Concepts inRelative expressive power of navigational querying on graphs

Hasse diagram

In order theory, a branch of mathematics, a Hasse diagram is a type of mathematical diagram used to represent a finite partially ordered set, in the form of a drawing of its transitive reduction. Concretely, for a partially ordered set (S, ¿) one represents each element of S as a vertex in the plane and draws a line segment or curve that goes upward from x to y whenever y covers x (that is, whenever x < y and there is no z such that x < z < y).
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Transitive closure

In mathematics, the transitive closure of a binary relation R on a set X is the transitive relation R on set X such that R contains R and R is minimal . If the binary relation itself is transitive, then the transitive closure is that same binary relation; otherwise, the transitive closure is a different relation.
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Binary relation

In mathematics, a binary relation on a set A is a collection of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A = A × A. More generally, a binary relation between two sets A and B is a subset of A × B. The terms dyadic relation and 2-place relation are synonyms for binary relations.
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Equality (mathematics)

Loosely, equality is the state of being quantitatively the same. More formally, equality (or the identity relation) is the binary relation on a set X defined by . The identity relation is the archetype of the more general concept of an equivalence relation on a set: those binary relations which are reflexive, symmetric, and transitive. The relation of equality is also antisymmetric.
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Complement (set theory)

In set theory, a complement of a set A refers to things not in (that is, things outside of), A. The relative complement of A with respect to a set B, is the set of elements in B but not in A. When all sets under consideration are considered to be subsets of a given set U, the absolute complement of A is the set of all elements in U but not in A.
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Function composition

In mathematics, function composition is the application of one function to the results of another. For instance, the functions f: X ¿ Y and g: Y ¿ Z can be composed by computing the output of g when it has an argument of f(x) instead of x. Intuitively, if z is a function g of y and y is a function f of x, then z is a function of x. Thus one obtains a composite function g ¿ f: X ¿ Z defined by (g ¿ f)(x) = g(f) for all x in X.
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Intersection (set theory)

In mathematics, the intersection (denoted as ¿) of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements. For explanation of the symbols used in this article, refer to the table of mathematical symbols.
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Union (set theory)

In set theory, the union (denoted as ¿) of a collection of sets is the set of all distinct elements in the collection. The union of a collection of sets gives a set .
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