In set theory, the transitive closure of a binary relation.

In particular, there is no transitive closure of set membership for such hypergraphs.

It is also called the reflexive transitive closure of .

Next consider the reflexive, transitive closure of the "successor" relation.

It is possible to define the plus and then the bit relations with a deterministic transitive closure.

Note that the computation of an exact transitive closure is undecidable.

To preserve transitivity, one must take the transitive closure.

The transitive closure of the Young-Fibonacci graph is a partial order.

Similarly, the class L is first-order logic with the commutative, transitive closure.

More precisely, it is the transitive closure of the relation "is the mother of".

Similarly, the implicative normal form can be expressed in first order logic with the addition of an operator for transitive closure.

For any relation R, the transitive closure of R always exists.

The trace is defined as the symmetric, reflexive and transitive closure of .

Transitive closure of this relation divides the set of labels into possibly much smaller sets.

In computer science, the concept of transitive closure can be thought of as constructing a data structure that makes it possible to answer reachability questions.

Efficient algorithms for computing the transitive closure of a graph can be found in Nuutila (1995).

Let denote the transitive closure of .

For example, the following tabled predicate defines the transitive closure of a relation as given by .

The relational example constitutes a relation algebra equipped with an operation of reflexive transitive closure.

Taking the reflexive, transitive closure of this relation gives the reduction relation for this language.

Note that this is the set of all of the objects related to X by the transitive closure of the membership relation.

The elements that need to be updated when a single element changes are given by the transitive closure of the dependency relation of the graph.

Here represents the reflexive and transitive closure of the step relation meaning any number of consecutive steps (zero, one or more).

Transitive closure of directed graphs (Warshall's algorithm).

Datalog also implements transitive closure computations (Silberschatz et al. 2010:C.3.6).