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))))