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single valued relation (SingleValuedRelation)

A Relation is a SingleValuedRelation just in case an assignment of values to every argument position except the last one determines at most one assignment for the last argument position. Note that not all SingleValuedRelations are total functions. To declare that a Relation is a total function, use both SingleValuedFunction and TotalValuedFunction.

Ontology

SUMO / BASE-ONTOLOGY

Class(es)

class
is instance of
  inheritable relation  
is instance of
  single valued relation  

Superclass(es)

[tree]
entity
is subclass of
  abstract  
is subclass of
  relation  
is subclass of
  single valued relation  

Instance(s)

valence  unique identifier  age  width  distance  altitude  depth  monetary value  date  mother  father 

Subclass(es)

function 

Coordinate term(s)

binary function  binary predicate  binary relation  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  spatial relation  temporal relation  ternary function  ternary predicate  ternary relation  total valued relation  unary function  variable arity relation 

Axioms (1)

rel is an instance of single valued relation if and only if for all ,item1,item2 holds: if rel(,item1) holds and rel(,item2) holds, then item1 is equal to item2. 
(<=>
      (instance ?REL SingleValuedRelation)
      (forall
            (@ROW ?ITEM1 ?ITEM2)
            (=>
                  (and
                        (holds ?REL @ROW ?ITEM1)
                        (holds ?REL @ROW ?ITEM2))
                  (equal ?ITEM1 ?ITEM2))))