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93-618: OntoClean was the first attempt to formalize notions of ontological analysis for information systems. The idea was to justify the kinds of decisions that experienced ontology builders make, and explain the common mistakes of the inexperienced. Alan Rector , during a debate at the KR-2002 conference in Toulouse , said, "What you have done is reduce the amount of time I spend arguing with medics." The notions Guarino & Welty focused on were drawn from philosophical ontology. They were not after

186-403: A generalized connection relation. Mere sums have no such relation since any decomposition of a mere sum is connected to any larger sum, which is not one of its parts, by the same relation. Unity is the metaproperty, indicated by +U , of classes all of whose individuals are wholes under the same relation. Like identity, OntoClean does not require that the relation itself be specified, often it

279-653: A logical principle, or merely an empirical principle. Both identity and indiscernibility are expressed by the word "same". Identity is about numerical sameness , and is expressed by the equality sign ("="). It is the relation each object bears only to itself. Indiscernibility , on the other hand, concerns qualitative sameness : two objects are indiscernible if they have all their properties in common. Formally, this can be expressed as " ∀ F ( F x ↔ F y ) {\displaystyle \forall F(Fx\leftrightarrow Fy)} ". The two senses of sameness are linked by two principles:

372-406: A logical tautology . In that case, the objects are distinguished by IsA, IsB, and all predicates that are materially equivalent to either of these. This argument can combinatorially be extended to universes containing any number of distinct objects. The equality relation expressed by the sign "=" is an equivalence relation in being reflexive (everything is equal to itself), symmetric (if x

465-511: A métropole in 2015, spanning 37 communes with 806,503 inhabitants in 2020 census. Identity of indiscernibles The identity of indiscernibles is an ontological principle that states that there cannot be separate objects or entities that have all their properties in common. That is, entities x and y are identical if every predicate possessed by x is also possessed by y and vice versa. It states that no two distinct things (such as snowflakes ) can be exactly alike, but this

558-406: A beard on one day and shave it off the next, yet I am the same entity at both times. How is it possible for me to be the same if I have changed ? There are many logical approaches to this classic dilemma (including simply ignoring it), the most common is to consider some properties to be essential ; an essential property (and, q.v. terminology above, properties are unary predicates) of an entity

651-444: A class means. A triangle, for example, can be identified by the length of its three sides, or by two sides and an interior angle, etc. This says a lot about what is intended by the triangle class here, e.g. the same triangle could be in many places at the same time. Someone else may have an ontology in which the triangle class has different identity criteria, such that different drawings are always different triangles, even if they are

744-456: A count and was annexed to the royal domain . The installation of numerous royal officers and the development of trade and crafts, which favoured the social ascension of merchants, renewed the city's elites. In 1298, King Philip the Fair greatly facilitated the possibility of ennobling the capitouls, whose council, renewed every year, was increasingly made up of rich merchants. The first half of

837-572: A flood of the Garonne devastated more than 1,000 houses and killed 200 people. It also destroyed all the bridges in Toulouse, except the Pont-Neuf . World War I brought to Toulouse (geographically sheltered from enemy attacks) chemical industries as well as aviation workshops ( Latécoère , Dewoitine ), which launched the city's aeronautical construction tradition and gave birth after the war to

930-414: A great autonomy, they created a municipal body of consuls, called capitouls in Toulouse, to lead the city. The Bourg , which had only a quarter of the inhabitants of Toulouse, obtained as many capitouls as the rest of the city. Economically, Toulouse, which was at the center of a large cereal-growing plain, was distinguished by its numerous mills that took advantage of the force of the Garonne, among which

1023-607: A growth of 15.3% for metropolitan France between 1990 and 2020, i.e. +0.48% per year. This was the second-highest population growth of any French metropolitan area larger than 500,000 inhabitants (only the Montpellier metropolitan area grew more than Toulouse between 1990 and 2019). The Toulouse metropolitan area reached 1,470,899 inhabitants in January 2020, and stood as the 5th most populated metropolitan area in France, behind

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1116-566: A kind of dependence that captures a meta-property of certain relational roles. A property is dependent if each instance of it implies the existence of another entity. The property Student, for example, is dependent, since to be a student there must be a teacher; for every instance of student there is at least one instance of teacher. In later work for [Dolce] this was noted to subsume two kinds of property dependence: specific constant dependence and generic constant dependence. The former accounts for dependence on specific entities, e.g. each person

1209-523: A metaproperty is a property of a property or class. The basis of OntoClean are the domain-independent properties of classes, the OntoClean metaproperties: identity, unity, rigidity, and dependence. Later work by Welty & Andersen has added two more metaproperties: permanence and actuality. Identity is fundamental to ontology, and especially to information systems ontologies. Identity is well known in metaphysics and in database conceptual modeling. In

1302-408: A person must not be essential and furthermore must be changeable (i.e. anti-rigid). Rigidity should not be confused with Kripke's notion of Rigid Designators , which are particulars. The term rigid in OntoClean is meant to describe the instanceOf link between an individual and a rigid class — it cannot be broken. Dependence is a varied notion. In the core OntoClean papers, Guarino & Welty used

1395-557: A property is what it means to be a member of a class. For example, we say that instances of the Person class have the property of "being a person." In the semantic web, a property is a binary relation. The distinction between property and class is subtle, and probably not critical to understanding OntoClean, however this article, follows the OntoClean publications and consistently uses "property" according to its original meaning, and one can treat "property" and "class" as synonymous. Thus

1488-571: A sense, arbitrary. For example, consider the class clay . An instance of this class might be some amount of the material (this is only one possible meaning, of course), such that any (in fact, every) arbitrary subsection of the amount would be a different instance of the same class. By contrast, instances of the class Person are, typically, not decomposable in this fashion. For the purposes of OntoClean, wholes are individuals all of whose parts are related to each other, and only to each other, by some distinguished relation. This relation can be viewed as

1581-445: A series of three papers published in 2000. The name OntoClean does not appear in the literature until 2002. According to Thompson-ISI, work on OntoClean was the most cited of academic papers on Ontology. OntoClean was important as it was the first formal methodology for ontology engineering , applying scientific principles to a field whose practice was mostly art. In logic, a property is a unary predicate in intention, in other words

1674-406: A single axiom by using a biconditional operator ( ↔ {\displaystyle \leftrightarrow } ) in place of material implication ( → {\displaystyle \rightarrow } ). Indiscernibility is usually defined in terms of shared properties: two objects are indiscernible if they have all their properties in common. The plausibility and strength of

1767-518: A situation where one changes and the other stays the same. In OntoClean, identity criteria are associated with, or carried by, some classes of entities, called sortals . A sortal is a class all of whose instances are identified in the same way. In information systems, these criteria are often extrinsic, like a social security number or universally unique id, which is not interesting from an ontological point of view. Identity criteria should be informative , they should help us and others understand what

1860-459: A sortal is the first OntoClean metaproperty, indicated with the +I superscript ( −I for non-sortals) on a class in the original notation. +I (but not −I ) is inherited down the class hierarchy, if a class is a sortal then all its subclasses are as well. There are certain properties that only hold of individuals that are wholes . In formal ontology, wholes are often distinguished from mere sums , which are individuals whose boundaries are, in

1953-425: A student — all students must possibly not be students. ~R (but not −R or +R ) is inherited down the class hierarchy. Note that these are just examples — it is certainly possible to have an ontology in which Person is anti-rigid. Imagine an ontology of mystical beliefs, for example, in which an entity changes from Person to Spirit upon death. In order for the individual to be the same across this change, being

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2046-724: A university population of nearly 140,000 students. Toulouse counts three UNESCO World Heritage Sites : the Canal du Midi (designated in 1996 and shared with other cities), and the Basilica of St. Sernin , the largest remaining Romanesque building in Europe, designated in 1998 along with the former hospital Hôtel-Dieu Saint-Jacques because of their significance to the Santiago de Compostela pilgrimage route . The city's unique architecture made of pinkish terracotta bricks has earned Toulouse

2139-427: Is a property that cannot change, and these are the properties for which Leibniz's law holds. Other properties of an entity that can change are non-essential and cannot be involved in identity. Some properties are essential to all their instances. Think of the property of being a person , usually represented by the class Person. For every entity that has this property, the property is essential. So at least one of

2232-476: Is dependent on having a particular brain. The latter accounts for the Student/Teacher case, where any instance of Teacher will do. There are many other kinds of dependence, see [Fine and Smith, 1983] and especially [Simons, 1987]. It is an open problem to adapt them into the OntoClean framework. Being dependent is indicated with +D , being independent with −D . +D (but not −D ) is inherited down

2325-401: Is enough to know that the relation exists. Intuitively, a class has unity if all its instances are the same type of whole, and is typically true of classes of natural objects. Non-unity, indicated by −U , is the meta-property of classes whose instances are not all wholes, or not all wholes by the same relation. A further and more useful refinement of non-unity is anti-unity, indicated by ~U ,

2418-419: Is equal to y then y is equal to x ) and transitive (if x is equal to y and y is equal to z then x is equal to z ). The indiscernibility of identicals and identity of indiscernables can jointly be used to define the equality relation. The symmetry and transitivity of equality follow from the first principle, whereas reflexivity follows from the second. Both principles can be combined into

2511-413: Is extrinsic while the property of having a mass of 60 kg is intrinsic. If the identity of indiscernibles is defined only in terms of intrinsic pure properties, one cannot regard two books lying on a table as distinct when they are intrinsically identical . But if extrinsic and impure properties are also taken into consideration, the same books become distinct so long as they are discernible through

2604-407: Is generally regarded as an a priori logical truth . Principle 2, on the other hand, is controversial; Max Black famously argued against it. In a universe of two distinct objects A and B, all predicates F are materially equivalent to one of the following properties: If ∀F applies to all such predicates, then the second principle as formulated above reduces trivially and uncontroversially to

2697-463: Is intended as a metaphysical principle rather than one of natural science. A related principle is the indiscernibility of identicals, discussed below. A form of the principle is attributed to the German philosopher Gottfried Wilhelm Leibniz . While some think that Leibniz's version of the principle is meant to be only the indiscernibility of identicals, others have interpreted it as the conjunction of

2790-661: Is the most dynamic French city. Founded by the Romans, the city was the capital of the Visigothic Kingdom in the 5th century and the capital of the province of Languedoc in the Late Middle Ages and early modern period (provinces were abolished during the French Revolution ), making it the unofficial capital of the cultural region of Occitania (Southern France). It is now the capital of

2883-538: The Consistori del Gay Saber was created in Toulouse to preserve the lyric art of the troubadours by organizing a poetry contest; and Toulouse became the centre of Occitan literary culture for the following centuries. The Consistori is considered to be the oldest literary society in Europe, at the origin of one of the most sophisticated treatise on grammar and rhetoric of the Middle Ages, and in 1694 it

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2976-544: The Atlantic Ocean and 680 km (420 mi) from Paris . It is the fourth-largest city in France after Paris , Marseille and Lyon , with 504,078 inhabitants within its municipal boundaries (2021); its metropolitan area has a population of 1.5 million inhabitants (2021). Toulouse is the central city of one of the 22 metropolitan councils of France. Between the 2014 and 2020 censuses, its metropolitan area

3069-744: The Battle of Tours , also called the Battle of Poitiers). The Frankish conquest of Septimania followed in the 750s, and a quasi-independent County of Toulouse emerged within the Carolingian sub-kingdom of Aquitaine by the late 8th century. The Battle of Toulouse of 844 , pitting Charles the Bald against Pepin II of Aquitaine , was key in the Carolingian Civil War. Charlemagne had created

3162-643: The Bazacle Milling Company was the first recorded European joint-stock company. At the beginning of the thirteenth century the County of Toulouse was caught up in another crusade that would last twenty years (1209-1229), of which it was the target this time. The reason for this was the development of Catharism in the south of France, which the Pope Innocent III wanted to eradicate by all possible means. After an initial victory of

3255-701: The French Empire to the nations of the Sixth Coalition (a fact that the two armies involved were not yet aware of), the Battle of Toulouse pitted the Hispanic-British troops of Field Marshal Wellington against the French troops of Napoleonic Marshal Soult , who, although they managed to resist, were forced to withdraw. Toulouse was thus the scene of the last Franco-British battle on French territory. Unlike most large French cities, there

3348-409: The French Revolution of 1789 and the reform or suppression of all royal institutions, Toulouse lost much of its power and influence: until then the capital of the vast province of Languedoc, with a parliament ruling over an even larger territory, the city then found itself simply at the head of the single small department of Haute-Garonne . On 10 April 1814, four days after Napoleon 's surrender of

3441-648: The Iron Age . The historical name of the city, Tolosa (Τολῶσσα in Greek , and of its inhabitants, the Tolosates , first recorded in the 2nd century BC), is of unknown meaning or origin, possibly from Aquitanian or Iberian , but it has also been connected to the name of the Gaulish Volcae Tectosages , or to the same root as Irish tulach or Welsh twlch , (little hill). Tolosa enters

3534-472: The Leibniz–Clarke correspondence ). Some philosophers have decided, however, that it is important to exclude certain predicates (or purported predicates) from the principle in order to avoid either triviality or contradiction. An example (detailed below) is the predicate that denotes whether an object is equal to x (often considered a valid predicate). As a consequence, there are a few different versions of

3627-469: The administrative region of Occitania , the second largest region in Metropolitan France . The University of Toulouse is one of the oldest in Europe (founded in 1229). Toulouse is also the home of prestigious higher education schools, notably in the field of aerospace engineering. Together with the university, they have turned Toulouse into the fourth-largest student city in France, with

3720-510: The 14th century was a prosperous period, despite the dismemberment in 1317 of the very large bishopric of Toulouse (which lost two thirds of its area and a large part of its income, a loss only partially compensated by its elevation to the rank of archbishopric), and the episode of the Shepherds' Crusade which brought a pogrom against Toulouse's Jewish population in 1320. In 1335, Toulouse had between 35,000 and 40,000 inhabitants. In 1323,

3813-522: The AZF fertiliser factory, causing 31 deaths, about 30 seriously wounded and 2,500 light casualties. The blast measured 3.4 on the Richter scale and the explosion was heard 80 km (50 mi) away. In 2016, a territorial reform made Toulouse the regional prefecture of Occitanie , the second largest region in metropolitan France, giving it a role commensurate with its past as a provincial capital among

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3906-547: The French Space Command and Space Academy. Safran , Thales Alenia Space , Airbus Defence and Space , Collins Aerospace and Liebherr-Aerospace also have a significant presence in Toulouse. The air route between Toulouse–Blagnac and the Parisian airports is the busiest in France, transporting 3.2 million passengers in 2019. According to the rankings of L'Express and Challenges , Toulouse

3999-529: The call of the Pope Urban II to join the First Crusade , of which he was one of the main leaders. This exodus of its warriors and nobles, reinforced by the creation of the faraway County of Tripoli by Raymond IV at the beginning of the 12th century, weakened the city militarily as well as the ascendancy that its counts had over it. The Duke William IX of Aquitaine challenged the possession of

4092-439: The city became the first European centre for the trade in woad, the only blue dye then known in Europe which was very much in demand in the textile industry at the time. Its humanist milieu developed thanks to its university and parliament, which trained and attracted intellectual elites. The wealth generated by this culturally and economically dynamic environment is the source of the superb Renaissance mansions in Toulouse. In 1550

4185-414: The city for fifteen days. After this dramatic event, King Louis XIII exempted the city from taxes for 100 years. The capitouls issued municipal decrees favouring the use of brick in buildings, rather than excessively flammable wood or cob. In the 16th century, and until 1562, the economy of Toulouse experienced a golden age: its Parliament made it the judicial capital of a large part of southern France, and

4278-611: The city of Toulouse proper. As of February 2004 estimate, the total population of the Community of Agglomeration of Greater Toulouse was 651,209 inhabitants, 65.5% of whom live in the city of Toulouse. Due to local political feuds, the Community of Agglomeration only hosts 61% of the population of the metropolitan area, the other independent suburbs having refused to join in. Since 2009, the Community of agglomeration has become an urban community (in French: communauté urbaine). This has become

4371-486: The city on the grounds that it should have been inherited by his wife Philippa (daughter of the previous count of Toulouse , whereas Raymond IV was only his brother). More than 50 years later his granddaughter Eleanor of Aquitaine still claimed the inheritance in vain. In the 12th century the city left its Roman limits and a new district developed around the church of Saint-Sernin : the Bourg . The church of Saint-Sernin

4464-539: The city was the key stronghold of the French defence in the south of France during the worst years of the Hundred Years' War, when the English troops from Aquitaine had taken Montauban and only Toulouse remained as an obstacle to their conquest of southern France. This military threat to the city and especially to the surrounding countryside was not conducive to its development, despite the strengthening of ties with

4557-473: The city's population. In 1963, Toulouse was chosen to become one of the country's eight "balancing Metropolis", regaining a position among the country's major cities that it had always had, but lost in the 19th century. The French state then encouraged the city's specialisation in aeronautics and space activities, sectors that had experienced strong growth in recent decades, fueling economic and population growth. On 21 September 2001, an explosion occurred at

4650-616: The class hierarchy. Toulouse Toulouse ( / t uː ˈ l uː z / too- LOOZ ; French: [tuluz] ; Occitan : Tolosa [tuˈluzɔ] ) is the prefecture of the French department of Haute-Garonne and of the larger region of Occitania . The city is on the banks of the River Garonne , 150 kilometres (93 miles) from the Mediterranean Sea , 230 km (143 mi) from

4743-462: The county of Toulouse in 778 to guard the border of Muslim Spain, but the disintegration of the kingdom of Aquitaine and the weakness of royal power in the following centuries led to the de facto independence of the county of Toulouse and many provinces. In the 11th and 12th centuries, southern France was still steeped in Latin culture. Unlike the north of France, justice followed written Roman law and

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4836-405: The crusaders led by Simon de Montfort who defeated the combined forces of Count Raymond VI of Toulouse and King Peter II of Aragon at the Battle of Muret , the following years saw the fate of the county of Toulouse swing alternately in favour of one party or the other. Finally, a late intervention by King Louis VIII of France in 1226 tipped the balance in favour of the crusaders, resulting in

4929-471: The establishment of colleges in the university towns of southern France, not only Toulouse but also Montpellier, Cahors and Avignon. The Black Death in 1348, then the Hundred Years' War caused a major crisis that lasted until the following century. Despite strong immigration, the population lost more than 10,000 inhabitants in 70 years. By 1405 Toulouse had only 19,000 people. In these hardships,

5022-409: The existence of himself (the famous cogito argument), but that he could doubt the existence of his body. This argument is criticized by some modern philosophers on the grounds that it allegedly derives a conclusion about what is true from a premise about what people know. What people know or believe about an entity, they argue, is not really a characteristic of that entity. A response may be that

5115-453: The famous Aéropostale , a pioneering airmail company based in Toulouse and whose epics were popularised by the novels of writers such as Joseph Kessel and Antoine de Saint-Exupéry (himself an Aéropostale pilot). In the 1920s and 1930s the rise of the Toulouse population was increased by the arrival of Italians and Spaniards fleeing the fascist regimes of their country. Then, in the early 1960s, French repatriates from Algeria swelled

5208-528: The historical period in the 2nd century BC, when it became a Roman military outpost. After the conquest of Gaul , it was developed as a Roman city in Gallia Narbonensis . Under the reign of Emperor Augustus and thanks to the Pax Romana , the Romans moved the city a few kilometres from the hills where it was an oppidum to the banks of the Garonne, which were more suitable for trade. In

5301-431: The identity of indiscernibles and the indiscernibility of identicals (the converse principle). Because of its association with Leibniz, the indiscernibility of identicals is sometimes known as Leibniz's law . It is considered to be one of his great metaphysical principles, the other being the principle of noncontradiction and the principle of sufficient reason (famously used in his disputes with Newton and Clarke in

5394-548: The import of olive oil, wine and other goods from the Mediterranean regions. In the 18th century, Toulouse was a provincial capital that prided itself on its royal academies (the only city in France, along with Paris, to have three royal academies), but sometimes seemed far removed from the debates of ideas that agitated the Enlightenment . A famous example illustrates this backwardness of Toulouse mentalities of

5487-413: The impure property of being identical to itself, which it does not share with any other entity. Another important distinction concerns the difference between intrinsic and extrinsic properties . A property is extrinsic to an object if having this property depends on other objects (with or without reference to particular objects), otherwise it is intrinsic . For example, the property of being an aunt

5580-408: The latter case, it is an accepted best practice to specify a primary key for rows in a table. If "two" rows have identical primary keys, they are considered the same row. More importantly for ontology are questions of identity that expose the existence of, or at least the need to represent, other entities. Here the issue at stake is finding the conditions under which a proposed entity would be both

5673-402: The latter properties. Max Black has argued against the identity of indiscernibles by counterexample. Notice that to show that the identity of indiscernibles is false, it is sufficient that one provide a model in which there are two distinct (numerically nonidentical) things that have all the same properties. He claimed that in a symmetric universe wherein only two symmetrical spheres exist,

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5766-412: The meta-property of classes all of whose instances are not wholes, such as classes of mere sums. +U and ~U (but not −U ) are inherited down the class hierarchy. Leibniz's law makes good sense when first considered, however it doesn't take long to see how considerations of time causes problems between most ontologies (especially semantic web ontologies) and Leibniz's law . For example, I might have

5859-442: The metropolitan areas of Paris, Lyon, Marseille, and Lille, but ahead of the metropolitan area of Bordeaux, which the Toulouse metropolitan area passed in population in the 1990s. A local Jewish group estimates there are about 2,500 Jewish families in Toulouse. A Muslim association has estimated there are some 35,000 Muslims in town. The Community of Agglomeration of Greater Toulouse ( Communauté d'agglomération du Grand Toulouse )

5952-490: The most important in France. The population of the city proper (French: commune ) was 498,003 at the January 2020 census, with 1,470,899 inhabitants in the metropolitan area , up from 1,268,438 at the January 2009 census. Thus, the metropolitan area registered a population growth rate of +1.36% per year between 2009 and 2020, the third-highest growth rate of any French metropolitan area larger than 500,000 inhabitants in France, after Montpellier and Bordeaux , although it

6045-592: The nickname La Ville rose ("The Pink city"). Toulouse is in the south of France, north of the department of Haute-Garonne, on the axis of communication between the Mediterranean Sea and the Atlantic Ocean. The city is about 100 km from the Pyrenees and the borders with Andorra and Spain. The city is traversed by the Canal de Brienne , the Canal du Midi , the Canal de Garonne and

6138-592: The nobles were highly educated. This was the time of the troubadours who wrote their poetry in Occitan (called "Provençal" at the time), then one of the most sophisticated languages in Europe. Like the other great lords of the Midi , the counts of Toulouse maintained and favoured these poets, this is how Count Raymond V employed for some time the famous Bernard de Ventadour , expert in singing courtly love . In 1096, Raymond IV, Count of Toulouse , left with his army at

6231-490: The population of the city made it the second or third largest city in France. It was estimated to have 50,000 inhabitants, a figure it would not regain until the 18th century. In 1562, the French Wars of Religion began and Toulouse became an ultra-Catholic stronghold in a predominantly Protestant region, the era of economic prosperity came to an end. The governor of Languedoc, Henri II de Montmorency , who had rebelled,

6324-400: The principle in the philosophical literature, of varying logical strength—and some of them are termed "the strong principle" or "the weak principle" by particular authors, in order to distinguish between them. The identity of indiscernibles has been used to motivate notions of noncontextuality within quantum mechanics. Associated with this principle is also the question as to whether it is

6417-411: The principle of indiscernibility of identicals and the principle of identity of indiscernibles . The principle of indiscernibility of identicals is uncontroversial and states that if two entities are identical with each other then they have the same properties. The principle of identity of indiscernibles , on the other hand, is more controversial in making the converse claim that if two entities have

6510-402: The principle of identity of indiscernibles depend on the conception of properties used to define indiscernibility. One important distinction in this regard is between pure and impure properties. Impure properties are properties that, unlike pure properties , involve reference to a particular substance in their definition. So, for example, being a wife is a pure property while being

6603-410: The properties that has not changed about me when I shave my beard is that I am a person. These properties, that are essential to all their instances, are rigid properties . Rigid properties are designated by +R , and properties that are not rigid −R . An important specialization of non-rigid properties are anti-rigid properties ( ~R ), which are properties that must be changeable. Think of being

6696-569: The rivers Garonne , Touch and Hers-Mort . Toulouse has a four-season humid subtropical climate ( Cfa in the Köppen climate classification ). Too much precipitation during the summer months prevents the city from being classified in the Mediterranean climate zone. The Garonne Valley was a central point for trade between the Pyrenees, the Mediterranean and the Atlantic since at least

6789-535: The royalty that it entailed. In 1369, pope Urban V attributed to the Dominican church of the Jacobins of Toulouse the bones of the Dominican theologian Saint Thomas Aquinas , perhaps to honor the city that had been the cradle of the Dominican order at the beginning of the previous century. The political and economic situation improved by the middle of the 15th century. In 1443 King Charles VII established

6882-401: The same and different. The classic example is an amount of clay that is shaped into a statue. If you use the same clay but reshape it into a different statue, is it the same entity? If so, how could it be different ? If not, how could it be the same . In conceptual modeling, it is understood that when such an ambiguity arises, one should treat it as two different entities to account for

6975-420: The same properties then they must be identical. This entails that "no two distinct things exactly resemble each other". Note that these are all second-order expressions. Neither of these principles can be expressed in first-order logic (are nonfirstorderizable ). Taken together, they are sometimes referred to as Leibniz's law . Formally, the two principles can be expressed in the following way: Principle 1

7068-539: The same size. Identity criteria (and OntoClean, for that matter) do not tell you that one of these definitions of triangle is right or wrong, just that they are different and thus that the classes are different. Identity criteria and sortals are intuitively meant to account for the linguistic habit of associating identity with certain classes. In the classical statue and clay example, we naturally say "the same clay " or "the same statue ", indicating that there are identity criteria that are peculiar to each class. Being

7161-496: The second parliament of France after that of Paris. Reinforcing its place as an administrative and judicial center, the city grew richer, participating in the trade of Bordeaux wine with England, as well as cereals and textiles. A major source of income was the production and export of pastel , a blue dye made from woad . Toulouse suffered several fires, but it was in 1463 that the Great Fire of Toulouse broke out, ravaging

7254-473: The second half of the 1st century, the emperor Domitian distinguished Toulouse by placing it under the patronage of the goddess Pallas Athena , so that the Latin poets Martial , Ausonius and Sidonius Apollinaris called the city Palladia Tolosa (Palladian Toulouse), a term that was still used in the Renaissance and even today when the city is presented as propitious to the arts and letters. Around

7347-400: The seemingly endless arguments about what the right ontology of the universe is, but rather the techniques these philosophers use to analyze, support, and criticize each other's arguments. These techniques make very little, if any, commitment to a particular ontology, instead they expose what are often very subtle distinctions. The ideas underlying OntoClean appeared first in the literature in

7440-476: The submission of Count Raymond VII to the French Crown and the end of the independence of the County of Toulouse. But beyond the military crusade, this struggle took on several important aspects for the city of Toulouse: In 1271, Joan of Toulouse and her husband Alphonse of Poitiers died without heirs. Toulouse, which since the treaty of 1229 had been subordinate to the kingdom of France , no longer had

7533-613: The time: in 1762 its powerful parliament sentenced Jean Calas to death. The philosopher Voltaire then accused the Parlement of Toulouse of religious intolerance (Calas was a Protestant), gave the affair a European repercussion and succeeded in having the judgment of the parliament quashed by the King's Council, which did much damage to the reputation of the parliament. It was on this occasion that Voltaire published one of his major philosophical works: his famous Treatise on Tolerance . With

7626-440: The two spheres are two distinct objects even though they have all their properties in common. Black argues that even relational properties (properties specifying distances between objects in space-time) fail to distinguish two identical objects in a symmetrical universe. Per his argument, two objects are, and will remain, equidistant from the universe's plane of symmetry and each other. Even bringing in an external observer to label

7719-464: The two spheres distinctly does not solve the problem, because it violates the symmetry of the universe. As stated above, the principle of indiscernibility of identicals—that if two objects are in fact one and the same, they have all the same properties—is mostly uncontroversial. However, one famous application of the indiscernibility of identicals was by René Descartes in his Meditations on First Philosophy . Descartes concluded that he could not doubt

7812-406: The wife of Socrates is an impure property due to the reference to the particular "Socrates". Sometimes, the terms qualitative and non-qualitative are used instead of pure and impure . Discernibility is usually defined in terms of pure properties only. The reason for this is that taking impure properties into consideration would result in the principle being trivially true since any entity has

7905-588: The year 250, Toulouse was marked by the martyrdom of Saturnin , the first bishop of Toulouse. This episode illustrates the difficult beginnings of Christianity in Roman Gaul. In the 5th century, Toulouse fell to the Visigothic kingdom and became one of its major cities, even serving as its capital , before it fell to the Franks under Clovis in 507 during the Battle of Vouillé . From that time, Toulouse

7998-470: Was created in 2001 to better coordinate transport, infrastructure and economic policies between the city of Toulouse and its immediate independent suburbs. It succeeds a previous district which had been created in 1992 with fewer powers than the current council. It combines the city of Toulouse and 24 independent communes , covering an area of 380 km (147 sq mi), totalling a population of 583,229 inhabitants (as of 1999 census), 67% of whom live in

8091-465: Was executed in 1632 in the Capitole in the presence of King Louis XIII and Cardinal Richelieu . In 1666, Pierre-Paul Riquet started the construction of the Canal du Midi which links Toulouse to the Mediterranean Sea, and is considered one of the greatest construction works of the 17th century. Completed in 1681, the canal stimulated the economy of Toulouse by promoting the export of cereals and

8184-430: Was famous and revered for its many relics, and the chapter of its canons, which had possessions as far away as Spain, was powerful enough to free itself from the control of the bishop of Toulouse. This dissent had important local political repercussions, making the Bourg in practice a separate district from the city. In 1152, the notables of Toulouse took advantage of a weakening of the county power to obtain for their city

8277-402: Was no real industrial revolution in 19th century Toulouse. The most important industries were the gunpowder factory, to meet military needs, and the tobacco factory. In 1856 the railway arrived in Toulouse and the city was modernised: the ramparts were replaced by large boulevards, and major avenues such as the rue d'Alsace-Lorraine and the rue de Metz opened up the historic centre. In 1875,

8370-521: Was slightly lower than the growth rate registered between the 1990 and 2009 censuses. Toulouse is the fourth most populated city in France, after Paris , Marseille and Lyon , and the fifth most populated metropolitan area after Paris, Lyon, Marseille, and Lille . Fueled by booming aerospace and high-tech industries, the Toulouse metropolitan area's population grew by 57.3% between the 1990 and 2020 censuses (within its 2020 borders), which means +1.52% per year on average during those 30 years, compared with

8463-485: Was the capital of Aquitaine within the Frankish realm. In 721, Duke Odo of Aquitaine defeated an invading Umayyad Muslim army at the Battle of Toulouse . Many Arab chroniclers consider that Odo's victory was the real stop to Muslim expansion into Christian Europe , incursions of the following years being simple raids without real will of conquest (including the one that ended with Charles Martel 's victory at

8556-671: Was the third fastest growing among metropolitan areas larger than 500,000 inhabitants in France. Toulouse is the centre of the European aerospace industry, with the headquarters of Airbus , the SPOT satellite system , ATR and the Aerospace Valley . It hosts the CNES 's Toulouse Space Centre (CST) which is the largest national space centre in Europe, but also, on the military side, the newly created NATO space centre of excellence and

8649-757: Was transformed into the Royal Academy of the Floral Games ( Académie des Jeux Floraux ), still active today, by king Louis XIV . The 14th century also saw a significant increase in the influence of the University of Toulouse, particularly following the move of the papacy from Rome to Avignon. Many law graduates from the University of Toulouse had brilliant careers in the Avignon curia , several became cardinals and three became popes: John XXII , Innocent VI and Urban V . These powerful prelates financed

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