The following notation is introduced to refer to the elements of a generic FCS in the figure below:

• Target Domain Concept (TDC) denotes the domain of discourse. The domain-specific concept targeted by the FCS.
• Facet_i denotes one of the facets of the FCS.
• F_iTerm_j denotes one of the terms of Facet_i.
• Item_x denotes one the items from the domain of discourse (TDC) to be classified.

Diagram

The symbol (≡) denotes an OWL defined class.

The figure below represents a further generalization of the Normalization ODP and introduces the following notation:

• :TDC denotes a primitive class representing the domain concept being normalized.
• :Module_i denotes a primitive class that represents one of the modules.
• :M_iClass_j denotes a primitive class that represents a subset of the module class :Module_i.
• :hasModule_i denotes an object property that links every module :Module_i to the different subclasses of the target domain concept :M_iClass_jTDC and :SpecificTDC_x.
• :M_iClass_jTDC denotes a defined class that represents a subset of the target domain concept class :TDC. Every class :M_iClass_jTDC is defined based on its relationship to the single corresponding class :M_iClass_j that it is derived from.
• :SpecificTDC_x denotes a primitive class that represents a subset of the target domain concept class :TDC and an entity from the domain to be classified. Every class :SpecificTDC_x is described based on its relationship to various classes :M_iClass_j from potentially different modules. As a consequence of this relationship, the classes :SpecificTDC_x could introduce the polyhierarchy scenarios in the ontology model that the Normalization ODP aims to manage and untangle.

The implementation of a generic defined class :M_iClass_jTDC is given as follows:

:M_iClass_jTDC rdf:type owl:Class ;
               rdfs:subClassOf :TDC ;
               owl:equivalentClass [ rdf:type owl:Restriction ;
                                     owl:onProperty :hasModule_i ;
                                     owl:someValuesFrom :M_iClass_j
                                   ] .

The implementation of a generic class :SpecificTDC_x is given as follows:

:SpecificTDC_x rdf:type owl:Class ;
               rdfs:subClassOf :TDC ,
                               [ rdf:type owl:Restriction ;
                                 owl:onProperty :hasModule_i ;
                                 owl:someValuesFrom :M_iClass_j
                               ] ,
                               [ ... rest of existential restrictions on property :hasModule_i
                                     for every class :M_iClass_j that participates
                                     in the description of :SpecificTDC_x
                               ] .

This implementation of the classes :M_iClass_jTDC and :SpecificTDC_x respectively, enable a reasoner to infer and maintain the subsumption relations between a given class :SpecificTDC_x and the various classes :M_iClass_jTDC that it is related to.

Diagram

The table below summarizes the alignment of the elements in the generic structure of both conceptual models. This alignment enables the conversion from a FCS to an OWL DL ontology by applying the Normalization ODP:

• The first column (leftmost), contains the elements of a generic FCS as introduced in section Non-Ontological Resource above.
• The second column contains the elements of the Normalization ODP generic structure

as introduced in section Ontology above.

• The third column represents the selected OWL notation for the elements of a generic FCS in the context of the Normalization ODP generic structure.
• The forth column (rightmost), indicates the OWL implementation chosen for every element. The selection complies with the requirements of the normalization mechanism.

Based on the principle of representating each facet of a FCS as a module of the Normalization ODP, the underlying ideas behind the mappings in the figure(table) above can be outlined as follows:

• The target domain concept TDC represents the domain of discourse of both a FCS and the Normalization ODP. The primitive class :TDC fulfills that role in the normalized ontology.
• A facet Facet_i from a generic FCS corresponds to a module :Module_i in the Normalization ODP, therefore it becomes a primitive class :Facet_i in the normalized ontology model.
• A facet Facet_i from a FCS also becomes an object property :hasFacet_i in the normalized ontology, given that for every module :Module_i in the Normalization ODP, there is an object property :has_Module_i.
• From the relationship between facet and module, it follows that a facet term F_iTerm_j from a FCS maps to a module subclass :M_iClass_j from the Normalization ODP. Both elements represents the same notion in their respective conceptual models. A subvidision, a refinement of the facet or module that they complement respectively. Therefore, a facet term F_iTerm_j from a FCS becomes a primitive class :F_iTerm_j in the normalized ontology.
• A facet term F_iTerm_j from a FCS also produces a defined class :F_iTerm_jTDC in the normalized ontology, given that for every primitive class :M_iClass_j in the Normalization ODP, there is a corresponding defined class :M_iClass_jTDC.
• Every item Item_x to be classified in the FCS aligns to a class :Specific_x that is automatically classified by a reasoner in the Normalization ODP. Therefore, every element Item_x is represented as a primitive class :SpecificTDC_x in the normalized ontology.

Diagram

• The TDC element is populated with the domain "Dishwashing Detergent".
• Facet_i elements are populated with the facets: "Agent", "Form", "Brand Name", "Scent", "Effect On Agent", and "Special Property".
• F_iTerm_j elements are populated with the terms or foci listed below (grouped by facet):
  • Agent: dishwasher, person.
  • Form: gel, gelpac, liquid, powder, tablet.
  • Brand Name: Cascade, Electrasol, Ivory, No Name, Palmolive, President's Choice, Sunlight.
  • Scent: green apple, green tea, lavender, lemon, mandarin, ocean breeze, orange blossom, orchard fresh, passion flower, ruby red grapefruit, ylang ylang.
  • Effect on Agent: aroma therapy (subdivisions: invigorating, relaxing).
  • Special Property: antibacterial.
• Item_x elements are populated in this case with two example items to classify:
  • "President's Choice Antibacterial Hand Soap and Dishwashing Liquid".
  • "Palmolive Aroma Therapy, Lavender and Ylang Ylang".

Diagram

The symbol (≡) denotes an OWL defined class.

[[Image:FacetedClassificationSchemeOntoExObjProp.png

Diagram

Diagram