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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] |
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] |
Fragment (logic)
In mathematical logic, a fragment of a logical language or theory is a subset of this logical language obtained by imposing syntactical restrictions on the language.. Hence, the well-formed formulae of the fragment are a subset of those in the original logic. However, the semantics of the formulae in the fragment and in the logic coincide, and any formula of the fragment can be expressed in the original logic. The computational complexity of tasks such as satisfiability or model checking for the logical fragment can be no higher than the same tasks in the original logic, as there is a reduction from the first problem to the other. An important problem in computational logic is to determine fragments of well-known logics such as first-order logic that are as expressive as possible yet are decidable or more strongly have low computational complexity. The field of descriptive complexity theory aims at establishing a link between logics and computational complexity theory, by identifyi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Table (database)
In a database, a table is a collection of related data organized in Table (information), table format; consisting of Column (database), columns and row (database), rows. In relational databases, and flat file databases, a ''table'' is a set of data elements (values) using a model of vertical column (database), columns (identifiable by name) and horizontal row (database), rows, the cell (database), cell being the unit where a row and column intersect. A table has a specified number of columns, but can have any number of rows. Each row is identified by one or more values appearing in a particular column subset. A specific choice of columns which uniquely identify rows is called the primary key. "Table" is another term for relation (database), "relation"; although there is the difference in that a table is usually a multiset (bag) of rows where a relation is a set (computer science), set and does not allow duplicates. Besides the actual data rows, tables generally have associated wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Candidate Key
A candidate key, or simply a key, of a relational database is any set of columns that have a unique combination of values in each row, with the additional constraint that removing any column could produce duplicate combinations of values. A candidate key is a minimal superkey, i.e., a superkey that does not contain a smaller one. Therefore, a relation can have multiple candidate keys, each with a different number of attributes. Specific candidate keys are sometimes called ''primary keys'', ''secondary keys'' or ''alternate keys''. The columns in a candidate key are called prime attributes, and a column that does not occur in any candidate key is called a non-prime attribute. Every relation without NULL values will have at least one candidate key: Since there cannot be duplicate rows, the set of all columns is a superkey, and if that is not minimal, some subset of that will be minimal. There is a functional dependency from the candidate key to all the attributes in the relatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Foreign Key
A foreign key is a set of attributes in a table that refers to the primary key of another table, linking these two tables. In the context of relational databases, a foreign key is subject to an inclusion dependency constraint that the tuples consisting of the foreign key attributes in one relation, R, must also exist in some other (not necessarily distinct) relation, S; furthermore that those attributes must also be a candidate key in S. In other words, a foreign key is a set of attributes that a candidate key. For example, a table called TEAM may have an attribute, MEMBER_NAME, which is a foreign key referencing a candidate key, PERSON_NAME, in the PERSON table. Since MEMBER_NAME is a foreign key, any value existing as the name of a member in TEAM must also exist as a person's name in the PERSON table; in other words, every member of a TEAM is also a PERSON. Summary The table containing the foreign key is called the child table, and the table containing the candidate ke ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inclusion Dependencies
Referential integrity is a property of data stating that all its references are valid. In the context of relational databases, it requires that if a value of one attribute (column) of a relation (table) references a value of another attribute (either in the same or a different relation), then the referenced value must exist. For referential integrity to hold in a relational database, any column in a base table that is declared a foreign key can only contain either null values or values from a parent table's primary key or a candidate key. In other words, when a foreign key value is used it must reference a valid, existing primary key in the parent table. For instance, deleting a record that contains a value referred to by a foreign key in another table would break referential integrity. Some relational database management systems (RDBMS) can enforce referential integrity, normally either by deleting the foreign key rows as well to maintain integrity, or by returning an error and n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Guarded Logic
Guarded logic is a choice set of dynamic logic involved in choices, where outcomes are limited. A simple example of guarded logic is as follows: if X is true, then Y, else Z can be expressed in dynamic logic as (X?;Y)∪(~X?;Z). This shows a guarded logical choice: if X holds, then X?;Y is equal to Y, and ~X?;Z is blocked, and Y∪block is also equal to Y. Hence, when X is true, the primary performer of the action can only take the Y branch, and when false the Z branch. A real-world example is the idea of paradox: something cannot be both true and false. A guarded logical choice is one where any change in true affects all decisions made down the line. History Before the use of guarded logic there were two major terms used to interpret modal logic. Mathematical logic and database theory (Artificial Intelligence) were first-order predicate logic. Both terms found sub-classes of first-class logic and efficiently used in solvable languages which can be used for research. But neither c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Datalog
Datalog is a declarative logic programming language. While it is syntactically a subset of Prolog, Datalog generally uses a bottom-up rather than top-down evaluation model. This difference yields significantly different behavior and properties from Prolog. It is often used as a query language for deductive databases. Datalog has been applied to problems in data integration, networking, program analysis, and more. Example A Datalog program consists of ''facts'', which are statements that are held to be true, and ''rules'', which say how to deduce new facts from known facts. For example, here are two facts that mean ''xerces is a parent of brooke'' and ''brooke is a parent of damocles'': parent(xerces, brooke). parent(brooke, damocles). The names are written in lowercase because strings beginning with an uppercase letter stand for variables. Here are two rules: ancestor(X, Y) :- parent(X, Y). ancestor(X, Y) :- parent(X, Z), ancestor(Z, Y). The :- symbol is read as "if", ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variable (mathematics)
In mathematics, a variable (from Latin language, Latin ) is a Mathematical symbol, symbol, typically a letter, that refers to an unspecified mathematical object. One says colloquially that the variable ''represents'' or ''denotes'' the object, and that any valid candidate for the object is the value (mathematics), value of the variable. The values a variable can take are usually of the same kind, often numbers. More specifically, the values involved may form a Set (mathematics), set, such as the set of real numbers. The object may not always exist, or it might be uncertain whether any valid candidate exists or not. For example, one could represent two integers by the variables and and require that the value of the square of is twice the square of , which in algebraic notation can be written . A definitive proof that this relationship is impossible to satisfy when and are restricted to integer numbers isn't obvious, but it has been known since ancient times and has had a big ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relational Database
A relational database (RDB) is a database based on the relational model of data, as proposed by E. F. Codd in 1970. A Relational Database Management System (RDBMS) is a type of database management system that stores data in a structured format using rows and columns. Many relational database systems are equipped with the option of using SQL (Structured Query Language) for querying and updating the database. History The concept of relational database was defined by E. F. Codd at IBM in 1970. Codd introduced the term ''relational'' in his research paper "A Relational Model of Data for Large Shared Data Banks". In this paper and later papers, he defined what he meant by ''relation''. One well-known definition of what constitutes a relational database system is composed of Codd's 12 rules. However, no commercial implementations of the relational model conform to all of Codd's rules, so the term has gradually come to describe a broader class of database systems, which at a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Term (logic)
In mathematical logic, a term denotes a mathematical object while a formula denotes a mathematical fact. In particular, terms appear as components of a formula. This is analogous to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact. A first-order term is recursively constructed from constant symbols, variable symbols, and function symbols. An expression formed by applying a predicate symbol to an appropriate number of terms is called an atomic formula, which evaluates to true or false in bivalent logics, given an interpretation. For example, is a term built from the constant 1, the variable , and the binary function symbols and ; it is part of the atomic formula which evaluates to true for each real-numbered value of . Besides in logic, terms play important roles in universal algebra, and rewriting systems. Definition Given a set ''V'' of variable symbols, a set ''C'' of constant symbols and sets ''F''''n'' of ''n''-ary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atomic Formula
In mathematical logic, an atomic formula (also known as an atom or a prime formula) is a formula with no deeper propositional structure, that is, a formula that contains no logical connectives or equivalently a formula that has no strict subformulas. Atoms are thus the simplest well-formed formulas of the logic. Compound formulas are formed by combining the atomic formulas using the logical connectives. The precise form of atomic formulas depends on the logic under consideration; for propositional logic, for example, a propositional variable is often more briefly referred to as an "atomic formula", but, more precisely, a propositional variable is not an atomic formula but a formal expression that denotes an atomic formula. For predicate logic, the atoms are predicate symbols together with their arguments, each argument being a first-order logic#Formation rules, term. In model theory, atomic formulas are merely string (computer science), strings of symbols with a given signature ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
