Project: Semantics of object model


Object model is used for the representation of conceptual structures composed of individual and abstract objects. The set of all objects is partially ordered reflecting the subclass and instantiation relationships. The representation of objects is based on three aspects: object is described by identity, its value and its interpretation. The value of individual object is its state while the value of the class object is its type. The interpretation of individual object is the object itself while the interpretation of the class object is the set of its instances. The representation of objects is dual in a sense that it is defined as a pair of identity and a value.

The paper presents the formalization of statical structure (of object model) comprising abstract and concrete (individual) objects. While the space of identifiers is organized into poset and the only building blocks used for the representation of object model are identifiers, single-valued and multi-valued functions, the space of values (including signatures) forms a poset of complex structures reflecting the poset of identifiers.

Static semantics of object model is presented using denotational semantics. \emph{Valuation} of object can be seen as detailing the information about corresponing (object) identifier. \emph{Interpretation} of object includes all its instances including the instances of all more specific abstract objects (classes). The consistency between identifier and value posets is shown by presenting the correspondence between sintactical ordering and denotational subsumption.

The first part of the paper presents the formalization of the classical object model where we have a strict distinction between the schema and instance levels of the representation. In the second part of the paper the consequences of releasing the boundary between the schema and the instance levels of an object model is observed by allowing the definition of objects which include data from both levels. We show that few changes are needed in order to augment the previously presented formal definition of the structural part of object language to represent the extended object model.


On formalization of object model by unifying intensional and extensional representations.
European Japanese Conference on Information Modelling and Knowledge Bases, Information Modelling and Knowledge Bases XXI, Frontiers in Artificial Intelligence and Applications, IOS Press, 2010.
[pdf, Technical report]