valence (valence)

Specifies the number of arguments that a relation can take. If a relation does not have a fixed number of arguments, it does not have a valence and it is an instance of VariableArityRelation. For example, holds is a VariableArityRelation.

Ontology

SUMO / STRUCTURAL-ONTOLOGY

Class(es)

class

inheritable relation

binary predicate
is instance of

asymmetric relation
is instance of

class

inheritable relation

single valued relation
is instance of

valence

Coordinate term(s)

back fn cardinality fn front fn principal host fn probability fn skin fn age altitude arc weight attribute authors before or equal causes causes subclass citizen closed on completely fills connected contains information cooccur copy crosses date decreases likelihood depth developmental form disjoint distance distributes documentation duration earlier editor element employs equal equivalence relation on exploits expressed in language faces family relation father fills finishes frequency graph part greater than greater than or equal to has purpose has skill holds during holds obligation holds right hole identity element immediate instance immediate subclass in list in scope of interest increases likelihood independent probability inhabits inhibits initial list instance inverse irreflexive on larger less than less than or equal to manner material measure meets temporally member modal attribute monetary value mother overlaps temporally parent partial ordering on partially fills partly located path length penetrates possesses precondition prevents proper part properly fills property publishes range range subclass realization refers reflexive on related internal concept sibling smaller starts sub attribute sub collection sub graph sub list sub process sub proposition subclass subrelation subsumes content class subsumes content instance successor attribute successor attribute closure surface temporal part time total ordering on trichotomizing on unique identifier uses version width

Type restrictions

valence(relation, positive integer)

Axioms (13)

If pred1 is a subrelation of pred2 and pred1 %&has number argument(s), then pred2 %&has number argument(s).

(=>
      (and
            (subrelation ?PRED1 ?PRED2)
            (valence ?PRED1 ?NUMBER))
      (valence ?PRED2 ?NUMBER))

If and ? are disjoint and rel1 is a member of "()" and rel2 is a member of "()" and rel1 %&has number argument(s), then rel2 %&has number argument(s).

(=>
      (and
            (disjointRelation @ROW)
            (inList
                  ?REL1
                  (ListFn @ROW))
            (inList
                  ?REL2
                  (ListFn @ROW))
            (valence ?REL1 ?NUMBER))
      (valence ?REL2 ?NUMBER))

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

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

(<=>
      (instance ?REL TotalValuedRelation)
      (exists
            (?VALENCE)
            (and
                  (instance ?REL Relation)
                  (valence ?REL ?VALENCE)
                  (=>
                        (forall
                              (?NUMBER ?ELEMENT ?CLASS)
                              (=>
                                    (and
                                          (lessThan ?NUMBER ?VALENCE)
                                          (domain ?REL ?NUMBER ?CLASS)
                                          (equal
                                                ?ELEMENT
                                                (ListOrderFn
                                                      (ListFn @ROW)
                                                      ?NUMBER)))
                                    (instance ?ELEMENT ?CLASS)))
                        (exists
                              (?ITEM)
                              (holds ?REL @ROW ?ITEM))))))

if rel %&has number argument(s),
then for all holds: if rel() holds, then "length of "()"" is equal to number

(=>
      (valence ?REL ?NUMBER)
      (forall
            (@ROW)
            (=>
                  (holds ?REL @ROW)
                  (equal
                        (ListLengthFn
                              (ListFn @ROW))
                        ?NUMBER))))

If function is an instance of unary function, then function %&has argument(s).

(=>
      (instance ?FUNCTION UnaryFunction)
      (valence ?FUNCTION 1))

If function is an instance of binary function, then function %&has argument(s).

(=>
      (instance ?FUNCTION BinaryFunction)
      (valence ?FUNCTION 2))

If function is an instance of ternary function, then function %&has argument(s).

(=>
      (instance ?FUNCTION TernaryFunction)
      (valence ?FUNCTION 3))

If function is an instance of quaternary function, then function %&has argument(s).

(=>
      (instance ?FUNCTION QuaternaryFunction)
      (valence ?FUNCTION 4))

If rel is an instance of binary predicate, then rel %&has argument(s).

(=>
      (instance ?REL BinaryPredicate)
      (valence ?REL 2))

If rel is an instance of ternary predicate, then rel %&has argument(s).

(=>
      (instance ?REL TernaryPredicate)
      (valence ?REL 3))

If rel is an instance of quaternary predicate, then rel %&has argument(s).

(=>
      (instance ?REL QuaternaryPredicate)
      (valence ?REL 4))

If rel is an instance of quintary predicate, then rel %&has argument(s).

(=>
      (instance ?REL QuintaryPredicate)
      (valence ?REL 5))

If rel is an instance of variable arity relation, then there doesn't exist int so that rel %&has int argument(s).

(=>
      (instance ?REL VariableArityRelation)
      (not
            (exists
                  (?INT)
                  (valence ?REL ?INT))))