Ternary Relationship

Requirements Analysis and Conceptual Data Modeling

Toby Teorey , ... H.V. Jagadish , in Database Modeling and Design (Fifth Edition), 2011

Ternary Relationships

Define ternary relationships carefully. We define a ternary relationship among three entities only when the concept cannot be represented by several binary relationships among those entities. For example, let us assume there is some association among entities Technician, Project, and Notebook. If each technician can be working on any of several projects and using the same notebooks on each project, then three many-to-many binary relationships can be defined (see Figure 4.2(a) for the ER model and Figure 4.2(c) for UML). If, however, each technician is constrained to use exactly one notebook for each project and that notebook belongs to only one technician, then a one-to-one-to-one ternary relationship should be defined (see Figure 4.2(b) for the ER model and Figure 4.2(d) for UML). The approach to take in ER modeling is to first attempt to express the associations in terms of binary relationships; if this is impossible because of the constraints of the associations, try to express them in terms of a ternary relationship.

Figure 4.2. Comparison of binary and ternary relationships: (a) binary relationships, (b) different meaning using a ternary relationship, (c) binary associations, and (d) different meaning using a ternary association.

The meaning of connectivity for ternary relationships is important. Figure 4.2(b) shows that for a given pair of instances of Technician and Project, there is only one corresponding instance of Notebook; for a given pair of instances of Technician and Notebook, there is only one corresponding instance of Project; and for a given pair of instances of Project and Notebook, there is only one instance of Technician. In general, we know by our definition of ternary relationships that if a relationship among three entities can only be expressed by a functional dependency involving the keys of all three entities, then it cannot be expressed using only binary relationships, which only apply to associations between two entities. Object-oriented design provides arguably a better way to model this situation (Muller, 1999).

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The Entity–Relationship Model

Toby Teorey , ... H.V. Jagadish , in Database Modeling and Design (Fifth Edition), 2011

Degree of a Relationship

The degree of a relationship is the number of entities associated in the relationship. Binary and ternary relationships are special cases where the degree is 2 and 3, respectively. An n-ary relationship is the general form for any degree n. The notation for degree is illustrated in Figure 2.3. The binary relationship, an association between two entities, is by far the most common type in the natural world. In fact, many modeling systems use only this type. In Figure 2.3 we see many examples of the association of two entities in different ways: Department and Division, Department and Employee, Employee and Project, and so on. A binary recursive relationship (e.g., "manages" in Figure 2.3) relates a particular Employee to another Employee by management. It is called recursive because the entity relates only to another instance of its own type. The binary recursive relationship construct is a diamond with both connections to the same entity.

A ternary relationship is an association among three entities. This type of relationship is required when binary relationships are not sufficient to accurately describe the semantics of the association. The ternary relationship construct is a single diamond connected to three entities as shown in Figure 2.3. Sometimes a relationship is mistakenly modeled as ternary when it could be decomposed into two or three equivalent binary relationships. When this occurs, the ternary relationship should be eliminated to achieve both simplicity and semantic purity. Ternary relationships are discussed in greater detail in the "Ternary Relationships" section below and in Chapter 5.

An entity may be involved in any number of relationships, and each relationship may be of any degree. Furthermore, two entities may have any number of binary relationships between them, and so on for any n entities (see n-ary relationships defined in the "General n-ary Relationships" section below).

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Transforming the Conceptual Data Model to SQL

Toby Teorey , ... H.V. Jagadish , in Database Modeling and Design (Fifth Edition), 2011

Ternary and n-ary Relationships

An n-ary relationship has (n + 1) possible variations of connectivity: all n sides with connectivity "one"; (n − 1) sides with connectivity "one" and one side with connectivity "many"; (n − 2) sides with connectivity "one" and two sides with "many"; and so on until all sides are "many."

The four possible varieties of a ternary relationship are shown in Figure 5.5 for the ER model and Figure 5.6 for UML. All variations are transformed by creating an SQL table containing the primary keys of all entities; however, in each case the meaning of the keys is different. When all three relationships are "one" (Figure 5.5a), the resulting SQL table consists of three possible distinct keys. This represents the fact that there are three functional dependencies (FDs) that are needed to describe this relationship. The optionality constraint is not used here because all n entities must participate in every instance of the relationship to satisfy the FD constraints. (See Chapter 6 for more discussion of functional dependencies.)

In general, the number of entities with connectivity "one" determines the lower bound on the number of FDs. Thus, in Figure 5.5(b), which is one-to-one-to-many, there are two FDs; in Figure 5.5(c), which is one-to-many-to-many, there is only one FD. When all relationships are "many" (Figure 5.5d), the relationship table is all one composite key unless the relationship has its own attributes. In that case, the key is the composite of all three keys from the three associated entities.

Foreign key constraints on delete and update for ternary relationships transformed to SQL tables must always be cascade because each entry in the SQL table depends on the current value of, or existence of, the referenced primary key.

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The multiple-context relational approach generated by the empirical research

Susie Andretta , in Ways of Experiencing Information Literacy, 2012

The multiple-context outcome space of information literacy

According to Edwards (2006: 62) the outcome space presents a picture of the relationship between the categories of description. Marton and Booth argue that this relationship is hierarchical because it demonstrates the progressive complexity 'in which the different ways of experiencing the phenomenon in question can be defined as subsets of the component parts and relationships within more inclusive or complex ways of seeing the phenomenon' (1997: 125). In this study the hierarchy of the outcome space generated by the final stage of the research consists of an incremental progression of the experience of information literacy in personal, information provision, academic and information education contexts. This hierarchy, shown in Table 4.4, operates in the following ways. First, the hierarchical order is illustrated by the type of relationship that characterises the categories of description, where complexity increases from binary to ternary (horizontal headings). Second, the hierarchy operates in terms of the nature of the information goal, where complexity increases from everyday information goals to right or wrong answers to the open-ended question (left-hand side headings). And third, the hierarchy is shown by the progression from passive to active information literacy (right-hand side headings).

Table 4.4. The multiple-context outcome space of information literacy

Binary relationship Ternary relationship
Open-ended question Information Education context – Information Literacy as Education Active IL (fosters independent learning in users)
Academic context – Information Literacy as Lifelong Learning
Right or wrong answer Information Provision context – Information Literacy as Provision Passive IL (satisfies the information needs of the users)
Every day information goals Personal context – Information Literacy as Functional Literacy

The binary relationship characterises Functional Literacy and Lifelong Learning, while the two professional categories of information literacy, Provision and Education, are characterised by the ternary relationship. In the case of the binary relationship the hierarchical order is determined by the type of information goal. For example, when information literacy is seen as Functional Literacy, the students' information goal is based on the need to find solutions to everyday problems. Information literacy as Lifelong Learning describes the dynamics between the students and the open-ended (and therefore complex) information goals situated in an academic context. It is the difference between the open-ended nature of the information goal in an academic scenario and the type of information goal associated with the everyday world of Functional Literacy that determines variation in the way information literacy is interpreted, establishing the hierarchical order between these two categories.

When the ternary relationship is examined then the passive and the active approaches to information literacy are the criteria determining the variation in the positioning of the information professional, the user and the information, and the hierarchical order between the categories of Provision and Education. The focal point in Provision is the information professional who practices information literacy to mediate the interaction between the user and the information, while the user plays a peripheral role of recipient of information (characterised by a right or wrong answer) found by the information professional. By contrast, in Education the user is positioned at the centre of the ternary relationship engaging with both information and educator directly, and therefore experiencing information literacy as the foundation of independent learning, or the ability to deal with open-ended questions. The implications of the ternary hierarchy are that in the Provision category information literacy is experienced by the user as a passive recipient and by the information professional as an active provision of information to satisfy the users' needs. Whereas in the Education category information literacy is experienced by the active learner (satisfying her own information needs) while the educator facilitates the learners' development or enhancement of their independent learning attitudes.

When the categories of description are analysed together, the following hierarchical order applies. Functional Literacy remains the first category in the hierarchy because of its association with everyday information goals. Provision becomes the second category in the hierarchy because it illustrates an increased complexity in the way information literacy is experienced through the expansion of the relationship from binary (person-information) to ternary (users, information professional and information). In this case, information literacy is employed by the information professional, although variation of this experience is generated by two types of users involved in the relationship: knowledge-expert users who are specific in their enquiries to the provider, and users who are unsure of the information they want and who are vague in the way they articulate their enquiries. As a result, the way the provider uses information literacy varies from finding 'quality' information that satisfies the short-term and focused queries from private users to active elicitation of the users information needs in public and educational sectors. Lifelong Learning is third in the hierarchy because it reflects the relationship between the students and open-ended, complex information goals, like reviewing a body of literature. Education remains the fourth and highest category because the ternary relationship reflects the user-centred interaction with open-ended information goals. Here variation occurs at two levels as the students play two different roles in this ternary relationship. In their professional role, as educator, they encourage learners to find information independently, although this role is inspired by the students' awareness of independent learning and is not fully integrated in their professional awareness or practice. The students also play a learner's role in this relationship as students of AIR and this experience raises their awareness of information literacy education from a learner's perspective.

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The Unified Modeling Language

Toby Teorey , ... H.V. Jagadish , in Database Modeling and Design (Fifth Edition), 2011

Publisher Summary

The Unified Modeling Language (UML) is a graphical language for communicating design specifications for software, currently very popular for communicating design specifications for software and, in particular, for logical database designs via class diagrams. The object-oriented software development community created UML to meet the special needs of describing object-oriented software design. UML has grown into a standard for the design of digital systems in general. The similarity between UML and the entity–relationship (ER) model is shown through some common examples in this chapter, including ternary relationships and generalization. UML activity diagrams are used to specify the activities and flow of control in processes. There are a number of different types of UML diagrams serving various purposes. The class and the activity diagram types are particularly useful for discussing database design issues. UML class diagrams capture the structural aspects found in database schemas. UML activity diagrams facilitate discussion on the dynamic processes involved in database design. This chapter is an overview of the syntax and semantics of the UML class and activity diagram constructs used in this book. These same concepts are useful for planning, documenting, discussing and implementing databases. UML activity diagrams are similar in purpose to flow charts. Processes are partitioned into constituent activities along with control flow specifications. This chapter is organized into three main sections. The first section presents class diagram notation, along with examples. The next section covers activity diagram notation, along with illustrative examples. Finally, the last section concludes with a few tips for UML usage.

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Data Modeling: Entity-Relationship Data Model

Salvatore T. March , in Encyclopedia of Information Systems, 2003

II.B.1. Relationship Degree

A relationship associating instances of the same entity, e.g., prerequisite is termed a unary or recursive relationship. It is said to have a degree of 1. A relationship associating instances of two different entities, e.g., reporting is termed a binary relationship (degree 2). A relationship associating instances of three entities, e.g., sale is termed a ternary relationship (degree 3). Generally a relationship associating instances of N entities is termed an N-ary relationship (degree N). The original ER model supports N-ary relationships. The binary relationship models restrict relationships to at most binary. The implications of this restriction are discussed below.

It is often important to distinguish the "roles" played by the entities in a relationship, particularly when a relationship associates instances of the same entity or when it is not clear from the entities themselves. In the relationship prerequisite, for example, it is crucial to distinguish which instance of Course plays the role "has-prerequisite" and which plays the role "is-prerequisite-for." Specifying that the courses Computer Science 101 and Mathematics 220 participate in the relationship named "prerequisite" is not very useful until the roles are specified. Typically this specification utilizes one role or the other to form a sentence: "Computer Science 101 has-prerequisite Mathematics 220" or "Mathematics 220 is-prerequisite-for Computer Science 101." In the relationship reporting, the roles of Employee and Department are clear, Employee instances "report-to" Department instances or Department instances "are the reporting units for" Employee instances.

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Network Database Systems

Frederick N. Springsteel , in Encyclopedia of Information Systems, 2003

III.B. Links in the Network Become "sets" in the DDL

To avoid confusion between the DBTG name for a link, set, and ordinary sets, we shall refer to links as DBTG-sets. Consider again the two links O.SUPPLIER and O.ITEM among the record-types SUPPLIER, ITEM, and OFFER (Figure 6 ) of the previous section. These links derived from the ternary relationship SUPPLIES described earlier. The "owner" record of each link is the "one" object, the actual record at the arrow's head in a link occurrence, and the "members" are the "many" records on the other (origin) end of the link's arrow. For example, as the supplier "Best Supplies" is linked to the several prices that it offers for items, the linked list of owner and members (prices) is considered one DBTG-set: a set occurrence of the DBTG-set O.SUPPLIER. (Conventionally, the name of a set may include its owner's name.) The items that "Best" supplies—say brushes, rotors and combs—may have various prices linked to each item, depending on what price the other suppliers offer them for. But, in the DBTG-set O.ITEM, the owner record of the rotor that Best supplies has a unique (member record) price that is also a member in the DBTG-set O.SUPPLIER and is thus linked to owner-record "Best." It is precisely the intersection of the DBTG-sets at common price member-records, like "$5.00," that actualizes in the DBTG DDL the ternary association SUPPLIES. This actualization makes it possible to "navigate" from the owner of one set, "Best Supplies," to the common member price ($5.00) and thence to this member's other owner, rotor, in the other DBTG-set. Note that the set occurrence diagram of Fig. 7 contains six price records, each involved in exactly two set occurrences. (There are also six set occurrences implied by Figure 7, one for each owner record of the two DBTG-Sets: O.ITEM and O.SUPPLIER.)

Figure 7. The set occurrences for the two SUPPLIES links.

The above two sets can be described in DBTG DDL briefly, without going into all of its low-level technical details, as follows:

To complete the DDL for Figure 7, we need to declare two more record-types, EMP and DEPT, and three DBTG-sets: WORKS_IN, MANAGES and USED_BY:

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Intentionally Linked Entities

V. Kantabutra , in Emerging Trends in Computational Biology, Bioinformatics, and Systems Biology, 2015

2 Introducing ILE for Health Care Applications

The best way to think of ILE is that it is a direct, straightforward implementation of the E/R model. There are differences and extensions, but we can deal with those as they come up.

As can be concluded from the previous discussion, the relational model favors relatively simple data models, even when these models are not necessarily as realistic as one would like. As an example, consider a relational model from a database for JMTZ Bee Healthcare, Inc., of a relationship between a provider (a doctor in this case) and a patient, shown in Figure 14.1 (Jin, 2000).

Figure 14.1. A partial E/R diagram showing the provider-patient relationship in a relational database for JMTZ Healthcare, Inc.

Suppose that we want to model the fact that a relationship between a provider and a patient comprises a set of visits. There are database models for the patient-provider relationship where the two people are related by a "visit" relationship. In such a representation, each visit is a separate relationship, and there is nothing that really binds all the visits of one patient to the same provider together.

In ILE, we can easily model both individual visits and the longer-term relationship between a provider and a patient. The most natural way to do this is shown in Figure 14.2.

Figure 14.2. A possible provider-patient relationship in ILE.

This can be easily implemented in ILE as a ternary relationship, where the roles are patient, provider, and visits. The third role, visits, is actually a set or an array. In relational databases, arrays are usually not permitted. For example, MySQL does not permit array data types. Workarounds are necessary; for example, see MySQL 5.7 reference manual, section 11.1 (n.d.). Oracle, which has some features that are beyond those of plain Relational databases, does have an array data type called ARRAY, and a variant of that data type called VARRAY (see the definition of ARRAY, in the Oracle database system, n.d.), but the elements don't appear to be full-fledged entities that can be conveniently linked in relationships as individuals or first-class citizens of the database.

As another example to use in comparing the various kinds of databases, we can look at prescriptions. In JMTZ's relational database, a prescription is an entity with two binary relationships, as shown in Figure 14.3.

Figure 14.3. Representing the Prescription relationship for JMTZ Healthcare, in an E/R diagram meant for implementation as a relational database

One of these relationships is with an invoice, and the other with one or more medicines. An invoice may have 0, 1, or more prescriptions.

The relational data model used by JMTZ allows for relationships with arbitrary arity. However, many designers of relational databases favor binary relationships because in a binary relationship, entities can be linked directly, without an extra table representing the relationship, and also because joins can be expensive, especially joins of more than two tables. Even query optimization can take considerable time. If this situation were to be modeled using a graph database or a pure OODB, then the type of relationships used would most likely be binary because only binary relationships are natively supported.

ILE, as opposed to these other database schemes, comfortably and natively supports relationships of practically any finite arity. Figure 14.4 shows how we can model a prescription in ILE as a relationship of arity 4.

Figure 14.4. The Prescription relationship in ILE.

In section 5 of this chapter, we will discuss, among other things, how such relationships are implemented in ILE using relationship objects that securely link the various entities playing the roles in each relationship so that navigation from the entities playing one set of roles to the entities playing another set of roles is direct and efficient.

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Conclusion

Susie Andretta , in Ways of Experiencing Information Literacy, 2012

Conclusion

The book offers a unique interpretation of the relational approach that generates a multiple-context outcome space of information literacy, where the description of the experience of information literacy, that is its conceptualisation and practice, needs to take into account the learners' interpretation of the context in which the information literacy experience occurs. The following inferences can be made from this multiple-context relational approach. In contrast with previous relational studies which developed a single-context outcome space underpinned by the binary person-information relationship, the multiple-context outcome space combines the binary relationship with the ternary relationship that reflects a three-way professional interaction, shown in this study as user–librarian–information (Provision) or librarian–user–information (Education). Through the combined use of binary and ternary relationships the multiple-context outcome space enables the experience of information literacy to be examined from a wider perspective, which takes into account the view of the user as a learner in addition to the views of the provider or the educator. In other words, the postgraduate students investigated in this study experience information literacy as learners, studying for the MA, and as librarians, who are professionally associated with delivery information literacy programmes. This makes the outcome space of this research better suited than those of previous studies to inform future relational investigations examining the ways in which information literacy is conceptualised and practised in an educational setting.

The book also proposes that in this multiple-context outcome space complex dynamics exist within and between the categories of description, and this enables the examination of a broader impact of the information literacy experience on the learner. These dynamics are defined as transformation, where the conceptualisation or practice of information literacy in one category may affect the conceptualisation or practice of information literacy in the same category, and transfer where the conceptualisation or practice of information literacy in one category may affect the conceptualisation or practice of information literacy in a different category. As we have seen in Chapter 4, the students who participated in this study carried out two research tasks and this turned out to be significant because it established the spatial awareness of 'before' and 'after' the experience of information literacy generated by these tasks. The completion of the two reviews gave the students an opportunity to reflect on how the information literacy practices involved in the first review (normally for the AIR proposal) influenced the information literacy practices employed to complete the second review (for the dissertation). Moving from the first to the second review generated instances of transformation and transfer. Transformation affects the first three categories of information literacy, Functional Literacy, Lifelong Learning and Provision. Transformation within the category of Lifelong Learning for example, shows that the changes from information literacy practices underpinning the review lead to a greater understanding of the role of the literature review in establishing the direction of the investigation (S_4; S_11) and promote a greater ability to deal with the unpredictability of real-world research (S_21), or with the uncertainty of the information 'void' (S_6). In Provision, transformation is described by some students as improved elicitation of the users' information needs (S_11; S_16; S_6; S_17). On the other hand, transfer from Lifelong Learning to Provision reflects the changes in the students' professional conceptualisation and practice of information literacy. An example of this change is shown by student 21 who began to question the assumption that librarians 'need to know the answer' to fulfil the users' information needs, stressing instead the importance of employing information literacy practices that can find 'any' answer. This view offers a clear example of what Fazey and Marton (2002) describe as 'mastering the process of variation', where this student begins to focus on the process of finding an answer that varies depending on the nature of the query. From the point of view of the information literacy educator the multiple-context relational approach offers the following benefits. First, it enables one to identify which conceptualisation and practice are associated with the experience of information literacy and tailor the support accordingly. Second, this relational approach provides the means by which the educator may encourage a particular experience of information literacy to expand the students' conceptualisation and/or practice in one category, or from one category to another.

In conclusion, this book makes a significant contribution to the relational approach for the following reasons. First, the multiple-context outcome space offers a wider interpretation of information literacy than the one generated by the relational approaches used in previous studies. This is because the conceptualisation and practice of information literacy proposed by the multiple-context outcome space relate to different contexts, types of information relationship and nature of the information goal. In other words, variation in this study is not based on the different aspects of information literacy that are associated with one context, but is generated by different information literacy experiences that are related by the students to the personal, the academic and the information professional contexts. For example, the Functional Literacy category describes different conceptualisations and practices of information literacy compared with the Lifelong Learning category because its everyday activities, such as looking for accommodation or booking a holiday, do not appear to the students to require the same levels of reflection and evaluation that are needed to address the open-ended questions found in Lifelong Learning, such as reviewing the literature for an unfamiliar topic. Second, the multiple-context outcome space generates complex patterns of interaction between the conceptualisations and practices of information literacy within and across the categories of description. In this study the impact of these interactions is described in terms of transformation and transfer. As we have seen at the beginning of this chapter, previous relational studies have explored transformation that occurs as a result of the information literacy experience. However, these studies cannot examine transfer, which by definition applies to the changes that occur across two categories of description that relate to different contexts. This suggests that in addition to providing a wider interpretation of information literacy, the multiple-context approach offers a more comprehensive way of measuring the impact of information literacy than a single-context approach and could be employed to assess the impact of other learning conditions.

Inevitably, some of the areas touched on by this investigation, such as the significance of personal disposition towards information and the development of librarians into educators, reach beyond the scope of this study and must remain topics for future research. But it is to be hoped that this multiple-context outcome space will be found productive by the diverse audiences identified at the beginning of this book. For example, educators could use this outcome space to explore different experiences of information literacy or of learning, with students from other academic disciplines or with communities operating outside the higher education sector. Supporting this view is the proposition that the relational approach to information literacy (or the relationship between person and information) describes the act of learning, and this necessarily complements the content learned. In addition, the 'how to apply the relational framework' approach presented in this book targets researchers and doctoral students who wish to investigate people's relationships with information and the impact that these have on the outcome of learning. And finally, the effective information literacy practices used to review the literature identified by the students who participated in this study may prove useful to postgraduate students who are embarking on similar research projects. In this wider context the research outlined in this book will have met its goal if it can form a small but significant step in furthering the debate on the way learners experience information literacy and on the suitability of the relational approach in examining these experiences.

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Conceptual Modeling

BERTHOLD DAUM , in Modeling Business Objects with XML Schema, 2003

2.5.1 AOM Basics

The main components in AOM for describing the structure of an information model are assets and arcs. Unlike the various flavors of Entity Relationship Modeling, AOM does not distinguish between entities and relationships (or between classes and associations as UML does). Assets are not the same as entities, and arcs are not the same as relationships. AOM uses assets and arcs more in the way the Resource Description Framework (RDF) uses nodes and arcs. The classical entities and relationships are both represented in AOM as assets. Or, to be precise, AOM treats everything—even entities—as relationships. Let's see how this works.

Take for example a classical entity type, Customer. Let's say this entity type is related to entity type Person by an is_a relationship, and with entity type Account by a has relationship. So the classical model would have three entity types: Customer, Person, and Account, and two relationship types: is_a and has.

However, we could interpret this situation quite differently. We could see Customer as a binary relationship that relates an account to a person. If we also want to include the fact that a customer resides at a given address, then Customer becomes a ternary relationship between Person, Account, and Address. In fact, a relationship might relate any number of items to each other. Generally, we allow n-ary relationships.

Do we also have 1-ary (unary) relationships? Of course we have. Take for example a bicycle. A bicycle can be seen as a binary relationship because it relates the front wheel and the back wheel to each other. What about a monocycle? Obviously, a monocycle represents a unary relationship. That might sound like one hand clapping, but mathematically it is perfectly correct.

Let's put this all together and look at a first example. What was said for the monocycle applies in the model in Figure 2.4 to OrderItem. OrderItem is a unary relationship referring to CD. The binary relationship orders relates the two relationships Customer and OrderItem to each other. Finally, the binary relationship receives relates the relationships orders and Shop to each other.

Figure 2.4. Simple model for a music shop. Note that arcs do not represent a relationship but simply connect an asset with other assets that play a role in the context of the first asset. Arcs can be decorated with role names.

Modeling this example in a classical modeling method would give us some trouble because in classic theory it is not clear if orders is a relationship or an entity. If we decided for a relationship orders, we would have trouble with relationship receives, as this relationship would now relate an entity (Shop) with another relationship (orders)—a concept that is not supported in classical modeling methods.

In classical ERM, if we decided for an entity, we would first have to reify the act of ordering into an entity Order. (To reify means to make into a thing.) Then we would have to invent additional relationships to relate Order to Customer and CD. The model gets bigger. Unfortunately, these scenarios where we would have to treat relationships as entities are not uncommon. In modern business scenarios, any business relationship manifests itself sooner or later as a business document and, alas, becomes an entity.

So far, we have not discussed how to represent the end nodes of our graph: Person, CD, Account, Address, and Shop. Shouldn't we represent these assets differently—as entities? I think not. These assets are always potential relationships. For example, if we add an asset Department to Shop, then Shop becomes a unary relationship. As long as Department is not added, Shop is, well, a 0-ary relationship. If this sounds a bit uncommon, consider that the concept of zero was uncommon itself until the number zero was invented only some time ago in Arabia. The advantage is that with this concept, a given model is easier to extend. When we want to add Department to Shop, we just connect it with an arc, but we do not have to convert Shop from an entity into a relationship.

AOM's concept of using relationships over relationships is based on Bernhard Thalheim's Higher Order Entity Relationship Modeling (HERM) [Thalheim-2000], although Thalheim still differentiates between entities and relationships. In this respect AOM is closer to the relational approach, where both entities and relationships are represented as tables. It was E. F. Codd, the father of relational algebra, who stated that there is no reason to distinguish between entity type and relationship type [Codd1991]). Consequently, relational database schemata translate nicely into AOM.

The following sections will introduce AOM's language elements in a more formal way.

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