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...e ordinary [[composition of relations]] but is robust to refinement of the relations into ([[Partial function|partial]]) functions or [[injective relation]]s. Unlike ordinary composition of relations, demonic composition is not [[Associative property|associative]]. ...

'''Logical relations''' are a [[proof method]] employed in [[programming language semantics]] to ...each [[data type|type]] <math>A</math>, there is a particular associated [[binary relation|relation]] <math>\sim</math> between <math>[\![A]\!]_1</math> and ...

{{Short description|Any binary relation equal to its composition with itself}} ....pdf}}</ref> This notion generalizes that of an [[idempotent function]] to relations. ...

In [[mathematics]], the '''symmetric closure''' of a [[binary relation]] <math>R</math> on a [[Set (mathematics)|set]] <math>X</math> is [[Category:Binary relations]] ...

{{Short description|French mathematician, developed calculus of relations (1921 to 2013)}} ...cite book|last1=Schmidt|first1=Gunther|last2=Ströhlein|first2=Thomas|title=Relations and Graphs: Discrete Mathematics for Computer Scientists|url={{google books ...

In [[mathematics]], the '''reflexive closure''' of a [[binary relation]] <math>R</math> on a [[Set (mathematics)|set]] <math>X</math> is [[Category:Binary relations]] ...

...=2|pages=137–167|doi=10.1007/BF00046585|s2cid=119731847 }}</ref> Tolerance relations provide a convenient general tool for studying [[indiscernibility]]/indisti ...in the two definitions are in [[one-to-one correspondence]]. The tolerance relations on an [[algebraic structure]] <math>(A,F)</math> form an [[algebraic lattic ...

...[[Symmetric relation|symmetric]] and [[Transitive relation|transitive]] [[Binary relation|relation]]. [[Category:Binary relations]] ...

* [[Dot product]] – also known as the "scalar product", a binary operation that takes two vectors and returns a [[scalar (mathematics)|scala * [[Cross product]] – also known as the "vector product", a binary operation on two vectors that results in another [[Euclidean vector|vector] ...

...respectively such that <math>a > b\,\!</math>. Another one is assigning a binary value <math>V(A,B) \in \{0,1\}\,\!</math> for all pairs <math>(A,B)\,\!</ma ===Preference relations=== ...

{{stack|{{Binary relations}}}} ...erial relation|serial]], which is also called total. Similarly, connected relations are sometimes called {{em|{{visible anchor|complete|Complete relation}}}},< ...

...that can reason about relations among objects. An example category of such relations is [[spatial relation]]s (above, below, left, right, in front of, behind).< RNs can infer relations, they are data efficient, and they operate on a set of objects without rega ...

...y, '''countable Borel relations''' are a class of [[Relation (mathematics)|relations]] between [[standard Borel space]] which are particularly well behaved. Thi ...invariant descriptive set theory is the relative complexity of equivalence relations. An equivalence relation <math>E</math> on a set <math>X</math> is consider ...

...''</sub> if and only if the product ''ef'' exists in ''E''. The following relations can be defined in ''E'': ...atement]] about ''E'' involving the partial binary operation and the above relations in ''E'', one can define the left-right [[Dual (mathematics)|dual]] of ''T' ...

...itle=On the approximability of minimizing nonzero variables or unsatisfied relations in linear systems |journal=Theoretical Computer Science |date=December 1998 * A binary relation ''R'', which is one of {=, ≥, >, ≠}; ...

[[Category:Mathematical relations]] [[Category:Properties of binary operations]] ...

{{Short description|Mathematical result on order relations}} A [[binary relation]] <math>R</math> on a set <math>X</math> is formally defined as a ...

...d [[Horn logic|Horn Logic]]. Supports modeling classes, attributes, binary relations and instances. ...

== Binary data == [[File:Binary Join Count.png|thumb|Join counts for binary data on a <math>10 \times 10</math> grid using 'rook' (north, south, east, ...

...S. S. Nambooripad|Nambooripad]]. The diagram below summarises the various relations among ''a'', ''b'', ''c'', ''d'': ...[[Green's relations|R-related]], elements in the same column are [[Green's relations|L-related]], and the order proceeds down the four diagonals (away from the ...