samUha yaa varga (SetOrClass)

The SetOrClass of Sets and Classes, i.e. any instance of Abstract that has elements or instances.

Ontology

SUMO / BASE-ONTOLOGY

Superclass(es)

astitva

amUrta

samUha yaa varga

Subclass(es)

varga varga yugmataH asambaddha samUha paarasparika asambaddha samUha

Coordinate term(s)

visheshtaa aalekha tatva aalekha prastaava parimaaNa sambandha

Constrains relations

cardinality fn complement fn generalized intersection fn generalized union fn intersection fn kappa fn power set fn relative complement fn union fn closed on disjoint domain domain subclass equivalence relation on instance irreflexive on partial ordering on range range subclass reflexive on subclass total ordering on trichotomizing on

Axioms (4)

subclass is a subclass of class agar hai

subclass is an instance of samUha yaa varga
class is an instance of samUha yaa varga
sab-kuch inst ke lie hai, ki: agar inst is an instance of subclass, to inst is an instance of class

(<=>
      (subclass ?SUBCLASS ?CLASS)
      (and
            (instance ?SUBCLASS SetOrClass)
            (instance ?CLASS SetOrClass)
            (forall
                  (?INST)
                  (=>
                        (instance ?INST ?SUBCLASS)
                        (instance ?INST ?CLASS)))))

class1 asansavat class2 se hai agar hai

class1 is an instance of samUha yaa varga
class2 is an instance of samUha yaa varga
sab-kuch inst ke lie hai, ki: inst is not an instance of class1 yaa inst is not an instance of class2

(<=>
      (disjoint ?CLASS1 ?CLASS2)
      (and
            (instance ?CLASS1 SetOrClass)
            (instance ?CLASS2 SetOrClass)
            (forall
                  (?INST)
                  (not
                        (and
                              (instance ?INST ?CLASS1)
                              (instance ?INST ?CLASS2))))))

samUha yaa varga is exhaustively partitioned into varga,varga.

(partition SetOrClass Set Class)

Agar class1 is an instance of samUha yaa varga aur class2 is an instance of samUha yaa varga, to "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))))