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Relationship

Relationship

See:
- Relational model
- Interpersonal relationship, including romantic relationships
- Mathematical relationship, including:
  - Inverse relationship
  - Direct relationship
- Relation (mathematics)

Relational model

The relational model for management of a database is a data model based on predicate logic and set theory.

The model

The fundamental assumption of the relational model is that all data are represented as mathematical relations, i.e., a subset of the Cartesian product of n sets. In the mathematical model, reasoning about such data is done in two-valued predicate logic (that is, without NULLs), meaning there are two possible evaluations for each proposition: either true or false. Data are operated upon by means of a relational calculus and algebra. The relational data model permits the designer to create a consistent logical model of information, to be refined through database normalization. The access plans and other implementation and operation details are handled by the DBMS engine, and should not be reflected in the logical model. This contrasts with common practice for SQL DBMSs in which performance tuning often requires changes to the logical model. The basic relational building block is the domain, or data type. A tuple is an ordered multiset of attributes, which are ordered pairs of domain and value. A relvar (relation variable) is a set of ordered pairs of domain and name, which serves as the header for a relation. A relation is a set of tuples. Although these relational concepts are mathematically defined, they map loosely to traditional database concepts. A table is an accepted visual representation of a relation; a tuple is similar to the concept of row. The basic principle of the relational model is the Information Principle: all information is represented by data values in relations. Thus, the relvars are not related to each other at design time: rather, designers use the same domain in several relvars, and if one attribute is dependent on another, this dependency is enforced through referential integrity.

Competition

Other models are the hierarchical model and network model. Some systems using these older architectures are still in use today in data centers with high data volume needs or where existing systems are so complex and abstract it would be cost prohibitive to migrate to systems employing the relational model; also of note are newer object-oriented databases, even though many of them are DBMS-construction kits, rather than proper DBMSs. The relational model was the first formal database model. After it was defined, informal models were made to describe hierarchical databases (the hierarchical model) and network databases (the network model). Hierarchical and network databases existed before relational databases, but were only described as models after the relational model was defined, in order to establish a basis for comparison.

History

The relational model was invented by Dr. Ted Codd as a general model of data, and subsequently maintained and developed by Chris Date and Hugh Darwen among others. In The Third Manifesto (1995) they show how the relational model can be extended with object-oriented features without compromising its fundamental principles. The foundation for the relational model included important works published by Georg Cantor (1874) and D.L Childs (1968). Cantor was a 19th century German mathematician who published a number of articles and was the principal creator of set theory. Childs is an American mathematician whose "Description of a Set-Theoretic Data Structure" was cited by Codd in his seminal 1970 paper "A Relational Model of Data for Large Shared Data Banks". Childs' STDS uses set theory as the basis for querying data using set operations such as union, intersection, domain, range, restriction, cardinality and Cartesian product. The use of sets and set operations provided independence from physical data structures, a pioneering concept at the time.

Misimplementation

SQL, initially pushed as the standard language for relational databases, was actually always in violation of it. SQL DBMS's are thus not actually RDBMS's, and the current ISO SQL standard doesn't mention the relational model or use relational terms or concepts.

Implementation

There have been several attempts to produce a true implementation of the relational database model originally developed by Codd, Date, Darwen and others, but none have been popular successes so far. [http://dbappbuilder.sourceforge.net/Rel.html Rel] is one of the more recent attempts to do this. SQL uses concepts "table", "column", "row" instead of "relvar", "attribute", "tuple".

Controversies

Codd himself proposed a three-valued logic version of the relational model, and a four-valued logic version has also been proposed, in order to deal with missing information. But these have never been implemented, presumably because of attending complexity. SQL NULLs were intended to be part of a three-valued logic system, but fell short of that due to logical errors in the standard and in its implementations.

Design

Database normalization is usually performed when designing a relational database, to improve the logical consistency of the database design and the transactional performance. There are two commonly used systems of diagramming to aid in the visual representation of the relational model: the entity-relationship diagram (ERD), and the related IDEF diagram used in the IDEF1X method created by the U.S. Air Force based on ERDs.

Example database

An idealized, very simple example of a description of some relvars and their attributes: Customer(Customer ID, Tax ID, Name, Address, City, State, Zip, Phone) Order(Order No, Customer ID, Invoice No, Date Placed, Date Promised, Terms, Status) Order Line(Order No, Order Line No, Product Code, Qty) Invoice(Invoice No, Customer ID, Order No, Date, Status) Invoice Line(Invoice No, Line No, Product Code, Qty Shipped) Product(Product Code, Product Description) In this design we have six relvars: Customer, Order, Order Line, Invoice, Invoice Line and Product. The bold, underlined attributes are candidate keys. The non-bold, underlined attributes are foreign keys. Usually one candidate key is arbitrarily chosen to be called the primary key and used in preference over the other candidate keys, which are then called alternate keys. A candidate key is a unique identifier enforcing that no tuple will be duplicated; this would make the relation into something else, namely a bag, by violating the basic definition of a set. A key can be composite, that is, can be composed of several attributes. Below is a tabular depiction of a relation of our example Customer relvar; a relation can be thought of as a value that can be attributed to a relvar.

Set Theory Formulation

Basic notions in the relational model are relation names and attribute names. We will represent these as strings such as "Person" and "name" and we will usually use the variables r, s, t, ... and a, b, c to range over them. Another basic notion is the set of atomic values that contains values such as numbers and strings. Our first definition concerns the notion of tuple, which formalizes the notion of row or record in a table: : Def. A tuple is a partial function from attribute names to atomic values. : Def. A header is a finite set of attribute names. : Def.- The projection of a tuple t on a finite set of attributes A is t[A] = . The next definition defines relation which formalizes the contents of a table as it is defined in the relational model. : Def. A relation is a tuple (H, B) with H, the header, and B, the body, a set of tuples that all have the domain H. Such a relation closely corresponds to what is usually called the extension of a predicate in first-order logic except that here we identify the places in the predicate with attribute names. Usually in the relational model a database schema is said to consist of a set of relation names, the headers that are associated with these names and the constraints that should hold for every instance of the database schema. : Def. A relation universe U over a header H is a non-empty set of relations with header H. : Def. A relation schema (H, C) consists of a header H and a predicate C(R) that is defined for all relations R with header H. : Def. A relation satisfies the relation schema (H, C) if it has header H and satisfies C.

Key constraints and functional dependencies

One of the simplest and most important types of relation constraints is the key constraint. It tells us that in every instance of a certain relational schema the tuples can be identified by their values for certain attributes. : Def. A superkey is written as a finite set of attribute names. : Def. A superkey K holds in a relation (H, B) if K ⊆ H and there are no two distinct tuples t1 and t2 in B such that t1[K] = t2[K]. : Def. A superkey holds in a relation universe U over a header H if it holds in all relations in U. : Def. - A superkey K holds as a candidate key for a relation universe U over H if it holds as a superkey for U and there is no proper subset of K that also holds as a superkey for U. : Def. A functional dependency (or FD for short) is written as X->Y with X and Y finite sets of attribute names. : Def. A functional dependency X->Y holds in a relation (H, B) if X and Y are subsets of H and for all tuples t1 and t2 in B it holds that if t1[X] = t2[X] then t1[Y] = t2[Y] : Def. A functional dependency X->Y holds in a relation universe U over a header H if it holds in all relations in U. : Def. A functional dependency is trivial under a header H if it holds in all relation universes over H. : Theorem A FD X->Y is trivial under a header H iff Y ⊆ X ⊆ H. : Theorem A superkey K holds in a relation universe U over H iff K ⊆ H and K->H holds in U. : Def. (Armstrong's rules) Let S be a set of FDs then the closure of S under a header H, written as S+, is the smallest superset of S such that: :: (reflexivity) if Y ⊆ X ⊆ H then X->Y in S+ :: (transitivity) if X->Y in S+ and Y->Z in S+ then X->Z in S+ :: (augmentation) if X->Y in S+ and Z ⊆ H then X∪Z -> Y∪Z in S+ : Theorem Armstrong's rules are sound and complete, i.e., given a header H and a set S of FDs that only contain subsets of H then the FD X->Y is in S+ iff it holds in all relation universes over H in which all FDs in S hold. : Def. If X is a finite set of attributes and S a finite set of FDs then the completion of X under S, written as X+, is the smallest superset of X such that: :: if Y->Z in S and Y ⊆ X+ then Z ⊆ X+ The completion of an attribute set can be used to compute if a certain dependency is in the closure of a set of FDs. : Theorem Given a header H and a set S of FDs that only contain subsets of H it holds that X->Y is in S+ iff Y ⊆ X+. : Algorithm (deriving candidate keys from FDs) INPUT: a set S of FDs that contain only subsets of a header H OUTPUT: the set C of superkeys that hold as candidate keys in all relation universes over H in which all FDs in S hold begin C := ∅; // found candidate keys Q := ; // superkeys that contain candidate keys while Q <> ∅ do let K be some element from Q; Q := Q - ; minimal := true; for each X->Y in S do K' := (K - Y) ∪ X; // derive new superkey if K' ⊂ K then minimal := false; Q := Q ∪ ; fi od if minimal and there is not a subset of K in C then remove all supersets of K from C; C := C ∪ ; fi od end : Def. Given a header H and a set of FDs S that only contain subsets of H an irreducible cover of S is a set T of FDs such that :# S+ = T+ :# there is no proper subset U of T such that S+ = U+, :# if X->Y in T then Y is a singleton set and :# if X->Y in T and Z a proper subset of X then Z->Y is not in S+.

See also


- Relational Database Management System
- List of truly relational database management systems
- Tuple-versioning
- TransRelational model

References


- Codd, E. F. (1970). "A relational model of data for large shared data banks". Communications of the ACM, 13(6):377–387. (Retrieved from [http://www.acm.org/classics/nov95/toc.html ACM], September 4, 2004.)
- Date, C. J., Darwen, H. (2000). Foundation for Future Database Systems: The Third Manifesto, 2nd edition, Addison-Wesley Professional. ISBN 0201709287.
- Date, C. J. (2003). Introduction to Database Systems. 8th edition, Addison Wesley. ISBN 0321197844.

External links


- [http://www.acm.org/classics/nov95/toc.html A Relational Model of Data for Large Shared Data Banks]
- [http://dmoz.org./Computers/Software/Databases/Relational/ DMoz category]
- [http://c2.com/cgi/wiki?RelationalModel Relational Model] Category:Data modeling Category:Databases

Interpersonal relationship

An interpersonal relationship is a social association, connection, or affiliation between two or more people. It varies in differing levels of intimacy and modes of connection, implying discovery or establishment of common ground, and may be centered around something(s) shared in common. Its study is one of the concerns of the social science known as sociology, and, to a lesser extent, of psychology and anthropology.

Types of interpersonal relationships


- Kinship relationships, including family relationships, being related to someone else by blood (consanguinity), e.g. fatherhood, motherhood; or through marriage (affinity), e.g. father-in-law, mother-in-law, uncle by marriage, aunt by marriage.
- Formalized intimate relationships or long term relationships through law and public ceremony, e.g. marriage and civil union.
- Non-formalized intimate relationships or long term relationships such as loving relationships or romantic relationships with or without living together; the other person is often called lover, boyfriend or girlfriend (not to be confused with just a male or female friend), or significant other. If the partners live together, the relationship may be similar to marriage, and the other person may be called husband or wife. Over a certain length of time they are so regarded by common law. Mistress is a somewhat old fashioned term for a female lover of a man who is married to another woman, or of an unmarried man. She may even be an official mistress (in French maîtresse en titre); an example is Madame de Pompadour.
- Soulmates, individuals who are intimately drawn to one another through a favorable meeting of the minds and who find mutual acceptance and understanding with one another. Soulmates may feel themselves bonded together for a lifetime; and, hence, they may be sexual partners but not necessarily.
- Casual relationships, relationships extending beyond one night stands that exclusively consist of sexual behavior, the participants of which may be known as friends with benefits when limited to considering sexual intercourse or sexual partners in a wider sense.
- Platonic love is an affectionate relationship into which the sexual element does not enter, especially in cases where one might easily assume otherwise.
- Friendship, which consists of mutual love, trust, respect, and unconditional acceptance, and usually implies the discovery or establishment of common ground between the individuals involved; see also internet friendship and pen pal.
- Brotherhood and sisterhood, individuals united in a common cause or having a common interest, which may involve formal membership in a club, organization, association, society, lodge, sorority, fraternity. This type of interpersonal relationship also includes the comradeship of fellow soldiers in peace or war.
- Partners or coworkers in a profession, business, or a common workplace.
- Acquaintanceship, simply being introduced to someone or knowing who they are by interaction.

Factors affecting interpersonal relationships

The discovery or establishment of common ground between individuals is a fundamental component for enduring interpersonal relationships other than familial relationship. Loss of common ground, which may happen over time, may tend to end interpersonal relationships. Interpersonal relationships through consanguinity and affinity would persist despite the absence of love, affection, or common ground. When these relationships are in prohibited degrees, sexual intimacy in them would be the taboo of incest. Marriage and civil union are relationships reinforced and regularized by their legal sanction to be "respectable" building blocks of society. In the United States the de-criminalization of homosexual sexual relations in the landmark Supreme Court decision, Lawrence v. Texas (2003) facilitated the "mainstreaming" of gay long term relationships, and broached the possibility of the legalization of same-sex marriages in that country. In intimate relationships there is often, but not always, an implicit or explicit agreement that the partners will not have sex with someone else monogamy. The extent to which physical intimacy with other people is accepted may vary. For example, a husband may be more receptive to his wife being physically affectionate with her female friend if she has one than with her male friend (see also jealousy). In friendship there is some transitivity: one may become a friend of an existing friend's friend. However, if two people have a sexual relationship with the same person, they may be competitors rather than friends. Accordingly, sexual behavior with the sexual partner of a friend may damage the friendship. See love triangle. Sexual relations between two friends may alter that relationship by either "taking it to the next level" or severing it if the sexual relationship ends. Sexual partners may also be friends: the sexual relationship may either enhance or depreciate the friendship. The rise of popular psychology has led to an explosion of concern about one's interpersonal relationships (often simply called: "relationships"). Intimate relationships receive particular attention in this context, but Sociology recognises many other interpersonal links of greater or less duration and/or significance. Relationships are not necessarily healthy. Examples include abusive relationships and co-dependency. In sociology there is a hierarchy of forms of activity and interpersonal relations, which divides them into: behavior, action, social behavior, social action, social contact, social interaction and finally social relation.

Theories of interpersonal relationships


- Social psychology has several approaches to the subject of interpersonal relationships, among them closure and also trust, as trust between parties can be mutual. This may lead to enduring relationships.
- Social exchange theory interprets relationships in terms of exchanged benefits. The way people feel about relationships will be influenced by the rewards of the relationship, as well as rewards they may potentially receive in alternate relationships.
- Equity theory is based on criticism of social exchange theory. Proponents argue that people care more than just maximizing rewards, they also want fairness and equity in their relationships.
- Relational dialectics is based on the idea that a relationship is not a static entity. Instead, a relationship is a continuing process, always changing. There is constant tension as three main issues are negotiated: autonomy vs. connection, novelty vs. predictability, and openness vs. closedness.
- Attachment styles are a completely different way of analyzing relationships. Proponents of this view argue that attachment styles developed in childhood continue to be influential throughout adulthood, influencing the roles people take on in relationships.

External links


- [http://www.love-calculator.info Love Calculator]
- [http://www.abookoflove.com Using romantic roleplay and bedroom games to bring greater dimension into relationships]
- [http://samvak.tripod.com/friend.html Altruism and egoism in interpersonal relationships]
- [http://www.guardian.co.uk/g2/story/0,,1396917,00.html What are friends for?] - three part article in UK Guardian newspaper
- [http://www.ipfeurope.com International Pen Friends] IPF is the biggest pen friends organization in the world, with more than 300,000 members in 192 countries.
- [http://www.intellectualwhores.com/masterladder.html Master Ladder Theory]: based on the idea that men and women cannot be friends, this theory (while sounding extremely tongue-in-cheek) is very thorough and interesting.
- [http://news-for-two.cloudworth.com/ News-for-Two] Daily edited review of headlines related to human relatioships, love and interpersonal communication.

See also


- Adultery
- Concubinage
- Dating
- Historical pederastic couples
- Monogamy, polyamory, polygamy, endogamy, exogamy
- Single (relationship) Category:Social psychology Category:Interpersonal relationships ---- Category:Anthropology ja:親族

Inverse relationship

A negative, or inverse relationship is a mathematical relationship in which one variable decreases as another rises. For example, there is an inverse relationship between education and unemployment. That is to say that as public education increases, the rate of unemployment decreases. Contrast with direct relationship. Category:Elementary mathematics

Direct relationship

In mathematics, a direct relationship in mathematics and statistics is a positive relationship between two variables in which they both increase or decrease in conjunction. For example, there is a direct relationship between age and risk for heart disease. The older you get, the more likely you are to get the disease, and the younger you are, the less likely you are to get it. Contrast with inverse relationship. Category:Elementary mathematics

Relation (mathematics)

In mathematics, an n-ary relation (or n-place relation or often simply relation) is a generalization of binary relations such as "=" and "<" which occur in statements such as "5 < 6" or "2 + 2 = 4". It is also the fundamental notion in the relational model for databases.

Definition

A relation over the sets X1, ..., Xn is an (n + 1)-tuple R=(X1, ..., Xn, G(R)) where G(R) is a subset of X1 × ... × Xn (the Cartesian product of these sets). If X=X1=X2=...=Xn, R is simply called a relation over X. G(R) is called the graph of R and, similar to the case of binary relations, R is often identified with its graph. An n-ary predicate is a truth-valued function of n variables.

Remarks

Because a relation as above defines uniquely an n-ary predicate that holds for x1, ..., xn if (x1, ..., xn) is in G(R), and vice versa, the relation and the predicate are often denoted with the same symbol. So, for example, the following two statements are considered to be equivalent: :(x_1,x_2,\dotsb)\in G(R) :R(x_1,x_2,\dotsb) Relations are classified according to the number of sets in the Cartesian product; in other words the number of terms in the expression:
- unary relation or property: R(x)
- binary relation: R(x, y) or x R y
- ternary relation: R(x, y, z)
- quaternary relation: R(x, y, z, w) Relations with more than 4 terms are usually called n-ary; for example "a 5-ary relation".

See also


- binary relation
- computable predicate Category:Set theory

Leopold I Koburg

Leopold I, (ur. 16 grudnia 1790, zm. 10 grudnia 1865) – książę Sachsen-Coburg-Gotha, król Belgów 1831 – 1865. Leopold, książę Sachsen-Coburg, został monarchą konstytucyjnym z wyboru. Jego pozycja utrwaliła się dopiero, gdy Brytyjczycy i Francuzi pokonali interwencyjną armię holenderską w roku 1832. W roku 1839 Belgia ogłosiła wieczystą neutralność. Jako wdowiec po brytyjskiej księżnej Charlocie i wuj królowej Wiktorii, Leopold miał pewien wpływ na wydarzenia na europejskiej scenie politycznej. Kategoria:Dynastia Saxe-Coburg-Gotha Kategoria:Władcy Belgii ja:レオポルド1世 (ベルギー王)

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