The developers of StarDog OWL/RDF DBMS have pioneered a new use of OWL as a schema language for RDF databases. This is achieved by adding integrity constraints (IC), also expressed in OWL syntax, to the traditional “open-world” OWL axioms. The new database paradigm requires a suitable visual schema editor. We propose here a two-level approach for integrated visual UML-style editing of extended OWL+IC ontologies: (i) introduce the notion of ontology splitter that can be used in conjunction with any OWL editor, and (ii) offer a custom graphical notation for axiom level annotations on the basis of compact UML-style OWL ontology editor OWLGrEd.
Web ontology language OWL [
The IC specification in [
There are a number of approaches and tools including UML/OWL profile [
Our aim here is to offer extended ontology editor and framework that are able to cope with both OWA-axioms and IC within a single notational space (single ontology or UML-style class diagram). The OWA vs. IC ontology separation then is left to an ontology post-processing step to be performed by some “ontology splitter” that can be defined as a procedure receiving as an input any OWL ontology (as a syntactic unit) and producing as the output its “partitioning” into OWA and IC parts.
For many practical use cases it might be sufficient for such ontology splitting procedure to rely just on the structure of input ontology axioms. An example splitter could, e.g. send all cardinality restrictions into the IC-part of the ontology, while all subClassOf(A,B) axioms with named A and B could go into the OWA-part. Another “splitter” could send all ontology into its OWA part, leaving the IC-part empty.
We note that even the basic functionality of any OWL editor (including all said
UML/OWL editors and e.g. Protégé [
The full generality of ontology splitters is easily obtained by allowing them to resort not only to axiom structure, but also to ontology entity and axiom annotations. For instance, a splitter may send to the OWA-part only those subPropertyOf(:p,:q) axioms, where :q is annotated by AnnotationAssertion(a:isInferred :q “true”) for a suitable annotation property a:isInferred.
The use of such “general” ontology splitter requires, however, availability of suitable entity and axiom annotation notation within the editor, that is a non-trivial task for UML-style OWL ontology editors. Although there are generic means for entity annotation in OWLGrEd, we offer and describe here its extended version OWLGrEd/S supporting a custom notation for entity and axiom annotations that is suitable for extended OWA+IC ontology specification.
From the methodological viewpoint we note that the ontology splitter to be applied to the resulting OWA+IC ontology should be viewed as belonging to the semantics of the editor used in the ontology authoring. There could be a number of concrete well established ontology splitters suitable for different application areas and modeling tasks based on OWA+IC ontologies that could be applied in appropriate situations. We briefly sketch here some principles of ontology splitter construction for semantic database schema definition and offer one possible candidate splitter definition.
In the following sections we briefly review the UML-style OWL ontology editor
OWLGrEd, comment on the integrity constraints and schema semantics of extended
ontologies and then move to ontology splitter and OWLGrEd/S notation description.
OWLGrEd (http://owlgred.lumii.lv/) provides a complete graphical notation for OWL
2, based on UML class diagrams. We visualize OWL classes as UML classes, data
properties as class attributes, object properties as association roles, individuals as
objects, cardinality restrictions on property domain class as UML cardinalities, etc. We
enrich the UML class diagrams with the new extension notations, e.g. (cf. [
• fields in associations and attributes for equivalent, disjoint and super properties and fields for property characteristics, e.g., functional, transitive, etc.; • anonymous classes containing equivalent class expression but no name (we show graphically only those anonymous classes that need to have graphic representation in order to be able to describe other ontology concepts in the diagram); • connectors (as lines) for visualizing binary disjoint, equivalent, etc. axioms; • boxes with connectors for n-ary disjoint, equivalent, etc. axioms; • connectors (lines) for visualizing object property restrictions some, only, exactly, as well as cardinality restrictions.
Figure 1 contains example mini-University ontology, shown in OWLGrEd notation
[
isTaughtBy
teaches {<relates} {<>takes} {disjoint}
AcademicProgram programName:string{<name} belongsTo 1 enrolled {>takes o belongsTo}
includes relates Course
courseName:string isTakenBy takes {<relates} 1..10 {<name} passed {<takes}
MandatoryCourse <isTaught by only (Professor or teaches some [1..*] (PermanentTeachingStaff and salary some integer [> 8000]))
Thing{owl} name:string{func} Regarding mini-University ontology of Figure 1 as a database schema would lead to certain un-intended consequences due to OWL standard “open-world” semantics, e.g.: - if an assistant X has registered, by an error, as taking (takes) a course, the system infers that X is a student since only students are allowed to take a course; - existence of a student with no taken courses specified does not rise an error; - if a course belongs to two academic programs (with no names specified yet), these would be inferred to be the same academic program; - if a student X takes a course Y belonging to (belongsTo) academic program W that is other than V, where X is enrolled, X is inferred to be enrolled also in W; - if a professor has a recorded salary of 9500, the system would infer that there is also another salary for the professor that is > 10000.
The integrity constraints (IC) [
Our interest here is to offer graphical editors for database schemas, defined as extended ontologies. Regarding <K,C> as a database schema means that there is some data expected to be “filled in” to it, and that the actual consistency checking and constraint validation tasks are to be performed in a <K+DK,C+DC> situation for a data ontology DK (typically consisting of A-Box axioms) and some (possibly empty) data-level constraint set DC. We say that the extended data ontology <DK,DC> conforms to the schema ontology <K,C> whenever the combined extended ontology <K+DK,C+DC> is consistent. The schema-semantics of the extended ontology <K,C> can then be defined as the set of all <DK,DC> conforming to <K,C>.
Note that within the “schema-semantics” of <K,C> the “satisfaction by all MEmodels” (= by ME-model “intersections”) for the constraint validity is considered for any K+DK, where DK is arbitrary “data ontology”, thus covering a large part of K models satisfying C as the representative ME-model “intersections” for suitable DK.
An ontology splitter is a function that, given ontology (a set of OWL 2.0 axioms) X, produces two sets of axioms O(X) and C(X), whose union has the same logical meaning, as X (i.e. O(X)+C(X) with both O(X) and C(X) viewed in OWA-sense is valid on a model M if and only if X is valid). In the context of separating IC-part out of the ontology, the application of such an ontology splitter would allow producing an extended ontology <O(X),C(X)> with O(X) interpreted in OWA-sense and C(X) interpreted in CWA-sense from the ontology X. A simple ontology splitter would just partition the ontology axiom set into two subsets, however, there may be cases when an axiom re-factoring is needed (e.g. an EquivalentClasses-axiom may be split into two SubClassOf-axioms). We note that for different application areas and different system modeling paradigms there might be different ontology splitters applied (e.g. there can be a “trivial” ontology splitter having O(X)=X and C(X)=∅, or there can be a splitter doing some ontology axiom differentiation). 2 In essence, a ME-model has no unnecessary equalities between named individuals.
An ontology splitter can be defined in terms of rules that determine for each source ontology X axiom A the action to be taken: (i) move A into C(X), (ii) move A into O(X), or (iii) re-factor A into parts to be further processed by the ontology splitter (i.e. moved into C(X), O(X) or re-factored further).
The action taken by the splitter on axiom A can be determined on the basis of:
- axiom A structure (e.g. by pattern matching over some A syntactical
presentation, we use here OWL Functional Syntax [
We summarize the possible re-factoring actions for translating an axiom into the
set of its parts in Figure 2 using an intuitive pattern matching notation over OFS,
where the variable placeholder, such as X?, stands for arbitrary OFS term and X1? ..
Xn? notation is used to denote a list of OFS terms. These rules do not change the
OWA-semantics of the ontology, as required by the ontology splitter definition.
a. EquivalentClasses(X? Y?) -> {SubClassOf(X? Y?), SubClassOf(Y? X?)}
b. EquivalentClasses(X1? .. Xn?) -> {EquivalentClasses(Xi? Xj?) | 1≤i<j≤n}
c. DisjointClasses(X1? .. Xn?) -> {DisjointClasses(Xi? Xj?) | 1≤i<j≤n}
d. SameIndividual(X1? .. Xn?) -> {SameIndividual(Xi? Xj?) | 1≤i<j≤n}
e. DifferentIndividuals(X1? .. Xn?) -> {DifferentIndividuals(Xi? Xj?) | 1≤i<j≤n}
f. SubClassOf(X? ObjectIntersectionOf(Y1? .. Yn?)) ->{ SubClassOf(X? Yi?) | 1≤i≤n}
g. SubClassOf(X? ObjectExactCardinality(Y? Z? W?))->{ SubClassOf(X? ObjectMinCardinality(Y? Z? W?)),
SubClassOf(X? ObjectMaxCardinality(Y? Z? W?))}
h. SubClassOf(X? DataExactCardinality(Y? Z? W?)) -> { SubClassOf(X? DataMinCardinality(Y? Z? W?)),
SubClassOf(X? DataMaxCardinality(Y? Z? W?))}
i. DisjointUnion(X? Y1?..Yn?)->{DisjointClasses(Y1?..Yn?),EquivalentClasses(ObjectUnionOf(Y1? .. Yn?) X?)}
j. EquivalentObjectProperties(X1? .. Xn?) -> {EquivalentObjectProperties(Xi? Xj?) | 1≤i<j≤n}
k. EquivalentObjectProperties(X? Y?) -> {SubObjectPropertyOf(X? Y?), SubObjectPropertyOf(Y? X?)}
l. EquivalentDataProperties(X1? .. Xn?) -> {EquivalentDataProperties(Xi? Xj?) | 1≤i<j≤n}
m.EquivalentDataProperties(X? Y?) -> {SubDataPropertyOf(X? Y?), SubDataPropertyOf(Y? X?)}
n. ClassAssertion(ObjectIntersectionOf(X1?..Xn?) Y?)->{ClassAssertion(ObjectIntersectionOf(Xi? Y?)|1≤i≤n}
o. f(ObjectComplementOf(ObjectComplementOf(Y?))) -> {f(Y?))} for any context f
p. f(ObjectComplementOf(ObjectUnionOf(X1? .. Xn?))) -> {f(ObjectIntersectionOf(X1? .. Xn?))} for any f
The example “database-style” ontology splitter of Figure 3 restricts the reasoner from
inferring the existence of new individuals in the knowledge base or un-stated
coincidence of two differently named individuals. We follow here also principle of
minimal model determinism (existence of a single “smallest” ME-model in the sense
of [
We note that the axiom-level annotations have not been necessary in the example ontology splitter and that there are only two rules resorting to entity-level annotations; simpler ontology splitters marking all sub-property assertions either as OWA or IC might also be perfectly sensible for database-style use of extended ontologies (the use of sub-property assertions in different senses is up to the used database modeling discipline; a similar situation is also with property domain/range assertions used either for open-world classification, or for closed-world constraint checking).
Thing{owl} name/i/:(c) string{(c) func} i {(i) disjoint} Section 4 provides a conceptual base for integrated extended OWA+IC ontology management within single ontology space or UML-style class diagram.
The OWLGrEd editor [
Figure 4 illustrates also a further OWLGrEd notation and editor extension, called OWLGrEd/S (http://owlgred.lumii.lv/s), with specific axiom-level notation for marking concrete axioms as belonging to the OWA or IC part of the extended ontology. The notation allows attaching the mark ‘(i)’ (standing for “inference”, meaning axiom inclusion in OWA-part of the ontology) or ‘(c)’ (standing for “constraint”, meaning axiom inclusion in the IC part) to the visual representations of ontology axioms. We offer explicit means for both marking an axiom to be OWA, or IC, since this axiom-level mark-up can be used in conjunction with other rules in ontology splitter that may be setting different “default” actions for the axiom not having an explicit “semantics markup” attached to it. The explicit (i)/(c) marking is not possible, however, on axiom “part” levels, as it may become possible in ontology splitter via axiom re-factoring. We note also that in the case, if an axiom is reflected in several parts of the diagram, the (i)/(c) marking of any single place of the axiom representation suffices to have the entire axiom marked as OWA/IC, respectively.
The conceptual tool chain for working with OWLGrEd/S editor involves defining
or referencing an ontology splitter, then editing the ontology in the editor, possibly
assigning the individual axiom markers. Further on two ontologies, say, open.owl and
ic.owl are exported from the editor and can be used in Stardog database environment
as ontology and integrity constraints files. Currently we are working with an
alternative implementation with an independent ontology splitter, where the ontology is
created in OWLGrEd or OWLGrEd/S, exported to Protégé [
The introduction of high-level integrity constraints [
We believe that the UML-style compact OWL editor OWLGrEd, whose one of the
main strengths is use of textual OWL Manchester Syntax [
The introduced ontology splitter notion provides also a base for further discussions on natural semantics variants for joint OWA+IC assertion specification within a single ontology schema. It allows also the “power users” of ontology editors to define ontology splitters fitting their specification purposes.
The creation of the OWLGrEd/S editor has been possible do to an
openarchitecture, model-based and highly customizable OWLGrEd implementation based
on TDA platform [