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.

(disjointDecomposition Relation BinaryRelation TernaryRelation QuaternaryRelation QuintaryRelation VariableArityRelation)

If rel is an instance of binary relation, then there don't exist item1,item2,item3, so that rel(item1,item2,item3,) holds.

(=>
      (instance ?REL BinaryRelation)
      (not
            (exists
                  (?ITEM1 ?ITEM2 ?ITEM3 @ROW)
                  (holds ?REL ?ITEM1 ?ITEM2 ?ITEM3 @ROW))))

rel is an instance of binary relation
the number argument of rel is an instance of class1 or the number argument of rel is a subclass of class1
the number argument of rel is an instance of class2 or the number argument of rel is a subclass of class2 or range of rel is an instance of class2 or the values returned by rel are subclasses of class2
class1 is disjoint from class2

, then rel is an instance of asymmetric relation.

(=>
      (and
            (instance ?REL BinaryRelation)
            (or
                  (domain ?REL 1 ?CLASS1)
                  (domainSubclass ?REL 1 ?CLASS1))
            (or
                  (domain ?REL 2 ?CLASS2)
                  (domainSubclass ?REL 2 ?CLASS2)
                  (range ?REL ?CLASS2)
                  (rangeSubclass ?REL ?CLASS2))
            (disjoint ?CLASS1 ?CLASS2))
      (instance ?REL AsymmetricRelation))

if rel is an instance of relation extended to quantities and rel is an instance of binary relation and number1 is an instance of real number and number2 is an instance of real number and rel(number1,number2) holds,
then for all unit holds: if unit is an instance of unit of measure, then rel("number1 unit(s)","number2 unit(s)") holds

(=>
      (and
            (instance ?REL RelationExtendedToQuantities)
            (instance ?REL BinaryRelation)
            (instance ?NUMBER1 RealNumber)
            (instance ?NUMBER2 RealNumber)
            (holds ?REL ?NUMBER1 ?NUMBER2))
      (forall
            (?UNIT)
            (=>
                  (instance ?UNIT UnitOfMeasure)
                  (holds
                        ?REL
                        (MeasureFn ?NUMBER1 ?UNIT)
                        (MeasureFn ?NUMBER2 ?UNIT)))))