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relation (Relation)

The Class of relations. There are three kinds of Relation: Predicate, Function, and List. Predicates and Functions both denote sets of ordered n-tuples. The difference between these two Classes is that Predicates cover formula-forming operators, while Functions cover term-forming operators. A List, on the other hand, is a particular ordered n-tuple.

Ontology

SUMO / BASE-ONTOLOGY

Superclass(es)

entity

abstract

relation

Subclass(es)

single valued relation total valued relation partial valued relation binary relation probability relation spatial relation temporal relation ternary relation quaternary relation quintary relation list predicate variable arity relation relation extended to quantities

Coordinate term(s)

attribute graph graph element proposition quantity set or class

Constrains relations

domain domain subclass holds subrelation valence

Related WordNet synsets

relation: an abstraction belonging to or characteristic of two entities or parts together
relationship, human relationship: (`relationship' is often used where `relation' would serve (as in "the relationship between inflation and unemployment")) preferred usage of `relationship' is for human relations or states of relatedness; "the relationship between mothers and children"
relational: having a relation or being related

See more related synsets on a separate page.

Axioms (6)

If and ? are disjoint and is a member of "()", then is an instance of relation.

(=>
      (and
            (disjoint relation )
            (in list
                  
                  (list fn )))
      (instance  relation))

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)

relation is exhaustively partitioned into predicate,function,list.

(partition relation predicate function list)

relation is exhaustively partitioned into total valued relation,partial valued relation.

(partition relation total valued relation partial valued relation)

If is an instance of relation, then () holds if and only if () holds.

(=>
      (instance  relation)
      (<=>
            (holds  )
            ( )))

is an instance of total valued relation if and only if there exists so that is an instance of relation and %&has argument(s) and

if for all ,, holds: if is less than and the number argument of is an instance of and is equal to "th element of "()"", then is an instance of ,
then there exists so that (,) holds

(<=>
      (instance  total valued relation)
      (exists
            ()
            (and
                  (instance  relation)
                  (valence  )
                  (=>
                        (forall
                              (  )
                              (=>
                                    (and
                                          (less than  )
                                          (domain   )
                                          (equal
                                                
                                                (list order fn
                                                      (list fn )
                                                      )))
                                    (instance  )))
                        (exists
                              ()
                              (holds   ))))))