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The Web Ontology Language version 2 (OWL 2) [26] is a formally recommended ontology language for the Semantic Web and much like its predecessor, OWL 1, it allows logical domain modeling by defining and describing classes, individ- uals, their properties and relationships with each other or data values, with the addition that OWL 2 ontologies are exclusively stored as Semantic Web docu- ments. Specifically, the current version OWL 2 is able to provide a wider range of constructs for expressing concepts such as transitive and inverse properties, cardinality restrictions, as well as inheritance, among others. By targeting specific modeling needs of the web, it is thence divided into three sub profiles, viz. the ’OWL 2 Expressive Language’ (OWL2EL), ’OWL 2 Query Language’ (OWL2QL), and the ’OWL 2 Rules Language’ (OWL2RL) [27, 28]. These sub- languages offer different expressiveness and computational desirability.

The ’OWL 2 RL’, which lays the foundation for the Semantic Web Rule Lan- guage (SWRL) (see Fig. 2.4: OWL Evolution and Contextual Relationship with SWRL), is suitable for rule-based applications. It enables additional rules (such as horn clause rules written in the SWRL language) to be added to ontologies for more expressive descriptions of application domain. SWRL is an OWL-based rule language, which utilizes the abstract syntax of OWL extended with horn clauses (having antecedent and consequence) for rule assertions. The SWRL formalism is discussed in Section 2.8.2 and the Fig. 2.4 below, summarizes the contextual relationship between OWL profiles and SWRL.

Reasoning tasks over OWL 2 RL ontologies are achieved in Polynomial times and due to its ability to manipulate RDF triples directly, it is used for applications

Figure 2.4: OWL Evolution and Contextual Relationship with SWRL

that need to access data directly or where data manipulation is important. The profile allows extending ontology with rules and OWL 2 RL semantics can be im- plemented using traditional rule-based engines [29] — the forward or backward chaining rule engines, including CLIPS and Jess. As such, the profile is basically more expressive than OWL 2 EL and OWL 2 QL, and allows developing applica- tions with scalable reasoning while retaining the expressive power of OWL 2.

2.2.3.1 Reasoning in OWL Ontologies

One of the key benefits of using DL-based ontologies and of using ontology (in general) over other knowledge representation techniques as a whole is the ability to invoke a reasoner to process those ontologies [30]. Processing ontologies by a reasoner involves testing the hierarchy definition of classes in the ontology and then automatically compute the class hierarchy and also infer additional classifi- cation. Reasoning in OWL ontologies also helps to provide consistency checking, where a reasoner checks based on the given class definition whether or not a class can have any individual instances. This helps to avoid impractical classification of concepts in OWL ontologies.

Common DL-based reasoners available in open ontology development envi- ronments include the Pellet reasoner, HermiT, and Fact++, among others. During ontology development, a reasoner needs to be invoked to maintain consistency and reasoning can be performed continuously at development time and during ontology run time. For very large ontologies such as SNOMED-CT ontology containing over 400, 000 clinical concepts [31], reasoning is crucial at the design and development time to ensure correct and consistent classification. Also during query evaluations at run time, reasoning is needed to ensure correct inference of relationships between concepts and also to support rules execution.

2.2.3.2 The Language Expressiveness of OWL-DL

In DL-based languages, factual knowledge during individual assertions and ter- minology definitions are stored as formulas in First Order Logic (FOL). However, restrictions are usually attached to these formulas to ensure decidability and ef- ficient reasoning over the ontology they represent [32]. These restrictions also specify the degree of expressiveness of the DL as compared to FOL, which can express almost everything, though is undecided in terms of computational com- plexities such as space and time.

To achieve decidability, OWL ontologies are generally restricted to their cor- responding DL expressiveness algorithms and the OWL-DL has the expressive equivalence of a SHOIN (D) algorithm. The basic OWL-DL restrictions, repre- sented by these letter-symbol keys are described below:

• S — An abbreviation of an Attributive (Concept) Language with Comple- ment (ALC) extended with transitive roles. The Attributive Language (AL) is the basic DL language that allows the use of Concept intersection (∩), universal restrictions (∀), limited existential quantification (∃) and atomic negation of concepts (¬), which do not appear on the left-hand-side of ax- ioms.

The ALC or short form S, is obtained when AL is extended with the full concept negation, i.e. complement of any concept, not only atomic con- cepts, can be expressed in the ALC such as for example, the Top concept (> ≡ C ∪ ¬C) and Floor concept (⊥ ≡ C ∩ ¬C), where C is any concept.

In owl, the Top concept is called ’Thing’ (owl:Thing) and all classes are subclasses of ’Thing’, while the floor concept is considered as ’Nothing’.

• H — An abbreviation of ALC extended with the role hierarchy (owl:subPropertyOf relationship).

• O — An abbreviation of ALC extended with Nominals (enumerated classes e.g. owl:oneOf or object value restrictions such as owl:hasValue relation- ship).

• I — An abbreviation of ALC extended with Inverse roles or properties, which allow expressing relationships in opposite directions (e.g. owl:hasPart and owl:isPartOf ).

• N — An abbreviation of ALC extended with a Number or cardinality re- striction. Semantics: ≥ n R.C or ≤ n R.C, where C is domain concept, n is the cardinality.

• D — The data values expressiveness (D), which is sometimes attached to the algorithm as subscript (SHOIN(D)), denotes the abilities of DL and its

family of languages, to use data values, datatype, and datatype properties to further express domain facts.