Select language: english | cesky | deutsch | italiano | simplified chinese | traditional chinese | hindi Concept: English word: Home

# intersection fn (IntersectionFn)

A BinaryFunction that maps two %SetOrClasses to the intersection of these SetOrClasses. An object is an instance of the intersection of two SetOrClasses just in case it is an instance of both of those SetOrClasses.

## Ontology

SUMO / SET/CLASS-THEORY

## Class(es)

 class

inheritable relation

binary function

intersection fn

## Coordinate term(s)

addition fn  day fn  density fn  division fn  edition fn  exponentiation fn  graph path fn  hour fn  interval fn  kappa fn  list concatenate fn  list order fn  log fn  max fn  maximal weighted path fn  measure fn  mereological difference fn  mereological product fn  mereological sum fn  min fn  minimal weighted path fn  minute fn  month fn  multiplication fn  periodical issue fn  recurrent time interval fn  relative complement fn  relative time fn  remainder fn  second fn  series volume fn  speed fn  subtraction fn  temporal composition fn  time interval fn  union fn  where fn

## Type restrictions

set or class IntersectionFn(set or class, set or class)

## Related WordNet synsets

intersection, product
the set of elements common to two or more sets; "the set of red hats is the intersection of the set of hats and the set of red things"

## Axioms (2)

entity is an instance of "the union of class1 and class2" if and only if entity is an instance of class1 and entity is an instance of class2.
```(<=>
(instance
?ENTITY
(IntersectionFn ?CLASS1 ?CLASS2))
(and
(instance ?ENTITY ?CLASS1)
(instance ?ENTITY ?CLASS2)))```

If class1 is an instance of set or class and class2 is an instance of set or class, then "the difference between class1 and class2" is equal to "the union of class1 and "the complement of class2"".
```(=>
(and
(instance ?CLASS1 SetOrClass)
(instance ?CLASS2 SetOrClass))
(equal
(RelativeComplementFn ?CLASS1 ?CLASS2)
(IntersectionFn
?CLASS1
(ComplementFn ?CLASS2))))```