The Marseille Constraint based Configuration Group
The web resource of the Configuration Team, member of the InCA Team, from the LSIS Laboratory, Marseille, France
Finite model search for constrained object models
Finite model semantics
We define finite model semantics through an interpretation of constrained object models.
LSIS
CNRS
Université de la Méditerranée
Université Paul CézannePeople
Laurent Henocque (Associate Pr.)
Nicolas Prcovic (Assistant Pr.)
Mathieu Estratat (Post doc.)
Mathias Kleiner (Doctor)
and formerly
Stephane Grandcolas (Assistant Pr.)
Related Links
Associations
the Association Française pour la Programmation par Contraintes
CP Online, the web site of the ACP
Configuration tool providers
Z
Semantic Web
Solving 
Finite model semantics
Finite model semantics
Definition (Interpretation of a constrained object model) The interpretation I(M) of a constrained object model M is defined by the recursive generalization of its elements interpretation. The elements classes, objects, attributes, roles and relations are given their own interpretation; whereas constraints have the usual interpretation of predicate logic on those elements.
Elements interpretation
Interpretation of Object, String and Class
I defines a projection of non-interpreted types on a finite set of integers. All objects are mutually distinct. The interpretation function associates a different integer to any element of type Object. This function is injective:
Any element of type String is also interpreted as an integer:
The interpretation of an integer is the integer itself:
The interpretation of the other elements naturally stems from I: By definition, any Class is a finite set of Objects and I thus associates a finite set of integers:
Interpretation of attributes
Any attribute is interpreted as a couple (integer interpreting the object, interpretation of the attribute value).
Attribute of type integer:
Attribute of type String:
Interpretation of arbitrary relations
Any arbitrary relation is interpreted as a couple of integers:
Interpretation of roles
Any role is interpreted as a set of couples (integers, set of integers):
Interpretation of composition relations
As a role, a composition relation is a function associating a set of objects to an object. Their interpretations are similar. The reverse partial function of a composition relation is equal to a set of couples (integer,integer):
