Theory - Properties

We distinguish between Data Properties (DP) and Object Properties (OP) and their Data Property Definitions (DPD) and Object Property Definitions (OPD). For both we give a short and a full definition pattern. The full two-triple definition patterns using the OPs ◊hasDomain and ◊hasRange are equivalent to the short one-triple definition patterns.

Intrinsic attributes of entities are treated as data properties (DP) according to the Semantic Web / OWL / RDF convention. These include data properties such as color, length, weight, age, etc., which define the corresponding quality dimensions. The full definition of a DP is built with two triples, e.g., (.LicensePlateNbr, »hasDomain, ^Vehicle) and (.LicensePlateNbr, »hasRange, :String). The short form of a DPD determines the associated type for the class, e.g. (^Vehicle, .LicensePlateNbr, :String) which instantiates, for example, to (>Toms_Lambo, .LicensePlateNbr, DO-IT 1954). Let a ∈ N. be the name of a data property, adt ∈ ADT an Atomic Data Type, and u ∈ N be the name of a universal. Both templates of the DPDs are equivalent according to the following rule:

{{axiom:DPDAx:Data Property Definition Axiom:(u, a, :adt) ∈ KG ⇔ (a, »hasDomain, u) ∈ KG ∧ (a, »hasRange, :adt) ∈ KG }}

Extrinsic properties of entities have been introduced as Object Properties (OP) according to the convention in the Semantic Web / OWL / RDF. Object properties bind entities to other entities or to themselves. The full definition of an object property, e.g., ◊hasMotor, is defined by the two triples (◊hasMotor, »hasDomain, ^Car) and (◊hasMotor, »hasRange, ^Motor). The short form of an Object Property Definition is (^Car, ◊hasMotor, ^Motor). As an example from a vehicle ontology we have (>Toms_Lambo, »hasCombMotor, >MTR_TL) where ◊hasCombMotor is a subobject property of ◊hasMotor. Let ◊op ∈ N◊ be the name of an object property, and c, d ∈ N^ be the names of classes. Both templates of OPDs are equivalent by the rule:

{{axiom:OPDAx:Object Property Definition Axiom:(c, ◊op, d) ∈ KG ⇔ (◊op, »hasDomain, c) ∈ KG ∧ (◊op, »hasRange, d) ∈ KG }}