|
Multivalued Dependency
In database theory, a multivalued dependency is a full constraint between two sets of attributes in a relation. In contrast to the functional dependency, the multivalued dependency requires that certain tuples be present in a relation. Therefore, a multivalued dependency is a special case of tuple-generating dependency. The multivalued dependency plays a role in the 4NF database normalization. A multivalued dependency is a special case of a join dependency, with only two sets of values involved, i.e. it is a binary join dependency. A multivalued dependency exists when there are at least three attributes (like X,Y and Z) in a relation and for a value of X there is a well defined set of values of Y and a well defined set of values of Z. However, the set of values of Y is independent of set Z and vice versa. Formal definition The formal definition is as follows: Let R be a relation schema and let \alpha \subseteq R and \beta \subseteq R be sets of attributes. The multivalue ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
|
Database Theory
Database theory encapsulates a broad range of topics related to the study and research of the theoretical realm of databases and database management systems. Theoretical aspects of data management include, among other areas, the foundations of query languages, Computational complexity theory, computational complexity and expressive power (computer science), expressive power of queries, finite model theory, database design theory, dependency theory (database theory), dependency theory, foundations of concurrency control and database recovery, deductive databases, temporal database, temporal and spatial databases, real-time databases, managing uncertain data and probabilistic databases, and Web data. Most research work has traditionally been based on the relational model, since this model is usually considered the simplest and most foundational model of interest. Corresponding results for other data models, such as object-oriented or semi-structured models, or, more recently, graph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
|
Relation Schema
In database theory, a relation, as originally defined by E. F. Codd, is a set of tuples (d1,d2,...,dn), where each element dj is a member of Dj, a data domain. Codd's original definition notwithstanding, and contrary to the usual definition in mathematics, there is no ordering to the elements of the tuples of a relation. Instead, each element is termed an attribute value. An attribute is a name paired with a domain (nowadays more commonly referred to as a type or data type). An attribute value is an attribute name paired with an element of that attribute's domain, and a tuple is a ''set'' of attribute values in which no two distinct elements have the same name. Thus, in some accounts, a tuple is described as a function, mapping names to values. A set of attributes in which no two distinct elements have the same name is called a heading. It follows from the above definitions that to every tuple there corresponds a unique heading, being the set of names from the tuple, paired with t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
|
Tuple-generating Dependency
In relational database theory, a tuple-generating dependency (TGD) is a certain kind of constraint on a relational database. It is a subclass of the class of embedded dependencies (EDs). An algorithm known as the chase takes as input an instance that may or may not satisfy a set of TGDs (or more generally EDs) and, if it terminates (which is a priori undecidable), outputs an instance that does satisfy the TGDs. Definition A tuple-generating dependency is a sentence in first-order logic of the form: :\forall x_1,\ldots, x_n . \phi(x_1, \ldots, x_n) \rightarrow \exists y_1, \ldots, y_m, \psi(x_1, \ldots, x_n, y_1, \ldots, y_m) where \phi is a possibly empty and \psi is a non-empty conjunction of relational atoms. A relational atom has the form R(w_1, \ldots, w_h), where each of the terms w, \ldots, w_h are variables or constants. Fragments Several fragments of TGDs have been defined. For instance, ''full TGDs'' are TGDs which do not use the existential quantifier. Full TGDs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
|
Armstrong's Axioms
Armstrong's axioms are a set of axioms (or, more precisely, inference rules) used to infer all the functional dependencies on a relational database. They were developed by William W. Armstrong in his 1974 paper. The axioms are sound in generating only functional dependencies in the closure of a set of functional dependencies (denoted as F^) when applied to that set (denoted as F). They are also complete in that repeated application of these rules will generate all functional dependencies in the closure F^+. More formally, let \langle R(U), F \rangle denote a relational scheme over the set of attributes U with a set of functional dependencies F. We say that a functional dependency f is logically implied by F, and denote it with F \models f if and only if for every instance r of R that satisfies the functional dependencies in F, r also satisfies f. We denote by F^ the set of all functional dependencies that are logically implied by F. Furthermore, with respect to a set of inferen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
|
Lossless-join Decomposition
In database design, a lossless join decomposition is a decomposition of a relation r into relations r_1, r_2 such that a natural join of the two smaller relations yields back the original relation. This is central in removing redundancy safely from databases while preserving the original data. Lossless join can also be called non-additive. Definition A relation r on schema R ''decomposes losslessly'' onto schemas R_1 and R_2 if \pi_(r) \bowtie \pi_(r) = r, that is r is the natural join of its projections onto the smaller schemas. A pair (R_1, R_2) is a ''lossless-join decomposition'' of R or said to ''have a lossless join'' with respect to a set of functional dependencies F if any relation r(R) that satisfies F decomposes losslessly onto R_1 and R_2. Decompositions into more than two schemas can be defined in the same way. Criteria A decomposition R = R_1 \cup R_2 has a lossless join with respect to F if and only if In logic and related fields such as mathematics and philo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
|
Superkey
In the relational data model a superkey is any set of attributes that uniquely identifies each tuple of a relation. Because superkey values are unique, tuples with the same superkey value must also have the same non-key attribute values. That is, non-key attributes are functionally dependent on the superkey. The set of all attributes is always a superkey (the trivial superkey). Tuples in a relation are by definition unique, with duplicates removed after each operation, so the set of all attributes is always uniquely valued for every tuple. A candidate key (or minimal superkey) is a superkey that can't be reduced to a simpler superkey by removing an attribute. For example, in an employee schema with attributes employeeID, name, job, and departmentID, if employeeID values are unique then employeeID combined with any or all of the other attributes can uniquely identify tuples in the table. Each combination, , , , and so on is a superkey. is a candidate key, since no subset of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
|
Fourth Normal Form
Fourth normal form (4NF) is a normal form used in database normalization. Introduced by Ronald Fagin in 1977, 4NF is the next level of normalization after Boyce–Codd normal form (BCNF). Whereas the second, third, and Boyce–Codd normal forms are concerned with functional dependencies, 4NF is concerned with a more general type of dependency known as a multivalued dependency. A table is in 4NF if and only if, for every one of its non-trivial multivalued dependencies ''X'' \twoheadrightarrow ''Y'', ''X'' is a superkey—that is, ''X'' is either a candidate key or a superset thereof."A relation schema R* is in fourth normal form (4NF) if, whenever a nontrivial multivalued dependency X \twoheadrightarrow Y holds for R*, then so does the functional dependency X → A for every column name A of R*. Intuitively all dependencies are the result of keys." Multivalued dependencies If the column headings in a relational database table are divided into three disjoint groupings ''X'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
 |
Database Normalization
Database normalization is the process of structuring a relational database in accordance with a series of so-called '' normal forms'' in order to reduce data redundancy and improve data integrity. It was first proposed by British computer scientist Edgar F. Codd as part of his relational model. Normalization entails organizing the columns (attributes) and tables (relations) of a database to ensure that their dependencies are properly enforced by database integrity constraints. It is accomplished by applying some formal rules either by a process of ''synthesis'' (creating a new database design) or ''decomposition'' (improving an existing database design). Objectives A basic objective of the first normal form defined by Codd in 1970 was to permit data to be queried and manipulated using a "universal data sub-language" grounded in first-order logic. An example of such a language is SQL, though it is one that Codd regarded as seriously flawed. The objectives of normalization ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
 |
McGraw-Hill
McGraw Hill is an American education science company that provides educational content, software, and services for students and educators across various levels—from K-12 to higher education and professional settings. They produce textbooks, digital learning tools, and adaptive technology to enhance learning experiences and outcomes. It is one of the "big three" educational publishers along with Houghton Mifflin Harcourt and Pearson Education. McGraw Hill also publishes reference and trade publications for the medical, business, and engineering professions. Formerly a division of The McGraw Hill Companies (later renamed McGraw Hill Financial, now S&P Global), McGraw Hill Education was divested and acquired by Apollo Global Management in March 2013 for $2.4 billion in cash. McGraw Hill was sold in 2021 to Platinum Equity for $4.5 billion. History McGraw Hill was founded in 1888, when James H. McGraw, co-founder of McGraw Hill, purchased the ''American Journal of Railway ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
Dependency Theory (database Theory)
Dependency theory is a subfield of database theory which studies implication and optimization problems related to logical constraints, commonly called dependencies, on databases. The best known class of such dependencies are functional dependencies, which form the foundation of keys on database relations. Another important class of dependencies are the multivalued dependencies. A key algorithm in dependency theory is the chase, and much of the theory is devoted to its study. Dependencies Some recognized dependency types are: * Functional dependency * Join dependency * Multivalued dependency * Tuple-generating dependency * Transitive dependency Transitivity or transitive may refer to: Grammar * Transitivity (grammar), a property regarding whether a lexical item denotes a transitive object * Transitive verb, a verb which takes an object * Transitive case, a grammatical case to mark ar ... * Equality-generating dependency * Embedded dependency * Inclusion dependency * Fu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
 |
Attribute (computing)
In computing, an attribute is a specification that defines a property of an object, element, or file. It may also refer to or set the specific value for a given instance of such. For clarity, attributes should more correctly be considered metadata. An attribute is frequently and generally a property of a property. However, in actual usage, the term attribute can and is often treated as equivalent to a property depending on the technology being discussed. An attribute of an object usually consists of a name and a value. For an element these can be a type and class name, while for a file these can be a name and an extension, respectively. Rules and typing * Rules: Each named attribute has an associated set of rules called operations: For example, one doesn't sum characters or manipulate and process an integer array the same way as an image object. Neither does one process text as if it was type of floating point ( decimal numbers). * Data types: It follows that an object d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
Join Dependency
In database theory, a join dependency is a constraint on the set of legal relations over a database scheme. A table T is subject to a join dependency if T can always be recreated by joining multiple tables each having a subset of the attributes of T. If one of the tables in the join has all the attributes of the table T, the join dependency is called trivial. The join dependency plays an important role in the fifth normal form (5NF), also known as ''project-join normal form'', because it can be proven that if a scheme R is decomposed in tables R_1 to R_n, the decomposition will be a lossless-join decomposition if the legal relations on R are restricted to a join dependency on R called *(R_1,R_2,\ldots,R_n). Another way to describe a join dependency is to say that the relationships in the join dependency are independent of each other. Unlike in the case of functional dependencies, there is no sound and complete axiomatization for join dependencies, though axiomatization exist f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |