Relation SATISFIES-CONSTRAINT

• Defined in theory: Parametric-constraints
• Source code: parametric-constraints.lisp

Slots on this relation:

Documentation:

An object-constraint is satisfied if its constraint.expression, when applied to an object, is a true sentence.

The "application" of the expression is a syntactic construction that transforms the expression into a KIF predicate. The constraint is satisfied by an object iff the predicate holds for the object.

Instance-Of: Relation

Arity: 2

Range: Object-constraint

Equivalence Axioms:

(<=> (Satisfies-Constraint ?Object ?Constraint)
     (And (Object-Constraint ?Constraint)
          (Holds (Denotation 
                     (Listof 
                         'Kappa
                         (Listof 
                             (The-Free-Variable-In 
                                 (Constraint.Expression ?Constraint)))
                         (Constraint.Expression ?Constraint)))
                 ?Object)))

Other Related Axioms:

(=> (Satisfies-Constraint $X $Y) (Object-Constraint $Y))

(<=> (Satisfies-Constraint ?Object ?Constraint)
     (And (Object-Constraint ?Constraint)
          (Holds (Denotation 
                     (Listof 
                         'Kappa
                         (Listof 
                             (The-Free-Variable-In 
                                 (Constraint.Expression ?Constraint)))
                         (Constraint.Expression ?Constraint)))
                 ?Object)))

Notes:

• (KAPPA (?x) (p ?x)) denotes the relation that holds
  for all ?x such that (P ?x) is true.
• (DENOTATION
  ) refers to the the semantic value of the expression. The semantic value of a KAPPA expression is a unary relation.
• (HOLDS R a) means that the relation R holds on the object a.
  A relation holds iff the associated predicate is true on the arguments.
• Example: (object-constraint c1)
  

  (= (constraint.expression c1) (quote (= (f ?x) (* (m ?x) (a ?x)))))
  

  (= (f body) 20)
  

  (= (m body) 10)
  

  (= (a body) 2)
  

  (satisfies-constraint body c1)