OWL-G: An extension package of DLG²

OWL-G, along with RDF-G, are the two default extension packages of DLG². OWL-G is built on top of RDF-G, and contains notations for vocabularies defined in the namespace of "http://www.w3.org/2002/07/owl#". Because OWL-G is intended to be a graphical notation language for Ontology Web Language (OWL), this document follow the general organization of Ontology Web Language Reference so to arrange the introduction the definition rule for OWL-G's graphical notations.

1.1 Class Descriptions

1.1.1 The owl:Class

Notation

OWL-G Definition 1: Symbols for owl:Class

owl:Class is a rdfs:subClassOf, but not the same as rdfs:Class. It needs its own notation to distinguish it from the rdfs:Class. The owl:Class is represented similarly to rdfs:Class . The difference is (1) the border is a single, instead of a double, line and (2) the second compartment is no longer optional (If so, it will be the box for literal). As usual, the top compartment is for the URI of the resource. The second compartment is used the for type information. Its default value is owl:Class, which is optional (see OWL-G Definition 1).

Design Rational

Reader may curious at our choice why rdfs:Class uses double- whereas owl:Class uses single- border. The reason is we anticipate most use of the Class concept will be using the owl:Class. Hence, make the drawing a bit simpler is definitely more convenient.

1.1.2 Enumeration: The owl:oneOf

Notation

OWL-G Definition 2: Symbols for Class Enumeration - owl:oneOf.

The Enumerative description of a Class can be simplified according by either merging the notation of owl:Class and rdf:List . or with the newly introduced symbols for owl:oneOf (see OWL-G Definition 2).

Design Rationale

Several alternative designs have been considered, such as attaching the list symbol as the third compartment to the class symbol etc. The final design choice choose to omit the type compartment with the reasoning that: if a class is described through enumeration, rarely will it need a super class. However, if a user has the need to indicate a super class, the alternative choice using the owl:oneOf can be used.

The second notation is designed to make it a bit easier to comprehend by using a logical symbol inside a circle. It is worth noting that the arrowhead cannot be omitted because otherwise it will be unclear which class is the domain of owl:oneOf.

Presentation options

Remember that a text pad can always be used. Text pad is in particularly convenient to show a list as shown in Figure 1b. Because the bottom resource is a List, so the subject of the text pad is a list, rather than a Class.

Example

The following example is an excerpt from the section 3.1.1 of OWL Reference :

<owl:Class>
  <owl:oneOf rdf:parseType="Collection">
    <owl:Thing rdf:about="#Eurasia"/>
    <owl:Thing rdf:about="#Africa"/>
    <owl:Thing rdf:about="#NorthAmerica"/>
    <owl:Thing rdf:about="#SouthAmerica"/>
    <owl:Thing rdf:about="#Australia"/>
    <owl:Thing rdf:about="#Antarctica"/>
  </owl:oneOf>
</owl:Class>

The above text message can be represented in three different forms shown in Figure 1.

Figure 1: Enumerated Class Example.

1.1.3 Property Restrictions: The owl:Restriction

Notation

OWL-G Definition 3: Restriction Symbol.

A property restriction has a general patterns using an anonymous instance of type owl:Restriction to connect the Class in question and the Property on which the Class will be retricted. This connecting pattern is abstracted as a triangle connecting the class and property. If in the context that would not cause any confusion, the triangle can be merged with the property symbol (see OWL-G Definition 3).

restriction is represented as an empty filled triangle connecting between a class and a property.

1.1.3.1 Value constraints

Notation

OWL-G Definition 4: Notation for owl:allValuesFrom.

OWL-G Definition 5: Notation for owl:someValuesFrom

OWL-G Definition 6: Notation for owl:hasValue

The value constraints of a Property restriction is graphically represented by a line connecting the Retriction triangle symbol to a Class that is the object of the value restriction.

As a memory tip, the line end for owl:allValuesFrom property is very similar to the logical "forall" symbol - ∀ (see OWL-G Definition 4). The line end for owl:someValuesFrom property is very similar to logical "exist" symbol - ∃ (see OWL-G Definition 5). In the same spirit, the line end for owl:hasValue is designed to be an "=" sign. (see OWL-G Definition 6).

1.1.3.2 Cardinality constraints

Notation

OWL-G Definition 7: Notation for owl:minCardinality.

OWL-G Definition 8: Noation for owl:maxCardinarlity

OWL-G Definition 9: Notation for owl:cardinality.

Cardinality constraints are placed inside the owl:Restriction symbol. They are typically shown in the format:

m..M

where "m" is the value of owl:minCardinality and "M" is the value of owl:maxCardinality. An asteroid (*) is used as part of the specification to indicate the unlimited upper bound.

1.1.4 Intersection, union and complement

Notations

OWL-G Definition 10Notation for owl:intersectionOf

OWL-G Definition 11 Noation for owl:unionOf

OWL-G Definition 12 Noation for owl:complementOf

Symbols for owl:intersectionOf and owl:unionOf are the identical for owl:someValuesFrom and owl:allValuesFrom. Because they are applied to different entities, they won't cause confusion. The reason we match owl:intersectionOf to owl:someValuesFrom is that they - sort of - share similar semantics because only "some" of the List members will be a member of the class in question. Similarly, owl:unionOf uses the same symbol of owl:allValuesFrom has both include the all-ish kind of meanings.

Similar to the notation of owl:oneOf , a logical symbol inside a circle can be used to denote a list with different semantics. To express the owl:intersectionOf of a list, the logical symbol of ∩ is used. To express the owl:unionOf of a list, the logical symbol of ∪ is used.

Examples

The following example is excerpted from the section 3.1.3.1 of OWL Reference:

<owl:Class>
  <owl:intersectionOf rdf:parseType="Collection">
    <owl:Class>
      <owl:oneOf rdf:parseType="Collection">
        <owl:Thing rdf:about="#Tosca" />
        <owl:Thing rdf:about="#Salome" />
      </owl:oneOf>
    </owl:Class>
    <owl:Class>
      <owl:oneOf rdf:parseType="Collection">
        <owl:Thing rdf:about="#Turandot" />
        <owl:Thing rdf:about="#Tosca" />
      </owl:oneOf>
    </owl:Class>
  </owl:intersectionOf>
</owl:Class>

The above RDF/XML code can be represented in the following two OWL-G diagrams (see Figure 2.

Figure 2: Example illustration of using owl:intersectionOf

1.2 Class Axioms

1.2.1 The owl:equivalentClass

Notation

OWL-G Definition 13: Notation for owl:equivalentClass

An owl:equivalentClass relationship is represented with a filled square connecting two classes. Since equivalent relationship is symmetric, the arrow can be omitted. If user wants to keep the original specification, the arrow head can be used.

1.2.2 The owl:disjointWith

Notation

OWL-G Definition 14: Notation for owl:disjointWith

The notation for owl:disjointWith is shown as square with inside crossed (see OWL-G Definition 14) Again, the arrow head is optional since owl:disjointWith is a symmetric property as well.

2.1 Relations to other properties

2.1.1 The owl:inverseOf

Notation

OWL-G Definition 15: Notation for owl:inverseOf

The notation for owl:inverseOf use the same symbol for owl:complementOf. Since the two notation is used at different context with one describing the relations between classes and the other between properties, the same symbol won't cause any confusion.

2.1.2 The owl:equivalentProperty

Notation

OWL-G Definition 16: Notation for owl:equivalentProperty

The notation for owl:equivalentProperty use the same sign as that for owl:equivalentClass. Due to different context where the symbol is used, it won't cause any confusion.

2.2 Sepecial Properties

OWL defines six special kinds of property. Regarding the classification on the ragne of the property, there are owl:ObjectProperty, owl:DatatypeProperty and owl:AnnotationProperty. Regarding the characteristics of global cardinality constraints, there are owl:FunctionalProperty and owl:InverseFunctionalProperty. In terms of the logical characteristics of the property, there are owl:TransitiveProperty and owl:SymmetricProperty.

OWL-G Definition 17-22 take advantage the RDF-G Definition 8 but uses a single letter to shorthand for longer URI. For instance, in OWL-G definition 18, instead of entering "<owl:InverseFunctionalProperty>", it can be shorthanded as <"D"> to indicate the property is an instance of owl:InverseFunctionalProperty.

2.2.1 Global cardinality constraints on properties

Notation

OWL-G Definition 17: Notation for owl:FunctionalProperty

OWL-G Definition 18: Notation for owl:InverseFunctionalProperty

2.2.2 Logical characteristics of properties

Notation

OWL-G Definition 19: Notation for owl:TransitiveProperty

OWL-G Definition 20: Notation for owl:SymmetricProperty

owl:AnnotationProperty, owl:ObjectProperty, and owl:DatatypeProperty

Notation

OWL-G Definition 21: Notation for owl:AnnotationProperty

OWL-G Definition 22: Notation for owl:ObjectProperty

OWL-G Definition 23: Notation for owl:DatatypeProperty

Instead of using a single letter, OWL-G Definition 23 defined a new graphical notation to shorthand owl:DatatypeProperty. The symbol can be considered as a combination of of the Property and literal box, which shall make sense since the object of an owl:DatatypeProperty must be a literal. The targeted datatype can be directly entered in the second compartment.

3.1 Individual Identity: owl:sameAs, owl:differentFrom and owl:AllDifferent

Notation

OWL-G Definition 24: Notation for owl:sameAs

OWL-G Definition 25: Notation for owl:differentFrom

OWL-G Definition 26: Notation for owl:AllDifferent

Memory tip: Anything symbol that is filled indicates some kind of equality. A squared shape is for "category" like of entities, such as class and property, both of which has sharp corner. A circle is for individual, which has round corner.

4.1 Ontology symbol

Because an ontology is uniquely labeled with a namespace URI, the package noation in the DLG²'s core DLG package is sufficient and no new notation will be introduced.

4.2 Compatibility symbol

Notations

OWL-G Definition 27: Notation for owl:backwardCompatibleWith

OWL-G Definition 28: Notation for owl:incompatibleWith

The notation used to indicate the ontology relationship is overloaded with those for individual's relationship. A solid circle indicates the backward compatibility where a crossed circle indicates incompatibility. Note, because the discussion of an ontology always has a central topic, i.e., the newest ontology, so the arrow head shall not be omitted.

4.3 Deprecated entities

Notations

OWL-G Definition 29: Notation for owl:DeprecatedClass

OWL-G Definition 30: Notation for owl:DeprecatedProperty

A deprecated entity, class or property, is shown as the regular notation with the top left corner marked by a filled triangle.

Examples

The following example is excerpted from OWL Refernece section 7.4.5

<owl:DeprecatedClass rdf:ID="Car">
  <rdfs:comment>Automobile is now preferred</rdfs:comment>
  <owl:equivalentClass rdf:resource="#Automobile"/>
</owl:DeprecatedClass>

can be depicted as Figure 3.

Figure 3 A deprecation example.