Relation Has-At-Most

Instance-Of: Relation, Set
Arity: 3
A binary relation HAS-AT-LEAST n values on domain instance i if there exist no more than n distinct values v_j such that R(i,v_j) holds.

When used in the definition of a class where ?i is the instance variable, (HAS-AT-MOST ?i R n) means that the slot R can have at most n values on any instances of the class.


Implication Axioms for Has-At-Most:

(=> (Has-At-Most ?Instance ?Binary-Relation ?N)
    (=< (Value-Cardinality ?Instance ?Binary-Relation) ?N))

Equivalence Axioms for Has-At-Most:

(<=> (Has-At-Most ?Instance ?Binary-Relation ?N)
     (And (Binary-Relation ?Binary-Relation)
          (Natural ?N)
          (=< (Value-Cardinality ?Instance ?Binary-Relation) ?N)))

Axioms for Has-At-Most:

(Natural ?N)

(Binary-Relation ?Binary-Relation)

(Nth-Domain Has-At-Most 3 Natural)

(Nth-Domain Has-At-Most 2 Binary-Relation)

Equivalence Axioms mentioning Has-At-Most:

(<=> (Can-Have-One ?Instance ?Binary-Relation)
     (Has-At-Most ?Instance ?Binary-Relation 1))