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.

Diagram

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) below 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.

[[Image:MappingFCSNormalizationODP.png

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