36 ◾ Rajendra Akerkar
an ontology to answer its competence questions. Bridge rules specify associations
among elements of two or more ontologies, for example:
Bridge Rule :
:
:
< >
< >
Oi Fi
Ok Fj
e schema reads: If Fi is a true formula within ontology Oi, then Fj is true in the
ontology Ok. Bridge rules support reasoning across ontologies. Embedding produc-
tion rules have been addressed at the symbolic level too. In a hybrid approach, a
separation is maintained between the predicates used in the ontologies and those
in the rules. In a homogeneous approach, both ontologies and rules are represented
with the same language.
2.8 Ontology Languages
To use ontologies within an application, they must be specied. Obviously, an
ontology must be delivered via some concrete representation. A variety of languages
may be used to represent conceptual models with varying characteristics in terms of
expressiveness, ease of use, and computational complexity. e eld of knowledge
representation (KR) has, of course, long been a focal point of research in the arti-
cial intelligence community. Languages used for specifying ontologies are usu-
ally categorized as (1) vocabularies dened using natural language, (2) object-based
knowledge representation languages such as frames and UML, and (3) languages
based on predicates expressed in logic, e.g., description logics. e next subsections
present brief overviews of frame-based and logic-based languages.
2.8.1 Frame-Based Languages
Frame-based systems are based on frames or classes that represent collections of
instances. Each frame has an associated collection of slots or attributes that can
be lled by values or other frames. In particular, a frame may include a “kind-of”
slot allowing the assertion of a frame taxonomy. is hierarchy can then be used
for inheritance of slots, allowing a sparse representation. Along with frames repre-
senting concepts, a frame-based representation may also contain instance frames
that represent specic instances. Frame-based systems (Akerkar et al., 2009) have
been used extensively in the KR world, particularly for applications in natural lan-
guage processing. e best known frame system is Ontolingua. Frames are popular
because frame-based modeling is similar to object-based modeling and is intuitive
for many users.
Frame-based ontology (Gruber, 1993) dening concepts such as frames, slots,
and slot constraints is a representational methodology. A frame is a single place in
Ontology: Fundamentals and Languages ◾ 37
which facts about a class are gathered (Bechhofer et al., 2001) in a simple fashion.
During modeling, the frames and their properties can be visualized by a tool in
such a way that all relevant properties are available simultaneously. A frame ontol-
ogy does not contain any static knowledge about the real world. Instead it is a rep-
resentational mechanism for creating an ontology that describes knowledge about
the real world.
Ontolingua (Gruber, 1993) is a system specially developed for representing
ontologies so that they may be translated easily into other ontology languages. e
syntax and semantics of denitions in Ontolingua are based on knowledge infor-
mation formats (KIFs). A very inuential frame-based knowledge representation
standard is Open Knowledge Base Connectivity (OKBC; Chaudhri et al., 1998).
In OKBC, a frame consists of either a class along with its properties and axioms
(expressing logic constraints) or an instance along with its property values.
According to Bruijn (2003), the general problem with using a frame-based lan-
guage as an ontology language is the lack of the well-dened semantics that enable
computers to “understand” an ontology, or at least process it according to well-
dened rules. For example, it is often not clear in frame-based systems whether a slot
constraint is universally or existentially quantied (Bechhofer et al., 2001). SHOE
(Hein et al., 1999], based on a frame language (F-logic), was an early attempt
to develop an ontology denition language to embed semantics inside HTML.
Naturally, the ontology denitions in SHOE consist of class name, inheritance,
and slots. e simplied syntax for the class inheritance diagram can be seen as
follows:
[gen .base . SHOEEntity]
[…]
Address
Person
Employee
In the above syntax, one can see two classes: Employee and Person. e employee
class inherits from the person class and also from the address class. e following
syntax gives a property of the STRING literal type that denes the city property
of an address class:
addressCity(Address,.STRING)
[..]
homeAddress(Person, Address)
[..]
father(Person:”child”, Person:”father”)
friend(Person, Person)
[..]
SHOE supports the import of other ontologies and also allows us to dene infer-
ence rules.
38 ◾ Rajendra Akerkar
2.8.2 Logic-Based Languages
To represent, access, and reuse knowledge eectively and eciently, frame-based
ontologies are not sucient. An alternative to frame-based methodology is logic,
notably description logic (DL; Baader et al., 2003), also called terminological
logic. A DL describes knowledge in terms of concepts and relations that are used
to automatically derive classication taxonomies. Concepts are dened in terms of
descriptions using other roles and concepts. A model is built from small pieces in a
descriptive way rather than through assertion of hierarchies. (Baader et al., 1991).
DL forms a decidable subset of rst order logic. is decidability is very con-
venient for reasoning about ontology. However, serious limitations surround the
expressiveness of DL, e.g., the absence of variables (Bruijn, 2003). is limited
expressiveness, however, ensures decidability and improves tractability. DL pro-
vides many reasoning services that allow the construction of classication hierar-
chies and the checking of consistency of the descriptions. ese reasoning services
can then be used by applications that prefer to use the knowledge represented in
the ontology.
DLs vary in expressivity, which determines the computational complexity of
the reasoning algorithms for each language. In DLs, class can include disjunction
and negation along with constraints on the relations to other classes. A relation
between a class (its domain) and another class (its range) can be constrained in car-
dinality and type. Relations can also be given denitions and thus have subclasses
too. Class partitions can be dened by specifying a set of subclasses that represent
the partitions. ese partitions may be exhaustive if all instances of the class belong
to some partition or disjoint if the subclasses do not overlap. A class can be denoted
as primitive and not given a denition; in that case, the subclasses and instances
must be explicitly shown.
DL systems use these denitions to automatically organize class descriptions
in a taxonomic hierarchy and automatically classify instances into classes whose
denitions are satised by their features. Specically, description logic reasoners
provide two key capabilities:
◾ Class subsumption in which a C1 class subsumes another class (C2) if its deni-
tion includes a superset of the instances included in C2
◾ Instance recognition in which an instance belongs to a class if its features (roles
and role values) satisfy the denition of the class
Early DL systems include KL-ONE (Brachman and Schmolze, 1985) and CLASSIC
(Borgida et al., 1989). Knowledge in DL is represented in a hierarchical structure
of classes (or concepts) that are dened intentionally via descriptions that spec-
ify the properties that objects must satisfy to belong to a concept (Fensel, 2003).
Obviously, DL presents advantages in comparison to other knowledge representa-
tion languages (Baader et al., 1991). Declarative semantics clearly indicate that the
Ontology: Fundamentals and Languages ◾ 39
meaning of a construct is not given operationally, but provided by the description
and its models. Well investigated algorithms have veried a number of properties
of an ontology (correctness, completeness, decidability, complexity). Ontology lan-
guages for the Semantic Web based on description logics are now de facto W3C
standards.
One major dierence between frame-based and DL-based languages is that the
former relies completely on explicit statements of class subsumption and the latter
can eciently compute the subsumption relationship between classes on the basis
of the intentional denition of the classes. Moreover, frames usually oer a rich set
of language constructs but impose very restrictive constraints on how they can be
used to dene a class. DL involves a more limited set of language constructs, but
allows primitives to be combined to create dened concepts. e taxonomy for
these dened concepts is automatically established by the logic reasoning system
of the DL.
2.8.3 Ontology Representation Languages
In the 1990s, Knowledge Interchange Format (KIF) was seen as the standard for
ontology modeling and ontology was applied slowly to the World Wide Web. In
1999, the RDF language (http://www.w3.org/RDF/) was developed to annotate
Web pages with machine-processable meta-data. RDF can be used to express
knowledge.
Figure2.5 shows the layers of languages used for the Semantic Web (Berners-
Lee, 2005). e components on the bottom layers mention Unicode URI and XML
schema along with dened standards and provide a syntactical basis for Semantic
Web languages. Unicode provides an elementary character encoding scheme used
by XML. e URI (Uniform Resource Identier; Beckett, 2003) standard provides
Unicode URI
Self-
Description
documents
Data
Rules
XML + NS + XML Schema
RDF + RDFSchema
Ontology vocabulary
Logic
Proof
Digital
signature
Trust
Complexity and sophistication
Structured ness and volume
User
ird
party
Engineer
Figure 2.5 Layers of Semantic Web languages.
40 ◾ Rajendra Akerkar
a means to uniquely identify content and other resources on the Web. All concepts
used in higher languages are specied using Unicode and are uniquely identied by
URIs. Layers atop the Unicode and URI bottom layer facilitate XML and RDF for
content representation and utilization. e next layer denes and describes vocabu-
lary used in ontology. Logic, proof, and trust layers provide functionalities of back-
ground logic, facility of deductive reasoning, and trust mechanisms by applying
digital signatures and certications from third parties. According to Eiter et al.
(2006a), for the realization of the Semantic Web, the integration of dierent layers
of its conceived architecture is a fundamental issue. In particular, the integration
of rules and ontology is currently under investigation and many proposals have
been made.
2.8.3.1 XML Schema
An XML schema formally describes the structure of an XML document. e
schema may be considered a denition language that enables us to constrain con-
forming XML documents to a specic vocabulary and specic hierarchical struc-
ture. XML schemas are analogous to database schemas that dene column names
and data types in database tables. XML schema became a W3C recommendation
(synonymous with standard) on May 5, 2001. Each schema should accompany
document type denitions (DTDs) and presentation cascade style sheets (CSSs).
A DTD contains a grammar describing a language. Using a schema to specify an
XML vocabulary gets us much closer to a true type declaration. We may dene our
tour for a system in a tourism domain as follows:
<tour>
<tour_name> …. </tour_name>
<tour_description> …… </tour_description>
…..
…..
</tour>
e tags utilized here must be dened in DTD documents to provide grammar and
denitions of user-dened tags. e XML is not presentation oriented; it requires a
separate CSS along with a DTD. is leads to the benets of presenting the same
content in dierent fashion by simply providing multiple CSSs. A le containing
an XML schema usually has an xsd extension. We will now illustrate the basic
structure of such a le:
<?xml version = “1.0”?>
<xsd:schema xmlns:xsd=”http://www.w3.org/2001/XMLSchema”>
<!-- global declarations go here -->
</xsd:schema>
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