Class Role-Class

• Defined in ontology: Enterprise-v0.1

Notes for Role-Class:

• In some cases, a Role-Class may be defined in terms of more than one Role. An entity is an instance of such a Role-Class if it is in one of two or more Roles in one or more Relations.
• Why not have Role-Class a super-class of various Role-Classes such as Purpose and Resource?

  I can think of no good reasons for it to be one way or the other, thus choice was mainly arbitrary. The other way would entail use of a different name for the superclass so as to suggest the right meaning (e.g. Role-Player, or Role-Playing-Entity).

• Example: Given Classes Person and Document are defined, we show below how a binary relation Read-Document and the Role-Class Reader might be defined.

   
  ;;; Read-Document
  
  (define-relation Read-Document (?person ?document)
  
  
    "A Relationship between an Person and a Document whereby the Person
  reads the Document"
    :def
    (and (Person ?person) (Document ?document)) )
  
  
  
  ;; Reader
  
  (define-frame Reader
  
  
    :own-slots
    ((Documentation "a Person in an Read-Document Relationship with 
  
  
  		 some Document")
    (Instance-Of Role-Class) (Subclass-Of Individual))
  
  
    :axioms
    (<
  
  
  => (Reader ?person)
         (and (Person ?person)
  
  
  	    (exists (?document) (Read-Document ?person ?document)))) )
  
  
  
  

  Note that the axiom above is equivelent to how it might be expressed using the general form given for defining a Role-Class:

    
  
  (<
  
  
  => (Reader ?person) 
       (exists (?args)
  
  
  	     (and (list ?args)
  
  
  		  (holds ?Read-Document ?args)
  
  
  		  (= (nth ?args 1) ?person))))
  
  
  
  

  Note also that the wording used to define role-classes is:
  'The Person in a R relationship.' rather than
  'The Role of a Person that ... in a R relationship.' which was used in the natural language version. This reflects that fact that we do not explicitly define what are called roles in the NL version; rather we define Role-Classes in terms of such roles which are [only] implicit in the definition of relations.

Slots on class Role-Class:

Arity: 1

Documentation:

A special kind of Class which is defined as the set of all Entities playing a particular Role in some Relation.

To the extent that updates may occur which change the particular set of tuples comprising a relation, being an instance of such a class is dynamically determined.

Has-Instance: Qua-Entity

Instance-Of: Class, Relation, Set

Subclass-Of: Class, Relation, Set

---

Slots on instances of Role-Class:

Arity: 1

Equivalence Axioms for Role-Class:

(<=> (Role-Class ?X)
     (Exists (?R ?N)
             (And (Relation ?R)
                  (Natural ?N)
                  (Forall (?Z)
                          (<=> (Instance-Of ?Z ?X)
                               (Exists (?Args)
                                       (And (List ?Args)
                                            (Holds ?R ?Args)
                                            (= (Nth ?Args ?N) ?Z))))))))

Other Related Equivalence Axioms for Role-Class:

(<=> (Qua-Entity ?X)
     (Exists (?Rc) (And (Role-Class ?Rc) (Instance-Of ?X ?Rc))))