And nondefinitional attributes are mapped to annotation properties. The inheritable nondefinitional
attributes (not supported in KL-ONE and OWL) are
modeled as annotation properties and the attribute
inheritance is handled in the application. These three
mappings are lossless, and the logical (roles and concepts) versus nonlogical (annotation properties and
application data) separation remains intact.
Finally, GSPAS value restriction (∀R.A ⊓ ∃R), which
restricts all fillers of R to concept A, is remodeled as
existential restriction ∃R.A in the OWL ontology,
which restricts R to have some fillers from concept A
and, optionally, other fillers from other concepts. It is
our observation that, in the GSPAS ontology, concepts that are best modeled using existential restriction are modeled using value restriction.
Observe that (∀R.A ⊓ ∃R) is a subclass of ∃R.A, and
so, the existential restriction admits more models
than the corresponding value restriction. This is a
widening or relaxing transformation that preserves
subsumption structure (subclass or is-a relation). We
will justify this for both assertion and inference links.
Consider two value restrictions in figure 5, and
their translation given by is-a1 and is-a2. If is-a3 is
asserted in the GSPAS ontology then is-a4 will be
asserted during ontology conversion. By is-a3 and is-
a1 all individuals of (∀R.A2 ⊓ ∃R) will belong to ∃R.A1,
making is-a5 true. By similar argument, is-a2 and is-a4
also make is-a5 true. As a result, the asserted is-a4
agrees with the assertion is-a3 (figure 5).
The sufficient conditions for inferring is-a link
between a concept Sub and a concept Super is stated
in Lipkis (1981). Two of the relevant conditions are
( 1) Each role of Super is modified by a role of Sub. ( 2)
Each value description of each role of Super subsumes
a value description of the corresponding role of Sub.
Accordingly, if A1 subsumes A2, then is-a3 will be
inferred, and correspondingly, is-a4 will be inferred
in OWL. Therefore is-a3 (be it an assertion or an infer-
ence) will have a corresponding is-a in the OWL
ontology, and thus subsumption links will be pre-
Table 1. Vocabulary Mapping.
GSPAS KL-ONE DL OWL
1 THING THING Top concept ‘T’ owl: Thing
2 Concept Concept Concept Class
3 Primitive Concept Primitive Concept Atomic Inclusion Partial Concept
4 Generic Concept De;ned Concept De;nition Complete Concept
5 Individual Individual Concept Individual Object
6 Role Restriction Role Restriction Role Restriction Property Restriction
7 Value Restriction Value Restriction Value Restriction Value Restricti
8 Number Restriction Number Restriction Number Restriction Cardinality restriction
9 Classi;able Attribute Role Role Object Property
10 Nonde;nitional Attribute Nonde;nitional Role n/a Annotation Property
11 Nonde;nitional Inheritable Attribute n/a n/a n/a
12 Classi;er Classi;er Reasoner Reasoner
Table 2. GSPAS KR Primitives (Modeling Elements) and Their OWL Translation.
*In DL expression, A is concept name; C, C1, C2 are concept forming expressions; R is role name.
GSPAS KL-ONE DL OWL
1 Primitive Concept Primitive Concept A C rdfs:subClassOf
2 Generic Concept De;ned Concept A " C owl:equivalentClass
3 Value Restriction (#R.A R) Value Restriction R.A owl:someValuesFrom
4 Conjunction Conjunction C1 C2 owl:intersectionOf
5 Classi;able Attribute Role Role owl:ObjectProperty
6 Nonde;nitional Attribute Non-de;nitional Role n/a owl:AnnotationProperty
7 Nonde;nitional Inheritable Attribute n/a n/a n/a