The OMG's MOF (Meta Object Facility) 4 Layer Architecture is a way of organizing and structuring models in object-oriented systems. It consists of four layers, each of which represents a different aspect of the model:

1. The metametamodel layer, which defines the structure and syntax of the modeling language used to create the model.

2. The metamodel layer, which represents the abstract definition of the model itself.

3. The model layer, which represents the actual instances of the model.

4. The object layer, which represents the actual objects that are created and manipulated within the system.

From a logical perspective, the MOF 4 Layer Architecture can be viewed as a hierarchy of abstraction levels, where each layer provides a different level of abstraction and encapsulation. The lower layers represent more abstract and general aspects of the model, while the higher layers represent more specific and concrete aspects of the model.

At the lowest level, the metametamodel layer provides a formal definition of the modeling language used to create the model. This layer defines the structure and syntax of the language, including the types of elements that can be represented in the model and the relationships between them. The metametamodel layer can be seen as a formal logic system, which defines the rules and syntax for building models.

The metamodel layer represents the abstract definition of the model, which is created using the modeling language defined in the metametamodel layer. This layer includes the concepts and relationships that are being modeled, such as classes, attributes, and relationships between them. The metamodel layer can be viewed as a logical theory, which defines the concepts and relationships that can be used to build models.

The model layer represents the actual instances of the model, which are created using the definitions in the metamodel layer. This layer includes specific instances of classes, attributes, and relationships between them. The model layer can be seen as a set of logical formulas, which represent specific instances of the concepts and relationships defined in the metamodel layer.

Finally, the object layer represents the actual objects that are created and manipulated within the system. Objects are specific instances of classes, which have specific values for their attributes and specific relationships with other objects. The object layer can be viewed as a set of logical propositions, which represent the current state of the system in terms of the specific objects that are present and their properties and relationships.