meghyn Bienvenu
email: meghyn.bienvenu@labri.fr

A Short Survey on Inconsistency Handling in Ontology-Mediated Query Answering

Keywords: Inconsistency Handling, Ontologymediated Query Answering, Description Logics

Introduction

It is widely acknowledged that real-world data is plagued by numerous data quality issues, among them the presence of erroneous facts. While already a serious issue for 'plain' databases, the problem of handling imperfect data is even more critical in the setting of ontologymediated query answering (OMQA), where an ontology is used to enrich the data with domain knowledge. Indeed, even a single erroneous fact can provoke a logical inconsistency, thereby rendering classical OMQA semantics (based upon first-order logic) useless, since everything is entailed from a contradiction. This has motivated researchers from knowledge representation and reasoning, and especially those from the description logic (DL) community, to study a variety of approaches for handling inconsistent data in OMQA, adapting and extending techniques initially proposed for databases. Now that there has been over a decade of research on inconsistency handling in OMQA, the time is ripe to take a step back and evaluate the progress that has been made and what remains to be done.

In this paper, we will try to summarize what is now quite a large body of work related to inconsistency handling in OMQA. Our treatment will necessarily be incomplete. We will concentrate on the case in which inconsistencies are due to errors in the data (i.e., we assume the ontology has been properly debugged) and mainly discuss how inconsistency-tolerant semantics can be used to obtain meaningful information from inconsistent knowledge bases. While our focus will be on ontologies formulated using DLs, the inconsistency-tolerant semantics presented in this chapter are language-agnostic and can be applied to any ontology language. In particular, there have been several works (see e.g. [START_REF] Lukasiewicz | Inconsistency handling in Datalog+/-ontologies[END_REF][START_REF] Lukasiewicz | From classical to consistent query answering under existential rules[END_REF][START_REF] Baget | Inconsistencytolerant query answering: Rationality properties and computational complexity analysis[END_REF][START_REF] Lukasiewicz | Complexity of inconsistency-tolerant query answering in Datalog+/-under cardinality-based repairs[END_REF]) which have explored such semantics for existential rules (aka Datalog +/-) [START_REF] Calì | A general datalogbased framework for tractable query answering over ontologies[END_REF][START_REF] Mugnier | An introduction to ontologybased query answering with existential rules[END_REF], which constitute another prominent class of ontology languages. Our treatment is based upon (and complementary to) a much more detailed tutorial chapter [START_REF] Bienvenu | Inconsistency-tolerant querying of description logic knowledge bases[END_REF] and incorporates some more recent literature and perspectives for future work.

Preliminaries

We briefly recall here some useful DL terminology and notation, and we direct readers to [START_REF] Baader | An Introduction to Description Logic[END_REF] for a comprehensive introduction to DLs. Throughout the paper, we shall assume that K = T , A is a DL knowledge base (KB) composed of a TBox T and ABox A. As usual, the TBox T will be a finite set of axioms whose syntax is dictated by the chosen DL, while the ABox A is a finite set of assertions (ground facts). Our running example (borrowed from [START_REF] Bienvenu | Inconsistency-tolerant querying of description logic knowledge bases[END_REF]) uses the following KB formulated in the core dialect of DL-Lite, a popular family of lightweight DLs [START_REF] Calvanese | Tractable reasoning and efficient query answering in description logics: The DL-Lite family[END_REF]: The ABox A univ contains assertions about specific people and courses:

Example
A univ ={Prof(sam), Lect(sam), Fellow(sam), Prof(kim), Lect(kim), Fellow(jane), Fellow(alex), Teaches(cs34, jane), Teaches(alex, cs48)}

Here for example, the assertion Prof(sam) state that sam is a professor, while Teaches(alex, cs48) states that alex teaches cs48.

Every DL KB can be translated into a first-order logic formula, and DL semantics corresponds to classical first-order semantics, in which interpretations give meaning to the basic symbols. We denote by I |= α that the interpretation I satisifies the (ABox or Tbox) statement α. An interpretation I that satisfies all statements of the KB T , A is called a model of T , A , and a KB is said to be consistent (or satisfiable) if has at least one model.

An ABox A is T -consistent if the KB T , A is consistent, and otherwise, it is T -inconsistent.
We recall that a conjunctive query (CQ) takes the form of a conjunction of relational atoms where some of the variables occurring in atoms may be existentially quantified. In the DL setting, the relations occurring in atoms will be either concept or role names. An instance query (IQ) is a CQ which has a single atom and no existentially quantified variables. The arity of a CQ is the number of its free variables. Under classical OMQA semantics, we are interested in finding certain answers of a CQ q w.r.t. a KB T , A , i.e. those tuples a of constants from A of the same arity as q such that q(a) (i.e. the first-order sentence obtained by substituting a for the free variables of q) holds in every model of T , A . The notation K |= q(a) indicates that a is a certain answer to q over K. We call a subset C ⊆ A a Tsupport of q(a) if C is T -consistent and T , C |= q(a).

Inconsistency-Tolerant Semantics

As mentioned in the introduction, the usual first-order semantics of DLs does not provide any useful information when the KB is inconsistent, as everything can be inferred from a contradiction. To address this limitation, several inconsistency-tolerant semantics have been proposed with the aim of returning meaningful answers to queries posed over inconsistent KBs.

A key notion that underlies many of the proposed semantics is that of a repair, which intuitively captures the different ways of restoring consistency while retaining as much of the original information as possible. If we use set inclusion to select the maximal ABoxes, as was proposed in [START_REF] Lembo | Inconsistency-tolerant semantics for description logics[END_REF] and many subsequent works, then repairs can be formalized as follows.

Definition 1 An (ABox) repair of an ABox A w.r.t. a TBox T is an inclusion-maximal subset of A that is T -consistent. We use Rep(A, T ) to denote the set of repairs of A w.r.t. T , which we abbreviate to Rep(K) when K = T , A .

Example 2

The KB T univ , A univ is inconsistent and has 12 repairs. For example, it is easily verified that the following two ABoxes are both repairs: R 1 = {Prof(sam), Prof(kim), Fellow(jane), Fellow(alex), Teaches(alex, cs48)} R 2 = {Fellow(sam), Lect(kim), Teaches(cs34, jane), Fellow(alex), Teaches(alex, cs48)} Each repair is T -consistent, so it is possible to query a repair using classical semantics. The difficulty, however, is that there are typically several different repairs of an inconsistent KB, so we need to decide how to combine the answers obtained from the different repairs. Arguably the most natural approach is to require that a tuple be a certain answer no matter which repair is considered. This idea is captured by the AR semantics, which was first defined in [START_REF] Lembo | Inconsistency-tolerant semantics for description logics[END_REF] and can be seen as the OMQA analog of the consistent query answering approach long studied in the database literature [START_REF] Arenas | Proceedings of PODS[END_REF][START_REF] Chomicki | Consistent query answering: Five easy pieces[END_REF][START_REF] Bertossi | Database Repairing and Consistent Query Answering[END_REF].

Definition 2 (AR semantics) A tuple a is an answer to q over K = T , A under the AR (ABox Repair) semantics, written K |= AR q(a), just in the case that T , B |= q(a) for every repair B ∈ Rep(K).

A more conservative semantics, termed the IAR semantics [START_REF] Lembo | Inconsistency-tolerant semantics for description logics[END_REF], is obtained by querying the intersection of the repairs (or equivalently, the set of assertions not participating in any minimal inconsistent subset). Definition 3 (IAR semantics) A tuple a is an answer to q over K under the IAR (Intersection of ABox Repairs) semantics, written K |= IAR q(a), just in the case that T , D |= q(a) where D = B∈Rep(K) B.

The more adventurous brave semantics, first explored in the OMQA setting in [START_REF] Bienvenu | Tractable approximations of consistent query answering for robust ontology-based data access[END_REF], merely requires that an answer hold w.r.t. at least some repair.

Definition 4 (Brave semantics) A tuple a is an answer to q over K = T , A under the brave semantics, written K |= brave q(a), just in the case that T , B |= q(a) for some repair B ∈ Rep(K).

Before proceeding further, let us illustrate the AR, IAR, and brave semantics on our running example:

Example 3 If we evaluate the query q(x) = Faculty(x) using the three semantics, we obtain:

-3 answers for AR semantics: sam, kim, alex -1 answer for IAR semantics: alex -4 answers for brave semantics: sam, kim, alex, jane

The preceding three semantics are related as follows:

K |= IAR q(a) ⇒ K |= AR q(a) ⇒ K |= brave q(a)
In other words, the brave and IAR semantics provide respectively upper and lower bounds on the set of answers w.r.t. the AR semantics.

We can also compare semantics based upon the properties they satisfy. Following [START_REF] Bienvenu | Inconsistency-tolerant querying of description logic knowledge bases[END_REF], we consider the following three desirable properties for an inconsistencytolerant semantics:

Consistent Support Semantics S has the Consistent Support property if for every KB T , A , query q, and tuple a, if T , A |= S q(a), then there exists a T -support C ⊆ A of q(a). Consistent Results Semantics S has the Consistent Results property if for every KB T , A , there exists a model I of T such that I |= q(a) for every q(a) with T , A |= S q(a). Unique Base Semantics S has the Unique Base property if for every KB K = T , A , there exists a Tconsistent ABox A such that for every query q and tuple a: T , A |= S q(a) iff T , A |= q(a).

The Consistent Support property means that every answer can be justified by exhibiting a consistent subset of the original ABox. The interest of Consistent Results is that it allows users to safely combine the query results obtained under semantics S (in the sense that no contradiction can be inferred from the returned information). Finally, the Unique Base property is a nice feature from the implementation point of view, since it means we can compute in an offline phase a consistent ABox, which can be queried using existing algorithms.

As seen in Fig. 1, the brave semantics satisfies only Consistent Support, the AR semantics satisfies both Consistent Support and Consistent Results, while the IAR semantics satisfies all three properties.

Let us now continue on to other semantics that have been proposed in the OMQA literature, starting with the ICR semantics, defined in [START_REF] Bienvenu | On the complexity of consistent query answering in the presence of simple ontologies[END_REF]:

Definition 5 (ICR semantics) Let close T (B) con- tain all ABox assertions β such that T , B |= β. A tuple
a is an answer to q over K = T , A under the ICR (Intersection of Closed Repairs) semantics just in the case that T , D |= q(a) where D = B∈Rep(K) close T (B).

By closing repairs before intersecting them, the ICR semantics provides a better lower approximation of the AR semantics than the IAR semantics, and it can be shown to satisfy the three properties. This semantics coincides with the AR semantics on instance queries, which means that for our example KB, the ICR semantics would return sam, kim, alex as answers to the query q(x) = Faculty(x).

The idea of adding inferred assertions to retain more information is also at the heart of the CAR and ICAR semantics proposed in [START_REF] Lembo | Inconsistency-tolerant semantics for description logics[END_REF]. The key difference is that a modified closure operator is applied to the original inconsistent ABox, and the enriched ABox is then used to define closed ABox repairs.

Definition 6 (Closed ABox repair) Let close * T (A) contain all ABox assertions β such that there is a T - consistent subset S ⊆ A such that T , S |= β. A subset R ⊆ close * T (A) is a closed ABox repair of A w.r.t. T if (i) it is T -consistent, and (ii) there is no T -consistent R ⊆ close * T (A) such that R ∩ A R ∩ A or R ∩ A = R ∩ A and R R . If K = T , A , the set of closed ABox repairs of A w.r.t. T is denoted ClosedRep(K).
Closed ABox repairs can be seen as maximally 'completing' the (plain) ABox repairs with assertions from close * T (A) \ A. Subsequent studies [START_REF] Rosati | On the complexity of dealing with inconsistency in description logic ontologies[END_REF][START_REF] Lembo | Query rewriting for inconsistent DL-Lite ontologies[END_REF] have adopted a different definition of closed ABox repair that simply takes the repairs of the KB T , close * T (A) . The two definitions do not coincide since a repair of T , close * T (A) need not be a closed ABox repair according to the previous definition (see [START_REF] Bienvenu | Inconsistency-tolerant querying of description logic knowledge bases[END_REF] for an example).

Definition 7 (CAR & ICAR semantics) A tuple

a is an answer to q over K = T , A under the CAR (Closed ABox Repair) semantics just in the case that T , R |= q(a) for every R ∈ ClosedRep(K). It is an answer under the ICAR (Intersection of Closed ABox Repairs) semantics if and only if T , D |= q(a) where

D = B∈ClosedRep(K) B.
Remark 1 While the variants of the CAR and ICAR semantics induced by the simpler definition of closed ABox repair may produce different query results, they possess similar computational properties [START_REF] Rosati | On the complexity of dealing with inconsistency in description logic ontologies[END_REF][START_REF] Lembo | Query rewriting for inconsistent DL-Lite ontologies[END_REF].

On the KB from Example 1, the CAR (resp. ICAR) semantics gives the same answers as the AR (resp. ICR semantics). We present another example (again borrowed from [START_REF] Bienvenu | Inconsistency-tolerant querying of description logic knowledge bases[END_REF]) to show how these semantics differ.

Example 4 Let T univ be obtained from T univ by adding ∃Teaches Faculty. Then close * T univ (A univ ) contains A univ as well as the following additional assertions: {Faculty(sam), Faculty(kim), Faculty(alex), Faculty(jane), Course(jane), Faculty(cs34), Course(cs48)} Since Faculty(cs34) is not involved in any contradictions, it appears in every closed ABox repair, so cs34 is an answer to q(x) = Faculty(x) under ICAR and CAR semantics. Note however that cs34 is not an answer under AR semantics. This is because some (standard) repairs contain the assertion Fellow(jane), and hence will not contain the conflicting assertion Teaches(cs34, jane), and it is only the latter assertion that allows us to infer Faculty(cs34).

As displayed in Fig. 1, the CAR semantics satisfies Consistent Results, and ICAR semantics further satisfies Unique Base, but neither semantics satisfies Consistent Support (here again we refer to [START_REF] Bienvenu | Inconsistency-tolerant querying of description logic knowledge bases[END_REF] for a counterexample).

We next consider a parameterized family of semantics, called the k-support semantics, that were introduced in [START_REF] Bienvenu | Tractable approximations of consistent query answering for robust ontology-based data access[END_REF] in order to provide increasingly more finegrained lower approximations of the AR semantics (while enjoying certain desirable computational properties, as discussed in Section 4).

Definition 8 (k-support semantics) Tuple a is an answer to q over K = T , A under the k-support semantics, written T , A |= k-supp q(a), if there exist (not necessarily distinct) subsets S 1 , . . . , S k of A that satisfy the following:

each S i is a T -support for q(a) in A for every R ∈ Rep(K), there is some S i with S i ⊆ R

The intuition for the k-support semantics is to restrict the number of distinct supports of the query that can be used to 'cover' all of the repairs. When k = 1, the same support must be present in every repair, so the 1-support semantics coincides with the IAR semantics. By increasing k and allowing larger and larger supports, the set of answers will increase until it coincides with the AR-answers. Like the AR semantics, the ksupport semantics satisfy both Consistent Results and Consistent Support.

Example 5 Continuing our running example, we evaluate Faculty(x) using the k-support semantics. When k = 1, the semantics coincides with the IAR semantics, so we only get alex. For k = 2, we gain an additional answer, kim, by considering the pair of supports {Prof(kim)} and {Lect(kim)}. Finally, for k ≥ 3, we have one further answer, sam, by considering the supports {Prof(sam)}, {Lect(sam)}, {Fellow(sam)}.

A second parameterized class of semantics, the kdefeater semantics, was introduced in the same work [START_REF] Bienvenu | Tractable approximations of consistent query answering for robust ontology-based data access[END_REF] in order to provide increasingly tighter upper approximations of the AR semantics.

Definition 9 (k-defeater semantics) A tuple a is an answer to q over K = T , A under the k-defeater semantics, written K |= k-def q(a), if there does not exist a T -consistent subset S of A with |S| ≤ k such that T , S ∪ C |= ⊥ for every inclusion-minimal T -support C ⊆ A of q(a).

It has been shown in [START_REF] Bienvenu | Tractable approximations of consistent query answering for robust ontology-based data access[END_REF] that 0-defeater semantics coincides with brave semantics and that the set of answers under k-defeater semantics decreases as the value of k increases, until the set of AR-answers is reached.

Let us also mention another parameterized family of semantics, called k-lazy [START_REF] Lukasiewicz | Inconsistency handling in Datalog+/-ontologies[END_REF] semantics, which was originally proposed for Datalog +/-ontologies and whose definition involves another notion of repair (omitted for lack of space). By taking k large enough, the klazy semantics coincides with the AR semantics. However, in contrast to the k-support semantics, the convergence is not monotone, i.e. a tuple might be an answer for k = but no longer an answer when k = + 1. Due to this behaviour, the k-lazy semantics are Fig. 2: Relationships between inconsistency-tolerant semantics, where an arrow S → S means that S is an under-approximation of S , i.e., T , A |= S q(a) ⇒ T , A |= S q(a). not always under-approximations of the AR semantics, though they do satisfy the Consistent Results and Consistent Support properties.

Another natural over-approximation of the AR semantics was proposed in [START_REF] Benferhat | Non-objection inference for inconsistencytolerant query answering[END_REF]: Definition 10 (Non-objection semantics) A tuple a is an answer to q over K = T , A under the nonobjection semantics if (i) there is some B ∈ Rep(K) with T , B |= q(a), and (ii) for every B ∈ Rep(K), there is a model of T , B where q(a) is satisfied.

The non-objection semantics lies between the brave and AR semantics, and it satisfies both Consistent Results and Consistent Support.

We summarize the relationships holding between the different semantics discussed thus far in Fig. 2.

As noted at the beginning of the section, repairs are usually defined using set inclusion. However, in some cases, it can be more appropriate to select only the most preferred repairs according to some criteria. Several different notions of preferred repair, based upon cardinality, priority levels, partial preorders, or weighted assertions, have been explored [START_REF] Staworko | Prioritized repairing and consistent query answering in relational databases[END_REF][START_REF] Bienvenu | Querying inconsistent description logic knowledge bases under preferred repair semantics[END_REF][START_REF] Du | Weight-based consistent query answering over inconsistent SHIQ knowledge bases[END_REF][START_REF] Baget | Inconsistencytolerant query answering: Rationality properties and computational complexity analysis[END_REF][START_REF] Lukasiewicz | Complexity of inconsistency-tolerant query answering in Datalog+/-under cardinality-based repairs[END_REF][START_REF] Belabbes | Inconsistency handling for partially preordered ontologies: Going beyond Elect[END_REF][START_REF] Lukasiewicz | Complexity of inconsistency-tolerant query answering in Datalog+/-under cardinality-based repairs[END_REF] and used as the basis for inconsistency-tolerant semantics.

We further note that the preceding works focused on repairing data given in the form of an ABox (or set of facts over the ontology vocabulary), and the definitions need to be adapted to handle the setting of ontologybased data access (OBDA), where existing data sources are linked to a TBox via mappings. This issue has been explored recently in [START_REF] Bienvenu | Inconsistency-tolerant ontology-based data access revisited: Taking mappings into account[END_REF], where two different approaches (repair-at-source, map-then-repair) are contrasted, and it is closely related to consistent query answering in data integration [START_REF] Bravo | Logic programs for consistently querying data integration systems[END_REF][START_REF] Calì | Query rewriting and answering under constraints in data integration systems[END_REF] and data exchange [START_REF] Ten Cate | Exchangerepairs -Managing inconsistency in data exchange[END_REF] settings.

Finally, we should emphasize that there is no single 'best' semantics, and the choice of which to use needs to be based upon the acceptable level of risk as well as performance requirements. Moreover, it can be fruitful to utilize multiple semantics in combination, either for computational benefit or to identify answers with different levels of plausibility.

Complexity of Querying DL KBs under Inconsistency-Tolerant Semantics

The complexity of query answering under inconsistencytolerant semantics has been the subject of numerous works. We briefly present what is known for DL ontologies and refer to [START_REF] Bienvenu | Inconsistency-tolerant querying of description logic knowledge bases[END_REF] for further details and references to where the stated results were proven.

We recall that there are two standard ways of measuring the complexity of query answering. Combined complexity is w.r.t. the size of the whole input (TBox, ABox, query), while data complexity is measured w.r.t. the size of ABox (with the query and TBox treated as fixed). Our results make reference to the well-known complexity classes P, NP, and coNP, as well as the following classes whose definitions we recall: AC 0 (problems that can be solved by a uniform family of circuits of constant depth and polynomial size, with unlimited fan-in AND gates and OR gates), NL (problems solvable in non-deterministic logarithmic space), ∆ p 2 [O(log n)](problems solvable in polynomial time with at most logarithmically many calls to an NP oracle), and Π p 2 (problems whose complement is solvable in nondeterministic polynomial time with access to an NP oracle). The classes AC 0 and NL are contained in P.

Let us start by the most well-studied case, namely, DL-Lite KBs. Fig. 3 displays the complexity landscape for querying DL-Lite1 KBs under various inconsistencytolerant semantics, considering both data and combined complexity measures and both conjunctive queries and instance queries. We observe that there are several semantics for which query answering is in AC 0 in data complexity. These upper bounds are shown by means of first-order query rewriting. For the IAR semantics, the rough idea is to modify a usual rewriting by adding negated atoms that forbid the use of ABox assertions that do not belong to the intersection of repairs [START_REF] Lembo | Query rewriting for inconsistent DL-Lite ontologies[END_REF][START_REF] Bienvenu | First-order expressibility results for queries over inconsistent DL-Lite knowledge bases[END_REF]. Subsequent work [START_REF] Bienvenu | Tractable approximations of consistent query answering for robust ontology-based data access[END_REF] established general rewritability

Semantics CQs IQs data comb data comb classical in AC 0 NP in AC 0 NL AR coNP Π p 2 coNP coNP IAR in AC 0 NP in AC 0 NL brave in AC 0 NP in AC 0 NL ICR coNP ∆ p 2 [O(log n)] coNP coNP CAR coNP Π p 2 in AC 0 NL ICAR in AC 0 NP in AC 0 NL k-support in AC 0 NP in AC 0 NL k-defeater in AC 0 NP in AC 0 NL k-lazy coNP Π p 2 in P in P non-objection in AC 0 NP in AC 0 NL
Fig. 3: Data complexity (data) and combined complexity (comb) of CQ and IQ answering over DL-Lite KBs.

All results are completeness results unless otherwise indicated.

results that apply to the families of k-support and kdefeater semantics and arbitrary FO-rewritable ontology languages. We note that the AC 0 result for nonobjection semantics2 has not been stated in the literature but can be shown by adapting query rewriting techniques for the brave and IAR semantics. For the AR semantics, which is arguably the most natural, query answering is intractable in data complexity, even in restricted settings, like IQs [START_REF] Lembo | Inconsistency-tolerant semantics for description logics[END_REF] or very simple TBoxes (a single disjointness axiom T ¬F suffices [START_REF] Bienvenu | On the complexity of consistent query answering in the presence of simple ontologies[END_REF]). Turning now to combined complexity, we observe that the semantics that are well behaved for data complexity remain so for combined complexity (i.e. their complexity matches that of classical semantics), while the semantics with intractable data complexity exhibit higher combined complexities than classical semantics. Finally, we note that the complexity of querying with variants of AR and IAR based upon preferred repairs (cardinality, weights, priorities) has also been studied (see e.g. [START_REF] Bienvenu | Querying inconsistent description logic knowledge bases under preferred repair semantics[END_REF]), and the general message is that incorporating preferences leads to higher complexity.

We now briefly consider the situation for DLs beyond DL-Lite. Fig. 4 displays complexity results for two representative DLs (the lightweight DL EL ⊥ and the expressive DL ALC) and three prominent semantics (AR, IAR, brave). The results for the AR and IAR semantics were established in [START_REF] Rosati | On the complexity of dealing with inconsistency in description logic ontologies[END_REF], while those for brave semantics can be found in [START_REF] Bienvenu | Inconsistency-tolerant querying of description logic knowledge bases[END_REF]. The main observation with regards to EL ⊥ (and other Horn DLs) is that the IAR and brave semantics are no longer tractable in data complexity. Essentially, the reason is that in contrast to DL-Lite and other FO-rewritable languages, it is not possible

DL Semantics Data Combined EL ⊥ classical P NP AR coNP Π p 2 IAR coNP ∆ p 2 [O(log n)] brave NP NP ALC classical coNP Exp AR Π p 2 Exp IAR Π p 2 Exp brave Σ p 2 Exp
Fig. 4: Complexity of answering CQs in EL ⊥ and ALC.

All results are completeness results.

in general to bound the size of minimal T -supports nor minimal T -inconsistent subsets (i.e., subsets of the ABox that are T -inconsistent but whose every proper subset is T -consistent). For the expressive DL ALC, the adoption of inconsistency-tolerant semantics leads to a rise in data complexity, but leaves the combined complexity unchanged (since the repairs can be enumerated in exponential time).

Implementing Inconsistency-Tolerant OMQA

We give a brief overview of systems that have been implemented and tested for inconsistency-tolerant query answering over DL knowledge bases.

QuID system [START_REF] Rosati | Evaluation of techniques for inconsistency handling in OWL 2 QL ontologies[END_REF][START_REF] Lembo | Inconsistency-tolerant query answering in ontologybased data access[END_REF] This system3 performs conjunctive query answering under the IAR semantics in an extension of DL-Lite A with denial and identification constraints. Three different approaches have been implemented and compared: first-order query rewriting, ABox annotation (in which assertions are marked as safe or problematic depending on whether they belong to the intersection of repairs, and the query is modified to only use safe assertions), and ABox cleaning (in which assertions not belonging to the intersection of repairs are removed, and the resulting dataset is queried as usual). The latter two approaches generally proved to be more efficient than the rewriting approach, but they have the downside of involving data modifications.

CQAPri system [START_REF] Bienvenu | Querying inconsistent description logic knowledge bases under preferred repair semantics[END_REF][START_REF] Bienvenu | Computing and explaining query answers over inconsistent DL-Lite knowledge bases[END_REF] This system 4 computes answers to CQs over DL-Lite R KBs under the IAR, brave, and AR semantics (as well as prioritized versions of AR and IAR). Answers are first computed for the IAR and brave semantics, by evaluating a UCQ-rewriting and filtering the results using a pre-computed set of minimal T -inconsistent subsets. To identify the AR-answers among the remaining tuples (i.e. those holding under brave semantics but not under IAR semantics), CQAPri constructs a (usually quite small) instance of UNSAT for every such tuple, which is passed to an off-the-shelf SAT solver. In addition to using the IAR and brave semantics to reduce the number of calls to the SAT solver, the three semantics are used to partition query answers into three levels of reliability: (Almost) Sure (those answers holding under IAR semantics), Likely (answers holding under AR but not IAR semantics), and Possible (answers only holding under brave semantics). Experiments conducted on the modified LUBM benchmark (which was further augmented with negative inclusions and conflicting assertions) showed that despite its intractable data complexity, it is feasible to compute query answers under the AR semantics, thanks in part to the fact that many AR-answers can be identifed using the tractable IAR semantics.

SaQAI system [START_REF] Tsalapati | Efficient query answering over expressive inconsistent description logics[END_REF] This system5 implements the IAR and ICAR semantics for DL-Lite R KBs and CQs. For the IAR semantics, the authors follow the ABox cleaning approach from QuID, using query rewriting to identify and then remove the assertions that do not appear in the intersection of repairs. For the ICAR semantics, a combination of saturation and query rewriting is employed, together with some optimizations. The experiments conducted using the CQAPri benchmark show a better performance than the QuID and CQAPri systems for the IAR semantics.

System from [START_REF] Trivela | A framework and positive results for IAR-answering[END_REF] This system targets the IAR semantics and currently supports the DL ELH dr ⊥ . It checks whether the sufficient conditions for producing a rewriting w.r.t. IAR semantics are fulfilled (by making calls to the FO-rewritability checking system Grind [START_REF] Hansen | Efficient query rewriting in the description logic EL and beyond[END_REF]) and constructs such a rewriting when one exists by adding negated conjuncts to a classical rewriting. Experiments were conducted on seven existing ontologies (which sometimes needed to be enriched with negative inclusions to allow for inconsistencies) and for six of them, the sufficient conditions were satisfied, suggesting that a rewriting-based approach to IAR may be feasible in practice for ontologies beyond DL-Lite.

System from [START_REF] Benferhat | Non-objection inference for inconsistencytolerant query answering[END_REF] This system implements the non-objection semantics for ground CQs (i.e. CQs without existentially quantified variables) for DL-Lite R KBs. Experiments on the CQAPri benchmark confirm that query answers can be efficiently computed (in accordance with the tractable data complexity).

System from [START_REF] Du | Weight-based consistent query answering over inconsistent SHIQ knowledge bases[END_REF] This system can be utilized to query SHIQ KBs under a variant of the AR semantics in which ABox assertions are assigned weights and querying is restricted to ground CQs. Like CQAPri, it employs SAT solvers as well as a form of reachability analysis to identify a query-relevant fragment of the KB.

Related Reasoning Services for Inconsistency Handling

We mention some related reasoning and analysis tasks. First, to render inconsistency-tolerant OMQA systems more usable, it is important to be able to explain the results to users. This issue has been taken up in [START_REF] Bienvenu | Explaining inconsistency-tolerant query answering over description logic knowledge bases[END_REF], where a formal framework was presented for justifying why a given tuple appears as an answer under the considered inconsistency-tolerant semantics (AR, IAR, or brave) or why it is not part of the results. The approach has been implemented by exploiting different functionalities of SAT solvers and integrated into the CQAPri system. Closely related is a line of work [START_REF] Arioua | Query answering explanation in inconsistent Datalog +/-knowledge bases[END_REF][START_REF] Arioua | Dialectical characterization of consistent query explanation with existential rules[END_REF] on utilizing argumentation and dialogues with users to explain query answers under various inconsistency-tolerant semantics (ICR, IAR, brave, and AR).

Another important question is how to aid users in repairing their data, in order to improve the quality of the data. An interactive query-driven approach to this question has been presented in [START_REF] Bienvenu | Query-driven repairing of inconsistent DL-Lite knowledge bases[END_REF]. The idea is to allow users to provide feedback on which query results are missing or erroneous, and then interact with the user in order to identify a set of ABox modifications (additions and deletions of assertions) that fix the identified flaws. The ABox update problem [START_REF] De Giacomo | On instance-level update and erasure in description logic ontologies[END_REF][START_REF] Liu | Foundations of instance level updates in expressive description logics[END_REF] is also concerned with modifying the ABox to ensure consistency, but does not involve interaction with a user and targets a setting in which inconsistencies result from changes to the actual state of affairs.

While we have assumed in this paper that errors originate from the data, this presupposes that the ontology has been properly debugged. Several different axiom pinpointing and justification finding algorithms [START_REF] Schlobach | Non-standard reasoning services for the debugging of description logic terminologies[END_REF][START_REF] Kalyanpur | Debugging unsatisfiable classes in OWL ontologies[END_REF][START_REF] Peñaloza | Complexity of axiom pinpointing in the DL-Lite family of description logics[END_REF] have been proposed to aid ontology engineers in identifying the sources of unwanted inferences. An approach to repairing DL KBs to be able to infer missing consequences while avoiding some undesired entailments has been presented in [START_REF] Nikitina | Interactive ontology revision[END_REF]. In the OBDA setting, recent works have examined reasoning tasks such as checking whether the mapping is coherent w.r.t. the ontology [START_REF] Lembo | Mapping analysis in ontology-based data access: Algorithms and complexity[END_REF], minimally modifying a mapping to reflect changes to the database schema or ontology [START_REF] Lembo | Mapping repair in ontology-based data access evolving systems[END_REF], and deciding if a database schema protects an OBDA specification [START_REF] Console | Data quality in ontologybased data access: The case of consistency[END_REF], i.e., every legal data instance for the database constraints is consistent w.r.t. the ontology and mapping.

Finally, let us also point out that some close connections have been identified between inconsistencytolerant OMQA and the areas of argumentation [START_REF] Croitoru | What can argumentation do for inconsistent ontology query answering?[END_REF][START_REF] Bienvenu | Querying and repairing inconsistent prioritized knowledge bases: Complexity analysis and links with abstract argumentation[END_REF] and privacy-aware query evaluation [START_REF] Lembo | Revisiting controlled query evaluation in description logics[END_REF].

Concluding Remarks and Future Work

We hope to have showcased the large body of research that has been developed over the past decade or so around the issue of inconsistency handling in OMQA. Significant progress has been made on proposing different semantics for querying inconsistent KBs in a principled manner and exploring their computational properties: complexity, algorithms, and implemented prototypes. There nevertheless remain several interesting theoretical and practical challenges to tackle going forward, let us mention just three.

First, while we start to have a reasonable idea of how to approach the problem for DL-Lite KBs, there remains a need to develop practical algorithms for DLs beyond DL-Lite. Indeed, due to the prevalence of data quality issues, every OMQA system should be equipped with some sort of inconsistency handling mechanism (beyond simply reporting that the KB is inconsistent!), and the challenge is to find ways of incorporating such features while limiting the impact on performance. First steps towards this goal can be found in [START_REF] Tsalapati | Efficient query answering over expressive inconsistent description logics[END_REF][START_REF] Trivela | A framework and positive results for IAR-answering[END_REF].

Second, a very nice but extremely challenging theoretical question is to classify the complexity of inconsistency-tolerant query answering at the level of ontologymediated queries (that is, ontology-query pairs). Some preliminary results in this direction have been presented in [START_REF] Bienvenu | First-order expressibility results for queries over inconsistent DL-Lite knowledge bases[END_REF][START_REF] Bienvenu | On the complexity of consistent query answering in the presence of simple ontologies[END_REF]. We note that this problem is closely related to work on classifying the complexity of consistent query answering in the presence of functional dependencies, where significant progress has been made (see e.g. [START_REF] Koutris | Consistent query answering for self-join-free conjunctive queries under primary key constraints[END_REF]), but a full classification has proven elusive.

Third, it would also be worthwhile to develop quantitative approaches to inconsistency-tolerant OMQA, both to be able to quantify the confidence in different results, and to be able to take advantage of numeric / probabilistic / statistical information when it is available. For instance, data that results from information extraction systems is often annotated with a confidence value, and mined data quality rules (see e.g. [START_REF] Ortona | Rudik: Rule discovery in knowledge bases[END_REF]) that act as soft constraints can prove useful in detecting inconsistencies and determining the most likely fixes.

Fig. 1 :

 1 Fig. 1: Properties of inconsistency-tolerant semantics.

1

  Consider the TBox T univ with the axioms: Course Lect ¬Fellow Faculty ¬Course where Prof, Lect, Fellow, Faculty, and Course are concept names (unary predicates) that represent the classes of professors, lecturers, research fellows, faculty members, and courses, respectively, and Teaches is a role (binary relation) linking teachers to what is taught. The TBox axioms state collectively that professors, lecturers, and fellows are three pairwise-disjoint classes of faculty, that professors and lecturers must teach something (i.e. occur in the first argument of some Teaches fact), that faculty and courses are disjoint, and that the second argument of Teaches ranges over courses.

	Prof Faculty	Prof ∃Teaches	Prof ¬Lect
	Lect Faculty	Lect ∃Teaches	Prof ¬Fellow
	Fellow Faculty ∃Teaches -

The results apply to common DL-Lite dialects, such as DL-Lite core , DL-Lite R , and DL-Lite A , see[START_REF] Bienvenu | Inconsistency-tolerant querying of description logic knowledge bases[END_REF] for details.

In[START_REF] Benferhat | Non-objection inference for inconsistencytolerant query answering[END_REF], only polynomial data complexity is proven, which we improve to AC 0 . It is also not too hard to show that the combined complexity matches classical semantics.

QuID: www.dis.uniroma1.it/ ~ruzzi/quid/

CQAPri: www.lri.fr/ ~bourgaux/CQAPri.

SaQAI: www.image.ece.ntua.gr/ ~etsalap/SaQAI/

Acknowledgements The author would like to thank Camille Bourgaux, who was a co-author of the survey chapter [12] and contributed to the running example reproduced here.