MLM Requirements

In [BrAl2016b] an axiomatic theory called MLM (Multi-Level Modeling Theory) is proposed to address multi-level modeling requirements. There four requirements are:

• Requirement R1: the ability to represent entities of multiple (related) classification levels, capturing chains of instantiation between the involved entities 
• Requirement R2: define principles for the organization of entities into levels
• Requirement R3: capture rules for the instantiation of types at different levels
• Requirement R4: allow the representation of domain relations between entities in different classification levels

These requirements were checked against the RDFS-languages RDFS(FA), OWL2, OWL_FA and PURO. None of these RDFS-languages meet all four requirements. In the following we will explain, that our approach fulfills all requirements.

• R1: We have argued, that our classifcation levels are depending on the types of data properties which are used in the class definitions. A subclass can be instantiated form another superior class in the subclass hierarchy, if and only if the superior class contains a class data property (CDP) or a transparent data property (TDP) type definition.
• R2: There are only three different ontological levels/layers in our approach: The Particulars layer (PL), the schema layer (SL) and the UMO meta-schema layer (see Figure UMO). Classes in the SL layer may be 1stOrderClasses or 2ndOrderClasses at the same time.
• R3: The rules for instantiations of types at different levels are clearly defined and are dependent on the type of data properties. Individual data properties (PDP) only instantiate into individuals of the IL. Class Data Properties (CDP) instantiate only into classes. Transparent Data Properties (TDPs) may instantiate into both PL and IL:
• R4: There are no restrictions regarding the representation of domain relations between entitites in different levels. particulars can be related to classes at any level, e.g. (>Miura, ◊Designer, >NPS-Marcello_Gandini). Relationship types like ◊isSubordinateOf can be used to arrange classes into orders, which are independent from the sub-classing or instantiating mechanism. A prominent example for that is the biological classification  ([AtKu2003], [CaAl2016]). In our approach we would have, e.g.
  (^Dog, ◊SubClass, ^Collie),
  (^Dog, ◊SubClass, ^Species),
  (^Breed, ◊SubClass, ^Collie),
  (^Species, ◊SubOrdinateOf, ^Breed).
  Compared to the other works, we do not see the need to model ^Dog as an instance of ^Species, since the semantics is given by the nature of the data properties (e.g. .^hasSpines, .^^Endangered), which have been defined in Figure SpeciesOntology.

Therefore we think, that we meet all requirements R1-R4 with the restriction, that some of the requirements are not completely applicable in our approach. But this does not affect the expressive power of our approach.