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Relational Calculus
The relational calculus consists of two calculi, the tuple relational calculus and the domain relational calculus, that are part of the relational model for databases and provide a declarative way to specify database queries. The raison d'être of the relational calculus is the formalization of query optimization, which is finding more efficient manners to execute the same query. The relational calculus is similar to the relational algebra, which is also part of the relational model: While the relational calculus is meant as a declarative language which prescribes no execution order on the subexpressions of a relational calculus expression, the relational algebra is meant as an imperative language: the sub-expressions of a relational algebraic expressions are meant to be executed from left-to-right and inside-out following their nesting. Per Codd's theorem, the relational algebra and the domain-independent relational calculus are logically equivalent. Example A relati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tuple Relational Calculus
Tuple calculus is a calculus that was created and introduced by Edgar F. Codd as part of the relational model, in order to provide a declarative database-query language for data manipulation in this data model. It formed the inspiration for the database-query languages QUEL and SQL, of which the latter, although far less faithful to the original relational model and calculus, is now the de facto standard database-query language; a dialect of SQL is used by nearly every relational-database-management system. Michel Lacroix and Alain Pirotte proposed domain calculus, which is closer to first-order logic and together with Codd showed that both of these calculi (as well as relational algebra) are equivalent in expressive power. Subsequently, query languages for the relational model were called ''relationally complete'' if they could express at least all of these queries. Definition of the calculus Relational database Since the calculus is a query language for relational databa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Domain Relational Calculus
In computer science, domain relational calculus (DRC) is a calculus that was introduced by Michel Lacroix and Alain Pirotte as a declarative database query language for the relational data model.Michel Lacroix, Alain PirotteDomain-Oriented Relational Languages VLDB 1977: 370-378 In DRC, ''queries'' have the form: : \ where each Xi is either a domain variable or constant, and p(\langle X_1, X_2, ...., X_n \rangle) denotes a DRC ''formula''. The result of the query is the set of tuples X1 to Xn that make the DRC formula true. This language uses the same operators as tuple calculus, the logical connectives ∧ (and), ∨ (or) and ¬ (not). The existential quantifier (∃) and the universal quantifier (∀) can be used to bind the variables. Its computational expressiveness is equivalent to that of relational algebra. E. F. CoddRelational Completeness of Data Base Sub-languages In R. Rustin, editor, Data Base Systems. Prentice Hall, 1972 Examples Let (A, B, C) mean (Rank, Nam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relational Model
The relational model (RM) is an approach to managing data using a structure and language consistent with first-order predicate logic, first described in 1969 by English computer scientist Edgar F. Codd, where all data is represented in terms of tuples, grouped into relations. A database organized in terms of the relational model is a relational database. The purpose of the relational model is to provide a declarative method for specifying data and queries: users directly state what information the database contains and what information they want from it, and let the database management system software take care of describing data structures for storing the data and retrieval procedures for answering queries. Most relational databases use the SQL data definition and query language; these systems implement what can be regarded as an engineering approximation to the relational model. A ''table'' in a SQL database schema corresponds to a predicate variable; the contents of a tabl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Query Optimization
Query optimization is a feature of many relational database management systems and other databases such as NoSQL and graph databases. The query optimizer attempts to determine the most efficient way to execute a given query by considering the possible query plans. Generally, the query optimizer cannot be accessed directly by users: once queries are submitted to the database server, and parsed by the parser, they are then passed to the query optimizer where optimization occurs. However, some database engines allow guiding the query optimizer with hints. A query is a request for information from a database. It can be as simple as "find the address of a person with Social Security number 123-45-6789," or more complex like "find the average salary of all the employed married men in California between the ages 30 to 39 who earn less than their spouses." The result of a query is generated by processing the rows in a database in a way that yields the requested information. Since data ... [...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 operator ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Codd's Theorem
Codd's theorem states that relational algebra and the domain-independent relational calculus queries, two well-known foundational query languages for the relational model, are precisely equivalent in expressive power. That is, a database query can be formulated in one language if and only if it can be expressed in the other. The theorem is named after Edgar F. Codd, the father of the relational model for database management. The domain independent relational calculus queries are precisely those relational calculus queries that are invariant under choosing domains of values beyond those appearing in the database itself. That is, queries that may return different results for different domains are excluded. An example of such a forbidden query is the query "select all tuples other than those occurring in relation R", where R is a relation in the database. Assuming different domains, i.e., sets of atomic data items from which tuples can be constructed, this query returns different res ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Equivalence
In logic and mathematics, statements p and q are said to be logically equivalent if they have the same truth value in every model. The logical equivalence of p and q is sometimes expressed as p \equiv q, p :: q, \textsfpq, or p \iff q, depending on the notation being used. However, these symbols are also used for material equivalence, so proper interpretation would depend on the context. Logical equivalence is different from material equivalence, although the two concepts are intrinsically related. Logical equivalences In logic, many common logical equivalences exist and are often listed as laws or properties. The following tables illustrate some of these. General logical equivalences Logical equivalences involving conditional statements :#p \implies q \equiv \neg p \vee q :#p \implies q \equiv \neg q \implies \neg p :#p \vee q \equiv \neg p \implies q :#p \wedge q \equiv \neg (p \implies \neg q) :#\neg (p \implies q) \equiv p \wedge \neg q :#(p \implies q) \wedge (p \impli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Query Optimization
Query optimization is a feature of many relational database management systems and other databases such as NoSQL and graph databases. The query optimizer attempts to determine the most efficient way to execute a given query by considering the possible query plans. Generally, the query optimizer cannot be accessed directly by users: once queries are submitted to the database server, and parsed by the parser, they are then passed to the query optimizer where optimization occurs. However, some database engines allow guiding the query optimizer with hints. A query is a request for information from a database. It can be as simple as "find the address of a person with Social Security number 123-45-6789," or more complex like "find the average salary of all the employed married men in California between the ages 30 to 39 who earn less than their spouses." The result of a query is generated by processing the rows in a database in a way that yields the requested information. Since data ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus Of Relations
In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables. What is now usually called classical algebraic logic focuses on the identification and algebraic description of models appropriate for the study of various logics (in the form of classes of algebras that constitute the algebraic semantics for these deductive systems) and connected problems like representation and duality. Well known results like the representation theorem for Boolean algebras and Stone duality fall under the umbrella of classical algebraic logic . Works in the more recent abstract algebraic logic (AAL) focus on the process of algebraization itself, like classifying various forms of algebraizability using the Leibniz operator . Calculus of relations A homogeneous binary relation is found in the power set of ''X'' × ''X'' for some set ''X'', while a heterogeneous relation is found in the power set of ''X'' × ''Y'', where ''X'' ≠ ''Y''. Whether a gi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Calculi
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises together with a conclusion. Premises and conclusions are usually und ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
