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binary relation (BinaryRelation)

BinaryRelations are relations that are true only of pairs of things. BinaryRelations are represented as slots in frame systems.

Ontology

SUMO / BASE-ONTOLOGY

Class(es)

class

inheritable relation

binary relation

Superclass(es)

entity

abstract

relation

binary relation

Instance(s)

distributes

Subclass(es)

reflexive relation irreflexive relation symmetric relation antisymmetric relation trichotomizing relation transitive relation intransitive relation unary function binary predicate

Coordinate term(s)

binary function binary predicate case role function intentional relation list object attitude partial valued relation predicate probability relation propositional attitude quaternary function quaternary predicate quaternary relation quintary predicate quintary relation relation extended to quantities single valued relation spatial relation temporal relation ternary function ternary predicate ternary relation total valued relation unary function variable arity relation

Constrains relations

equivalence relation on inverse irreflexive on partial ordering on reflexive on total ordering on trichotomizing on

Axioms (4)

relation is disjointly decomposed into binary relation,ternary relation,quaternary relation,quintary relation,variable arity relation.

(disjoint decomposition relation binary relation ternary relation quaternary relation quintary relation variable arity relation)

If is an instance of binary relation, then there don't exist ,,, so that (,,,) holds.

(=>
      (instance  binary relation)
      (not
            (exists
                  (   )
                  (holds     ))))

is an instance of binary relation
the number argument of is an instance of or the number argument of is a subclass of
the number argument of is an instance of or the number argument of is a subclass of or range of is an instance of or the values returned by are subclasses of
is disjoint from

, then is an instance of asymmetric relation.

(=>
      (and
            (instance  binary relation)
            (or
                  (domain   )
                  (domain subclass   ))
            (or
                  (domain   )
                  (domain subclass   )
                  (range  )
                  (range subclass  ))
            (disjoint  ))
      (instance  asymmetric relation))

if is an instance of relation extended to quantities and is an instance of binary relation and is an instance of real number and is an instance of real number and (,) holds,
then for all holds: if is an instance of unit of measure, then (" (s)"," (s)") holds

(=>
      (and
            (instance  relation extended to quantities)
            (instance  binary relation)
            (instance  real number)
            (instance  real number)
            (holds   ))
      (forall
            ()
            (=>
                  (instance  unit of measure)
                  (holds
                        
                        (measure fn  )
                        (measure fn  )))))