relative complement fn (RelativeComplementFn)

A BinaryFunction that maps two SetOrClasses to the difference between these SetOrClasses. More precisely, the relative complement of one class C1 relative to another C2 consists of the instances of C1 that are instances of the ComplementFn of C2.

Ontology

SUMO / SET/CLASS-THEORY

Class(es)

class

inheritable relation

binary function

relative complement fn

Coordinate term(s)

addition fn day fn density fn division fn edition fn exponentiation fn graph path fn hour fn intersection 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 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 RelativeComplementFn(set or class, set or class)

Axioms (1)

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))))