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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, 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 for more e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fifth Normal Form
Fifth normal form (5NF), also known as projection–join normal form (PJ/NF), is a level of database normalization designed to remove redundancy in relational databases recording multi-valued facts by isolating semantically related multiple relationships. A table is said to be in the 5NF if and only if every non-trivial join dependency in that table is implied by the candidate keys. It is the final normal form as far as removing redundancy is concerned. A 6NF also exists, but its purpose is not to remove redundancy and it is therefore only adopted by a few data warehouses, where it can be useful to make tables irreducible. A join dependency * on R is implied by the candidate key(s) of R if and only if each of A, B, …, Z is a superkey for R. The fifth normal form was first described by Ronald Fagin in his 1979 conference paper ''Normal forms and relational database operators''. Example Consider the following example: The table's predicate is: products of the type designated b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 and expressive power of queries, finite model theory, database design theory, dependency theory, foundations of concurrency control and database recovery, deductive databases, 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 data models and XML, are often derivable from those for the relational model. A central focus of database theory is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 * functional dependency * join dependency * multivalued dependency * 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 ... * equality-generating dependency * embedded dependency * inclusion dependency * full typed dependency {{database-stub Database theory Datab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relational Algebra
In database theory, relational algebra is a theory that uses algebraic structures with a well-founded semantics for modeling data, and defining queries on it. The theory was introduced by Edgar F. Codd. The main application of relational algebra is to provide a theoretical foundation for relational databases, particularly query languages for such databases, chief among which is SQL. Relational databases store tabular data represented as relations. Queries over relational databases often likewise return tabular data represented as relations. The main purpose of the relational algebra is to define operators that transform one or more input relations to an output relation. Given that these operators accept relations as input and produce relations as output, they can be combined and used to express potentially complex queries that transform potentially many input relations (whose data are stored in the database) into a single output relation (the query results). Unary operators ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 database In computing, a database is an organized collection of data stored and accessed electronically. Small databases can be stored on a file system, while large databases are hosted on computer clusters or cloud storage. The design of databases s ...s while preserving the original data. Criteria Lossless join can also be called nonadditive. If R is split into R_1 and R_2, for this decomposition to be lossless (i.e., R_1 \bowtie R_2 = R) then at least one of the two following criteria should be met. Check 1: Verify join explicitly Projecting on R_1 and R_2, and joining them back, results in the relation you started with. Check 2: Via functional dependencies Let R be a relation schema. Let be a set of functional dep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Dependencies
In relational database theory, a functional dependency is a constraint between two sets of attributes in a relation from a database. In other words, a functional dependency is a constraint between two attributes in a relation. Given a relation ''R'' and sets of attributes X,Y \subseteq R, ''X'' is said to functionally determine ''Y'' (written ''X'' → ''Y'') if and only if each ''X'' value in ''R'' is associated with precisely one ''Y'' value in ''R''; ''R'' is then said to ''satisfy'' the functional dependency ''X'' → ''Y''. Equivalently, the projection \Pi_R is a function, i.e. ''Y'' is a function of ''X''. In simple words, if the values for the ''X'' attributes are known (say they are ''x''), then the values for the ''Y'' attributes corresponding to ''x'' can be determined by looking them up in ''any'' tuple of ''R'' containing ''x''. Customarily ''X'' is called the ''determinant'' set and ''Y'' the ''dependent'' set. A functional dependency FD: ''X'' → ''Y'' is called ''t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soundness
In logic or, more precisely, deductive reasoning, an argument is sound if it is both valid in form and its premises are true. Soundness also has a related meaning in mathematical logic, wherein logical systems are sound if and only if every formula that can be proved in the system is logically valid with respect to the semantics of the system. Definition In deductive reasoning, a sound argument is an argument that is valid and all of its premises are true (and as a consequence its conclusion is true as well). An argument is valid if, assuming its premises are true, the conclusion ''must'' be true. An example of a sound argument is the following well-known syllogism: : ''(premises)'' : All men are mortal. : Socrates is a man. : ''(conclusion)'' : Therefore, Socrates is mortal. Because of the logical necessity of the conclusion, this argument is valid; and because the argument is valid and its premises are true, the argument is sound. However, an argument can be valid without ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Completeness (logic)
In mathematical logic and metalogic, a formal system is called complete with respect to a particular property if every formula having the property can be derived using that system, i.e. is one of its theorems; otherwise the system is said to be incomplete. The term "complete" is also used without qualification, with differing meanings depending on the context, mostly referring to the property of semantical validity. Intuitively, a system is called complete in this particular sense, if it can derive every formula that is true. Other properties related to completeness The property converse to completeness is called soundness: a system is sound with respect to a property (mostly semantical validity) if each of its theorems has that property. Forms of completeness Expressive completeness A formal language is expressively complete if it can express the subject matter for which it is intended. Functional completeness A set of logical connectives associated with a formal system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Full Typed Dependencies
Full may refer to: * People with the surname Full, including: ** Mr. Full (given name unknown), acting Governor of German Cameroon, 1913 to 1914 * A property in the mathematical field of topology; see Full set * A property of functors in the mathematical field of category theory; see Full and faithful functors * Satiety, the absence of hunger * A standard bed size, see Bed * Fulling Fulling, also known as felting, tucking or walking ( Scots: ''waukin'', hence often spelled waulking in Scottish English), is a step in woollen clothmaking which involves the cleansing of woven or knitted cloth (particularly wool) to elimin ..., also known as tucking or walking ("waulking" in Scotland), term for a step in woollen clothmaking (verb: ''to full'') * Full-Reuenthal, a municipality in the district of Zurzach in the canton of Aargau in Switzerland See also *" Fullest", a song by the rapper Cupcakke * Ful (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 and let \alpha \subseteq R and \beta \subseteq R be sets of attributes. The multivalued depend ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
If And Only If
In logic and related fields such as mathematics and philosophy, "if and only if" (shortened as "iff") is a biconditional logical connective between statements, where either both statements are true or both are false. The connective is biconditional (a statement of material equivalence), and can be likened to the standard material conditional ("only if", equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of either one of the connected statements requires the truth of the other (i.e. either both statements are true, or both are false), though it is controversial whether the connective thus defined is properly rendered by the English "if and only if"—with its pre-existing meaning. For example, ''P if and only if Q'' means that ''P'' is true whenever ''Q'' is true, and the only case in which ''P'' is true is if ''Q'' is also true, whereas in the case of ''P if Q'', there could be other scenarios where ''P'' is true and ''Q'' is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chase (algorithm)
The chase is a simple fixed-point algorithm testing and enforcing implication of data dependencies in database systems. It plays important roles in database theory as well as in practice. It is used, directly or indirectly, on an everyday basis by people who design databases, and it is used in commercial systems to reason about the consistency and correctness of a data design. New applications of the chase in meta-data management and data exchange are still being discovered. The chase has its origins in two seminal papers of 1979, one by Alfred V. Aho, Catriel Beeri, and Jeffrey D. Ullman and the other by David Maier, Alberto O. Mendelzon, and Yehoshua Sagiv. In its simplest application the chase is used for testing whether the projection of a relation schema constrained by some functional dependencies onto a given decomposition can be recovered by rejoining the projections. Let ''t'' be a tuple in \pi_(R) \bowtie \pi_(R) \bowtie ... \bowtie \pi_(R) where ''R'' is a relation a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |