The category of OML Terms

Every OML Term can be categorized in two ways.

Categorization as a kind of relation

Formally, every OML Term is a logical relationship of arity 1 or 2.

• An OML UnaryTermKind such as an OML Concept or an OML Scalar defines a word intended for describing things whose existence is independent of anything else describable using the vocabulary.

  For example, an OML Terminology for the domain of vehicle registrations in the USA could define an OML Concept for Vehicle and an OML Scalar for LicensePlateNumber. This vocabulary would allow systems engineers to use make precise descriptions of state of affairs about Vehicles and about LicensePlateNumbers independently of any other concern; including their material existence.

• An OML DirectedBinaryRelationshipKind such as an OML ScalarDataProperty formalizes a verb word used for describing a relationship involving a subject and an object.

  The vehicle registration example above could include an OML ScalarDataProperty, hasLicensePlateNumber with domain Vehicle and range LicensePlateNumber.

Categorization by identity criteria

The criteria for identifying an instance of an OML Term leads to the following categories:

• OML Term with intrinsic identity semantics

  An instance of an OML Term with intrinsic identity is uniquely identified via its IRI. Different instances with the same IRI are can be replaced with a structurally and logically equivalent single instance with that IRI.

  OML Entity defines the abstract category of OML Terms with intrinsic identity:

  • OML Aspect for defining common characteristics that any kind of OML Entity can inherit.
  • OML Concept, a kind of OML UnaryTermKind.
  • OML ReifiedRelationship, a kind of OML DirectedBinaryRelationshipKind.

• OML Term with structural equivalence semantics

  An instance of an OML Term with structural equivalence does not have an intrinsic identity; instead, it is semantically equivalent to another instance that it is structurally equivalent to. Structural equivalence depends on the kind of OML Term:

  • OML DataType (OML DataRange and OML Structure), which have OML UnaryRelationshipKind.

    Structural equivalence for an instance of an OML DataType is defined inductively according to the structure of the OML DataType.

    For an OML DataRange, an instance is an atomic value represented as a string; such instances are equivalent if they have the same string representation.

    For an OML Structure, an instance is an OML DataStructureTuple; which maps to an OWL2 NamedIndividual. Distinct OML DataStructureTuples with different OWL2 Entitys are structurally equivalent if they have equivalent values for the OML DataRelationshipFromStructure properties defined on the OML Structure.

  • OML DataRelationshipFromStructure, a kind of OML DirectedBinaryRelationshipKind.

    OML DataRelationshipToScalar => ScalarDataPropertyValue OML DataRelationshipToStructure => StructuredDataPropertyValue

• Instance of an OML Term with equivalent reference semantics

  • OML UnreifiedRelationshipInstanceTuple is an instance of an OML UnreifiedRelationship, a kind of OML DirectedBinaryRelationshipKind.

    An OML UnreifiedRelationshipInstanceTuple maps to an OWL2 NamedIndividual. Distinct OML UnreifiedRelationshipInstanceTuples with different OWL2 Entitys are structurally equivalent if they refer to the same OML UnreifiedRelationship and the same instances of OML ConceptualEntity playing the role of domain and range for the tuple.

  • ...

Combined Categorization

Combining the two categorizations yields a 2x2 matrix of OML Term categories as follows:

OML [data properties] fall in a 2x2 matrix according to their domain and range as follows:

An OML DataRange maps to an OWL2 Data Range as follows:

OML defines several [restricted data ranges] according to the allowable facet restrictions for OWL2 Datatype Maps as follows: