Figure 4.15: An example of the similar domain ontology
• Domain concepts are structured as taxonomies in the form of subsumption rela-tionships. By EnOntoModel, conceptual levels among domain concepts are further divided in terms of sort categoriess such as type, Quasi-type, role, and phase. Be-cause these sort categories are disjoint to each other, they aid in in determining the scopes of correspondences in ontology matching. Said another way, EnOntoModel intends to accelerate the matching process.
• By the conceptual constraints, enriched ontologies can be verified for conceptual consistency.
• Each sort possesses a specific property by the conceptual constraints, by which, correspondence between two similar sorts can be detected efficiently by using a restricted property instead of all available properties.
Figure 4.16: A structure of sortal meta-classes
2. In addition, Prot´eg´e provides Prot´eg´e Axiom Language (PAL) to define internal constraints, and to embed these constraints in OWL format.
4.4.1 Purpose and Scope
There are two purposes in implementing a sortal meta-class ontology.
• The first purpose is to support for the usability of EnOntoModel.
• The second purpose is to provide conceptual analysis of the enriched ontologies.
The basic motivation of my enrichment is to clarify and enrich the semantics of concepts for the issue of semantic heterogeneity. The role of ontologies is to provide a well-defined structure of domain knowledge that acts as the heart of any system of knowledge represen-tation on that domain for the purposes of reasoning, knowledge sharing, and integration.
Thus, it is also essential to verify taxonomies that provide a substantial structural in-formation of ontologies. Properly structured taxonomies help bring substantial order to elements of a model and play a critical role in reuse and integration tasks. Improperly structured taxonomies have the opposite effect, making models confusing and difficult to reuse and integrate. I define conceptual analysis as follows:
Conceptual analysis is a framework for cleaning the taxonomic structure of ontologies by validating subsumption relationships.
It is also known asontological analysis[147]. By the second purpose, I embed a system of conceptual analysis in the meta-class ontology, using Prot´eg´e Axiom Language (PAL) that is an internal language of prot´eg´e to author constraints which axiomatize subsumption relationships between super-classes and sub-classes logically.
The scope of this meta-class ontology is bounded to sorts, and the ontology employs some conceptual constraints in order to maintain subsumption consistency.
4.4.2 Design and Implementation
There are two major components in the meta-class ontology: (a) specification of sortal meta-classes, and (b) axiomatization for conceptual analysis.
Table 4.7: Meta-classes and their properties Meta-class Properties
TypeSort sort-categoryhas “type”
nameofOwnIC
Quasi-typeSort sort-categoryhas “quasi-type”
nameOfCVA
RoleSort sort-categoryhas “role”
nameOfEDR
PhaseSort sort-categoryhas “phase”
nameOfCC
Specification of Sortal Meta-classes
Meta-class ontology consists of five meta-classes labeledSort,TypeSort,Quasi-type Sort,RoleSort, andPhaseSort, as shown in Figure 4.16. Sortmeta-class is defined as the root of other four meta-classes. It has a datatype property namedsort-category to define the category of a certain sort. Then, four meta-classes are defined as the sub-classes of Sortmeta-class and they will be mainly used to represent ontological concepts as sorts. By property inheritance, sort-category is inherited to all sub-classes.
I describe the specification of four classes in Table 4.7. For each of four meta-classes, there is an additional property such asnameOfOwnIC,nameOfCVA,nameOfEDR, and nameOfCC. This means, for any instance class of TypeSort meta-class, an ownIC must be necessarily defined. Thus, the name of ownIC is recorded as a property in TypeSort meta-class in order to utilize in the matching process. It is also similar for other meta-classes.
Figure 4.17 shows a screenshot of the specification ofRoleSortmeta-class in Prot´eg´e.
This specification states thatRoleSortis a sub-class ofSort, each instance ofRoleSort meta-class has at least one EDR, and the value ofsort-categoryis restricted by “role”
for every role sort.
Axiomatization for Conceptual Analysis
I define five PAL constraints in the meta-class ontology for the purpose of conceptual analysis. These constraints are written based on (a) ontological assumption “anti-rigid sort never subsumes rigid sorts”, and (b) the disjointness between rigid sorts and between anti-rigid sorts. The names and meanings of these PAL constraints are:
1. notRoleToType: a role sort never subsume a type sort;
2. notQuasi-typeToType: a quasi-type sort never subsume a type sort;
3. notPhaseToType: a phase sort never subsume a type sort;
4. notRoleToQuasi-type: a role sort never subsume a quasi-type sort; and 5. notPhaseToQuasi-type: a phase sort never subsume a quasi-type sort.
Figure 4.17: A specification of RoleSort meta-class in Prot´eg´e
Table 4.8: The meanings of some PAL keywords
PAL keywords Meaning
super super-class
sub sub-class
?sub sub-class variable
subclass-of ?sub ?super ?sub is the sub-class of ?super
forall ∀
exists ∃
not ¬
and ∧
or ∨
own-slot-not-null if the given property (or slot) is not null
! " # $%
! %
& ! ! ! ! " %%
! " $ $%%%%%
&
# ' (
Figure 4.18: The screenshot of “PAL constraint” editor
In order to understand well the meaning of a PAL constraint, I first express the meanings of some PAL keywords in Table 4.8. To write a PAL constraint, we need to make sure PAL constraints tab is successfully installed and visible in the user interface of Prot´eg´e editor. A screenshot of PAL constraint edior is shown in Figure 4.18.
The editor provides not only for writing the logical statements of a constraint, but also for syntax checking of the statements.
The meaning of the PAL constraint written in Figure 4.18 is “every sub-class which has sort category “type” can not be subsumed by a super-class that has sort category
“role”. Briefly, that states “a role sort never subsume a type sort”. The statements of all five constraints are described in Figure 4.19. I built meta-class ontologysort.owl, and uploaded it in Prot´eg´e ontology library29as an open source. Thus, users can download the meta-class ontology via Prot´eg´e ontology library. The complete source code is attached in Appendix.