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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] |
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] |
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 relational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edgar F
Edgar is a commonly used English given name, from an Anglo-Saxon name ''Eadgar'' (composed of '' ead'' "rich, prosperous" and '' gar'' "spear"). Like most Anglo-Saxon names, it fell out of use by the later medieval period; it was, however, revived in the 18th century, and was popularised by its use for a character in Sir Walter Scott's '' The Bride of Lammermoor'' (1819). People with the given name * Edgar the Peaceful (942–975), king of England * Edgar the Ætheling (c. 1051 – c. 1126), last member of the Anglo-Saxon royal house of England * Edgar of Scotland (1074–1107), king of Scotland * Edgar Angara, Filipino lawyer * Edgar Barrier, American actor * Edgar Baumann, Paraguayan javelin thrower * Edgar Bergen, American actor, radio performer, ventriloquist * Edgar Berlanga, American boxer * Edgar H. Brown, American mathematician * Edgar Buchanan, American actor * Edgar Rice Burroughs, American author, creator of ''Tarzan'' * Edgar Cantero, Spanish author in Catalan, ... [...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] |
Quantification (science)
In mathematics and empirical science, quantification (or quantitation) is the act of counting and measuring that maps human sense observations and experiences into quantities. Quantification in this sense is fundamental to the scientific method. Natural science Some measure of the undisputed general importance of quantification in the natural sciences can be gleaned from the following comments: * "these are mere facts, but they are quantitative facts and the basis of science." * It seems to be held as universally true that "the foundation of quantification is measurement." * There is little doubt that "quantification provided a basis for the objectivity of science." * In ancient times, "musicians and artists ... rejected quantification, but merchants, by definition, quantified their affairs, in order to survive, made them visible on parchment and paper." * Any reasonable "comparison between Aristotle and Galileo shows clearly that there can be no unique lawfulness discovered wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bulletin Of The American Mathematical Society
The ''Bulletin of the American Mathematical Society'' is a quarterly mathematical journal published by the American Mathematical Society. Scope It publishes surveys on contemporary research topics, written at a level accessible to non-experts. It also publishes, by invitation only, book reviews and short ''Mathematical Perspectives'' articles. History It began as the ''Bulletin of the New York Mathematical Society'' and underwent a name change when the society became national. The Bulletin's function has changed over the years; its original function was to serve as a research journal for its members. Indexing The Bulletin is indexed in Mathematical Reviews, Science Citation Index, ISI Alerting Services, CompuMath Citation Index, and Current Contents ''Current Contents'' is a rapid alerting service database from Clarivate Analytics, formerly the Institute for Scientific Information and Thomson Reuters. It is published online and in several different printed subject sectio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aggregate Function
In database management, an aggregate function or aggregation function is a function where the values of multiple rows are grouped together to form a single summary value. Common aggregate functions include: * Average (i.e., arithmetic mean) * Count * Maximum * Median * Minimum * Mode * Range * Sum Others include: * Nanmean (mean ignoring NaN values, also known as "nil" or "null") * Stddev Formally, an aggregate function takes as input a set, a multiset (bag), or a list from some input domain and outputs an element of an output domain . The input and output domains may be the same, such as for SUM, or may be different, such as for COUNT. Aggregate functions occur commonly in numerous programming languages, in spreadsheets, and in relational algebra. The listagg function, as defined in the SQL:2016 standard aggregates data from multiple rows into a single concatenated string. Decomposable aggregate functions Aggregate functions present a bottleneck, because they pot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transitive Closure
In mathematics, the transitive closure of a binary relation on a set is the smallest relation on that contains and is transitive. For finite sets, "smallest" can be taken in its usual sense, of having the fewest related pairs; for infinite sets it is the unique minimal transitive superset of . For example, if is a set of airports and means "there is a direct flight from airport to airport " (for and in ), then the transitive closure of on is the relation such that means "it is possible to fly from to in one or more flights". Informally, the ''transitive closure'' gives you the set of all places you can get to from any starting place. More formally, the transitive closure of a binary relation on a set is the transitive relation on set such that contains and is minimal; see . If the binary relation itself is transitive, then the transitive closure is that same binary relation; otherwise, the transitive closure is a different relation. Conversely, transit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expressive Power (computer Science)
In computer science, the expressive power (also called expressiveness or expressivity) of a language is the breadth of ideas that can be represented and communicated in that language. The more expressive a language is, the greater the variety and quantity of ideas it can be used to represent. For example, the Web Ontology Language expression language profile (OWL2 EL) lacks ideas (such as negation) which can be expressed in OWL2 RL (rule language). OWL2 EL may therefore be said to have less ''expressive power'' than OWL2 RL. These restrictions allow for more efficient (polynomial time) reasoning in OWL2 EL than in OWL2 RL. So OWL2 EL trades some expressive power for more efficient reasoning (processing of the knowledge representation language). Information description The term ''expressive power'' may be used with a range of meaning. It may mean a measure of the ideas expressible in that language: * regardless of ease (''theoretical expressivity'') * concisely and readily ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Null (SQL)
In SQL, null or NULL is a special marker used to indicate that a data value does not exist in the database. Introduced by the creator of the relational database model, E. F. Codd, SQL null serves to fulfil the requirement that all ''true relational database management systems (RDBMS)'' support a representation of "missing information and inapplicable information". Codd also introduced the use of the lowercase Greek omega (ω) symbol to represent null in database theory. In SQL, NULL is a reserved word used to identify this marker. A null should not be confused with a value of 0. A null value indicates a lack of a value, which is not the same thing as a value of zero. For example, consider the question "How many books does Adam own?" The answer may be "zero" (we ''know'' that he owns ''none'') or "null" (we ''do not know'' how many he owns). In a database table, the column reporting this answer would start out with no value (marked by Null), and it would not be updated ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Three-valued Logic
In logic, a three-valued logic (also trinary logic, trivalent, ternary, or trilean, sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating ''true'', ''false'' and some indeterminate third value. This is contrasted with the more commonly known bivalent logics (such as classical sentential or Boolean logic) which provide only for ''true'' and ''false''. Emil Leon Post is credited with first introducing additional logical truth degrees in his 1921 theory of elementary propositions. The conceptual form and basic ideas of three-valued logic were initially published by Jan Łukasiewicz and Clarence Irving Lewis. These were then re-formulated by Grigore Constantin Moisil in an axiomatic algebraic form, and also extended to ''n''-valued logics in 1945. Pre-discovery Around 1910, Charles Sanders Peirce defined a many-valued logic system. He never published it. In fact, he did not even number the three pages of notes whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiset
In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements. The number of instances given for each element is called the multiplicity of that element in the multiset. As a consequence, an infinite number of multisets exist which contain only elements and , but vary in the multiplicities of their elements: * The set contains only elements and , each having multiplicity 1 when is seen as a multiset. * In the multiset , the element has multiplicity 2, and has multiplicity 1. * In the multiset , and both have multiplicity 3. These objects are all different when viewed as multisets, although they are the same set, since they all consist of the same elements. As with sets, and in contrast to tuples, order does not matter in discriminating multisets, so and denote the same multiset. To distinguish between sets and multisets, a notation that incorporates square brackets is so ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
