For the concept related to databases, see Relational algebra.
In mathematics and abstract algebra, a relation algebra is a residuated Boolean algebra expanded with an involution called converse, a unary operation. The motivating example of a relation algebra is the algebra 2X 2 of all binary relations on a set X, that is, subsets of the cartesian square X2, with R•S interpreted as the usual composition of binary relations R and S, and with the converse of R as the converse relation.
Relation algebra emerged in the 19th-century work of Augustus De Morgan and Charles Peirce, which culminated in the algebraic logic of Ernst Schröder. The equational form of relation algebra treated here was developed by Alfred Tarski and his students, starting in the 1940s. Tarski and Givant (1987) applied relation algebra to a variable-free treatment of axiomatic set theory, with the implication that mathematics founded on set theory could itself be conducted without variables.
In mathematics and abstract algebra, a relationalgebra is a residuated Boolean algebra expanded with an involution called converse, a unary operation...
main purpose of relational algebra is to define operators that transform one or more input relations to an output relation. Given that these operators...
In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector...
represented by a set relation. The negative answer opened the frontier of abstract algebraic logic. Algebraic logic treats algebraic structures, often bounded...
Serial relation Ternary relation (or triadic, 3-adic, 3-ary relation) Relation may also refer to: Directed relationRelationalgebra, an algebraic structure...
In mathematics and physics CCR algebras (after canonical commutation relations) and CAR algebras (after canonical anticommutation relations) arise from...
"is congruent to" relation in geometry; the "is adjacent to" relation in graph theory; the "is orthogonal to" relation in linear algebra. A function may...
mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables...
partial order. Equality is also the only relation on a set that is reflexive, symmetric and antisymmetric. In algebraic expressions, equal variables may be...
algebra, an interior algebra is a certain type of algebraic structure that encodes the idea of the topological interior of a set. Interior algebras are...
In mathematics, a Heyting algebra (also known as pseudo-Boolean algebra) is a bounded lattice (with join and meet operations written ∨ and ∧ and with...
algebras can be used to study arbitrary sets of operators with little algebraicrelation simultaneously. From this point of view, operator algebras can...
Linear algebra is the branch of mathematics concerning linear equations such as: a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b...
topical guide to algebra: Algebra is one of the main branches of mathematics, covering the study of structure, relation and quantity. Algebra studies the effects...
In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...
isomorphism of either the canonical commutation relationalgebra or canonical anticommutation relationalgebra. This induces an autoequivalence on the respective...
The subset relation defines a partial order on sets. In fact, the subsets of a given set form a Boolean algebra under the subset relation, in which the...
Ampersand is the name of a reactive programming language, which uses relationalgebra to specify information systems. In SGML, XML, and HTML, the ampersand...
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