Inconsistency, Incompleteness and Redundancy
Muhammad Fahad, Muhammad Abdul Qadir
Center for Distributed and Semantic Computing, M.A.J.U, Islamabad, Pakistan
Muhammad Wajahat Noshairwan
National Engineerning and Sceintific Comission, Islamabad, Pakistan
Keywords: Ontological Errors Taxonomy, Ontology Evaluation, Ontology Validation and Verification, Ontology
Design Anomalies, Ontology Merging, Ontology Mapping, Semantic Web.
Abstract: Mapping and merging of multiple ontologies to produce consistent, coherent and correct merged global
ontology is an essential process to enable heterogeneous multi-vendors semantic-based systems to
communicate with each other. To generate such a global ontology automatically, the individual ontologies
must be free of (all types of) errors. We have observed that the present error classification does not include
all the errors. This paper extends the existing error classification (Inconsistency, Incompleteness and
Redundancy) and provides a discussion about the consequences of these errors. We highlight the problems
that we faced while developing our DKP-OM, ontology merging system and explain how these errors
became obstacles in efficient ontology merging process. It integrates the ontological errors and design
anomalies for content evaluation of ontologies under one framework. This framework helps ontologists to
build semantically correct ontology free from errors that enables effective and automatic ontology mapping
and merging with lesser user intervention.
To furnish the semantics for emerging semantic
web, Ontologies should represent formal
specification about the domain concepts and the
relationships among them (Antoniou, 2004). They
have played a fundamental role for describing
semantics of data not only in the emerging semantic
web but also in traditional knowledge engineering,
and act as a backbone in knowledge base systems
and semantic web applications (Gomez-Perez,
2001). Like any other dependable component of a
system, Ontology has to go through a repetitive
process of refinement and evaluation during its
development lifecycle before its integration in the
semantic applications. Ontology content evaluation
is one of the critical phases of Ontology Engineering
because if ontology itself is contaminated with errors
then the applications dependent on it, may have to
face some critical and catastrophic problems and
ontology may not serve its purpose (Fahad 2007b).
Several approaches for evaluation of taxonomic
knowledge on ontologies are contributed in the
research literature. Ontologies can be evaluated by
considering design principles (Gomez-Perez, 1994,
1999), requirements and logical correctness of
axioms, relations, instances, etc. Other approaches
would be to evaluate ontologies in terms of their use
in an application (Porzel, 2004) and predictions from
their results, comparison with a golden standard or
source of data (Maedche, 2002). Considering design
principles Gomez formed error taxonomy for
assistance in the ontology evaluation. Ontology
engineers use that error taxonomy to build well-
formed classification of concepts that enable better
reasoning support for fulfilment of sound semantic
web vision and to evaluate their ontologies in
perspective of these errors. Besides taxonomic
errors, there are some design anomalies which raise
the issues of maintainability of ontologies
(Baumeister and Seipel 2005).
This paper presents the ontological errors based
on design principles for evaluation of ontologies. It
provides the overview of ontological errors and
design anomalies that reduces reasoning power and
creates ambiguity while inferring from concepts. It
Fahad M., Abdul Qadir M. and Wajahat Noshairwan M. (2008).
ONTOLOGICAL ERRORS - Inconsistency, Incompleteness and Redundancy.
In Proceedings of the Tenth International Conference on Enterprise Information Systems - ISAS, pages 253-258
DOI: 10.5220/0001696502530258
shows our contribution in taxonomic errors that we
experience while development of ontology merging
system, DKP-OM (Fahad, 2007a). Finally it
integrates the design anomalies and taxonomic
errors under one framework that helps practitioners,
developers and ontologists to build well formed
ontologies free from errors that serve their purposes,
and develop tools for ontology evaluation for
fulfilment of sound semantic web vision.
Rest of the paper is organized as follows: section
2 presents classification of ontological errors and
design anomalies; section 3 contributes our
identified ontological errors and extends the classes
of errors formed by Gomez. Section 4 presents the
related work of our domain. Section 5 concludes the
paper and gives insight on future work.
Gomez-Perez (1994; 1999; 2001) identified three
main classes of taxonomic errors that might occur
when modelling the conceptualization into
taxonomies. These are:
2.1 Inconsistency Errors
There are mainly three types of errors that cause
inconsistency and ambiguity in the ontology. These
are Circulatory errors, Partition errors and Semantic
inconsistency errors.
Circulatory Errors. They occur when a class is
defined as a subclass or superclass of itself at any
level of hierarchy in the ontology. They can occur
with distance 0, 1 or n, depending upon the number
of relations involved when traversing the concept
down the hierarchy of concepts until we get the
same from where we started traversal. For example,
circulatory error of distance 0 occurs when
ontologist models OddNumber concept as subclass
of NaturalNumber and NaturalNumber as subclass
of OddNumber. As OWL ontologies provide
constructs to form property hierarchies, so we have
observed that circulatory errors in property
hierarchies can occur.
Partition Errors. There are mainly several ways of
classification depending upon the type of
decomposition of superclass into subclasses. When
all the features of subclasses are independently
described and subclasses do not overlap with each
other then it leads to disjoint decomposition. When
ontologists follow the completeness constraint
between the subclasses and the superclass, then it
leads to a complete or exhaustive decomposition.
The other can depend on both the disjoint and
exhaustive decomposition. Three types of errors are:
Common Instances and Classes in Disjoint
Decomposition and Partitions. These errors occur
when ontologists create the instances that belong to
various disjoint subclasses or a common class as a
subclass of disjoints classes. An example of former
error is when ontologist decomposes the Course
concept into disjoint subclasses GradCourse and
UndergradCourse, and furthermore he classifies
CS6304 course as an instance of both disjoint
classes. An example of later error is when ontologist
decomposes the NaturalNumber concepts into
disjoint subclasses Odd and Even, furthermore he
classifies Prime number class as a subclass of both
Odd and Even subclasses.
External Instances in Exhaustive Decomposition
and Partitions. These errors occur when ontologists
made an exhaustive decomposition or partition of a
class into many subclasses but not all the instances
of the base class belong to the subclasses, i.e., one or
more instances of base class do not belong to any of
the subclasses. For example ontologist decomposes
Accommodation into Hotel, House and Shelter
subclasses. This error occurs if he defines an
instance TrainStation as an instance of the class
Semantic Inconsistency Errors. These errors occur
when ontologists make an incorrect class hierarchy
by classifying a concept as a subclass of a concept to
which it does not really belong. For example he
classifies the concept Airbus as a subclass of the
concept Train. Or the same might did when
classifying instances. We find three main reasons
that result incorrect semantic classification and
classify the semantic inconsistency errors into three
subclasses, explained in extension in taxonomic
errors section.
2.2 Incompleteness Errors
Sometimes ontologists made the classification of
concepts but overlook some of the important
information about them. Such incompleteness often
creates ambiguity and lacks reasoning mechanisms.
The following subsections give the overview of
incompleteness errors.
Incomplete Concept Classification. This error
occurs when ontologists overlook some of the
concepts present in the domain while classification
of particular concept. For example ontologists
classify concept Location into CulturalLocation,
ICEIS 2008 - International Conference on Enterprise Information Systems
MountainLocation, and overlook other location
types such as BeachLocation, HistoricLocation, etc.
Partition Errors. Gomez identified that sometimes
ontologist omits important axioms or information
about the classification of concept, reducing
reasoning power and inferring mechanisms. He has
identified two types of errors that cause incomplete
partition errors to occur, that are:
Disjoint Knowledge Omission. This error occurs
when ontologists classify the concept into many
subclasses and partitions, but omits disjoint
knowledge axiom between them. For example
ontologist models the BeachLocation,
HistoricLocation and MountainLocation as
subclasses of Location concept, but omits to model
the disjoint knowledge axiom between subclasses.
We developed the ontology of Access_Policy, where
disjoint knowledge omission between User and
Administrator causes catastrophic results (Qadir,
2007a), and provided the algorithm for identification
of disjoint knowledge omission (Noshairwan,
Due to significant importance of disjoint axiom
between classes, OWL 1.1 allows to specify disjoint
axioms between properties as well. So we also
emphasis that ontologists should check and specify
disjoint knowledge between properties, and avoid
creating common instances between them.
Exhaustive Knowledge Omission. This error
occurs when ontologists do not follow the
completeness constraint while decomposition of
concept into subclasses and partitions. For example
ontologist models the BeachLocation,
HistoricLocation and MountainLocation as disjoint
subclasses of Location concept, but does not specify
that whether or not this classification forms an
exhaustive decomposition.
2.3 Redundancy Errors
Redundancy occurs when particular information is
inferred more than once from the relations, classes
and instances found in ontology. The following are
the types of redundancies that might be made when
developing taxonomies.
Redundancies of SubclassOf, Subproperty - Of
and InstanceOf Relations. Redundancies of
SubclassOf error occur when ontologists specify
classes that have more than one SubclassOf relation
directly or indirectly. Directly means that a
SubclassOf relation exist between the same source
and target classes. Indirectly means that a
SubclassOf relations exist between a class and its
indirect superclass of any level. For example
ontologists specify BeachLocation as a subclass of
Location and Place, and furthermore Location is
defined as a SubclassOf Place. Here indirect
SubclassOf relation exists between BeachLocation
and Place creating redundancy. Likewise
Redundancy of SubpropertyOf can exist while
building property hierarchies. Redundancies of
InstanceOf relation occur when ontologists specify
instance Swat as an InstanceOf Location and Place
classes, and it is already defined that Location is a
subclass of Place. The explicit InstancesOf relation
between Swat and Place creates redundancy as Swat
is indirect instance of Place as Place is a superclass
of Location.
Identical Formal Definition of Classes, Properties
and Instances. Identical formal definition of
classes, properties or instances may occur when
ontologist defines different (or same) names of two
classes, properties or instances respectively, but
provides the same formal definition.
2.4 Design Anomalies in Ontologies
Besides taxonomic errors, Baumeister and Seipel
(2005) identified some design anomalies that
prohibit simplicity and maintainability of taxonomic
structures with in ontology. These do not cause
inaccurate reasoning about concepts, but point to
problematic and badly designed areas in ontology.
Identification and removal of these anomalies should
be necessary for improving the usability, and
providing better maintainability of ontology.
Property Clumps. Datatype properties and Object
properties that are associated with classes provide us
powerful mechanisms for reasoning and inferring
about concepts. Sometimes ontologists badly design
ontology using repeatedly a group of properties in
different class definitions. This repeated group of
properties is called property clump and should be
replaced by an abstract concept composing those
properties in all the class definitions where this
clump is used.
Chain of Inheritance. Ontology defines taxonomy
of concepts and allows classifying concepts as
subClassOf other concepts up to any level. When
such hierarchy of inheritance is long enough and all
classes have no appropriate descriptions in the
hierarchy accept inherited child then that ontology
suffers from chain of inheritance. For
maintainability and simplicity, this chain of
inheritance should be break-up into subhierarchies.
Lazy Concepts. Lazy concept is a leaf concept (or a
property) in the taxonomy that never appears in the
ONTOLOGICAL ERRORS - Inconsistency, Incompleteness and Redundancy
application and does not have any instances. Such
concepts should be replaced with specialized or
generalized concepts that occupy such instances and
would be used in the application domain.
Lonely Disjoints. Sometimes ontologists need to
modify the taxonomy of concepts and move
concepts within the class hierarchy. Consider a
scenario, where many disjoint siblings were created
and later on a single sibling is moved to another
place somewhere in the hierarchy, and ontologist
forgets to delete the disjoint axiom between them.
Such disjoint axioms should be removed from lonely
disjoint concepts to enable better maintainability and
reasoning support.
We have identified several ontological errors
(Fahad, 2007b; Qadir, 2007b; Noshairwan, 2007a)
while evaluating taxonomic knowledge on
ontologies and knowledge based systems, and
extended the main three classes of Taxonomy
evaluation, i.e., Inconsistency, Incompleteness and
Redundancy. Some of these are experienced while
developing DKP-OM: Disjoint Knowledge Preserver
based Ontology Merger (Fahad, 2007a), a solution
we provide for effective ontology merging. The
subsections present our identified ontological errors.
3.1 Semantic Inconsistency Errors
There are mainly three reasons due to which
incorrect semantic classification originates (Fahad,
2007b). According to these reasons, we categorize
Semantic inconsistency errors into three subclasses.
These subclasses can be used as a check list for class
hierarchy evaluation and help in building well-
formed class hierarchy to provide better
interpretation of concepts.
Weaker Domain specified by Subclass Error.
According to Fahad et al. (2007b), when classes that
represent the larger domain are kept subclasses of
concept that possess smaller domain then such an
error might occur. For example ontologist classifies
UniversityMember, AcademicStaff, AdminStaff and
LabStaff concepts as a subclass of a concept Staff
superclass. Here the semantic inconsistency occurs
as he classified more generalized concept
UniversityMember as subclass of the concept Staff.
A subclass should always specializes (subsumed by)
the superclass concept’s properties by specifying
stronger domain and make the super concept’s
domain narrower.
Domain Breach specified by Subclass Error.
According to Fahad et al. (2007b), subclasses should
possess all the features of the parent concept and
should not violate any feature of their parent concept
in their own domain. Superclass domain breach
occurs when concepts treated as subclasses add more
features that are not present in superclass but the
additional features are violating some features of
their superclasses. For example consider a Pizza
class hierarchy where ontologist classifies concept
Vegetarian_Pizza as a subclass concept of Pizza.
Furthermore he classifies Chinese_Pizza and
Italian_Pizza concepts as the subclasses of the
concept Vegetarian_Pizza. Semantic Inconsistency
arises as the definition of Chinese_Pizza allows
having any toppings made from boiled vegetables
and any kind of meat.
Disjoint Domain specified by Subclass Error.
According to Fahad et al. (2007b), when ontologists
specify disjoint domain concepts as subclasses of a
concept that occupies a different domain. For
example he classifies concepts Drink and Burger as
subclasses of Eatable_thing concept. None of the
features of Drink match with superclass concept
Eatable_thing i.e. they belong to disjoint domains.
These semantic inconsistency errors can be
applied same to the instances of superclass and
subclasses to whether their conformance with each
3.2 Extension in Incompleteness Errors
For powerful reasoning and enhanced inference,
OWL ontology provides some tags that can be
associated with properties of classes (ODM, 2005).
OWL functional and inverse-functional tags
associated with properties indicate how many times
a domain concept can be associated with range
concept via a property. Sometimes ontologists do
not give significance to these property tags and do
not declare datatype or object properties as
functional or inverse-functional. As a result machine
can not reason about a property effectively leading
to serious complications (Qadir, 2007b).
Functional Property Omission (FPO) for Single
valued Property. According to Ontology Definition
Metamodel (ODM, 2005), when there is only one
value for a given subject then that property needs to
be declared as functional. The tag Functional can be
associated with both the object properties and
datatype properties. For example hasBlood_Group
as an object property between Person and
ICEIS 2008 - International Conference on Enterprise Information Systems
Blood_Group is an example of functional object
property. Every subject Person belongs to only one
type of BloodGroup, so hasBlood_Group property
should be tagged as functional so that person should
be associated with one blood group. Likewise
functional datatype properties allow only one range
R for each domain instance D. Ignoring Functional
tag allows property to have more than one values
leading to inconsistency. One of the main reason for
such inconsistency is that ontologist has ignored that
OWL ontology by default supports multi-values for
datatype property and object property.
Inverse-Functional Property Omission (IFPO)
for a Unique valued Property. According to
Ontology Definition Metamodel (ODM, 2005),
inverse-functional property of the object is one that
determines the subject uniquely, i.e. it acts like a
unique key in databases. This means that if we state
P as an owl InverseFunctionalProperty, then this
restricts that for a single instance there can only be a
value x, i.e. there cannot exist two different
instances y and z such that both pairs (y, x) and (z,
x) are valid instances of P. In OWL Full, datatype
property can be tagged as inverse-functional
property because datatype property is a subclass of
object property. But in OWL DL datatype property
can not be tagged as inverse-functional property
because object properties and datatype properties are
disjoint. An example of inverse object property is
National_SecurityNo that belong to the Person as it
uniquely identifies the Person. Ignoring inverse-
functional tag with the property
National_SecurityNo creates inconsistency within
the ontology due to incomplete specification of
concept. We consider such lack of information as an
error, because such ignorance leads machine not to
infer and reason about concepts uniquely.
Sufficient Knowledge Omission Error (SKO).
Ontology comprises concepts and properties that can
be arranged in hierarchies. These concepts in
hierarchies should posses some features so that
inference engine can distinguish them appropriately.
According to principles of Description Logic, there
should be Necessary description and Sufficient
description associated with each concept (Nardi,
2000). Necessary description only defines the basic
criteria by which new concept is formed like its
hierarchal information, and Sufficient description
elaborates the characteristics of concept like its self
description by using intersection, union, complement
or restriction axioms in OWL (Noshairwan, 2007a).
Sometimes during ontology designing, ontologists
define the concepts but don’t provide their Sufficient
descriptions. As a result, machine can’t reason about
them properly and cannot use them effectively to
achieve the goals of semantic web.
Finding incompleteness in ontologies
automatically is a difficult task. One of the possible
ways to detect such incompleteness errors is to
evaluate ontology on test data (Brewster, 2004)
(valid and invalid both) that can be generated
according to tester’s domain knowledge (Supekar,
2005), experience with similar concepts and
information about soft spots of ontology.
3.3 Extension in Redundancy Errors
While detecting disjoint knowledge omission in
ontology and generating warnings on its omission
(Noshariwan, 2007a), we detect redundancy of
disjoint relation in ontologies. The following
subsection provides detail on it.
Redundancy of Disjoint Relation (RDR) Error.
Redundancy of Disjoint Relation occurs when the
concept is explicitly defined as disjoint with other
concepts more than once (Noshairwan, 2007a). By
Description Logic rules (Nardi, 2000), if a concept is
disjoint with any concept then it is also disjoint with
its sub concepts. The one possible way of occurrence
of RDR is that the concept is disjoint with parent
concept and also with its child concept for example,
concept Male is disjoint with Female and also with
sub concepts of Female. This type of redundancy
can occur due to direct disjointness (directly
disjoint) and indirect disjointness (concept is disjoint
with other because its parent is disjoint with it).
There are many other approaches for ontology
evaluation in research literature but still there is a
big gap which needs to be filled for sound semantic
web ontologies. The standard ontology evaluation
approach by Maedche and Staab (2002) is to
compare ontology with gold standard ontology for
evaluating lexical and vocabulary level of ontology.
Besides comparison with gold standard, Brewster et
al. (2004) gave the corpus or data driven ontology
evaluation approach. Comparison of ontology with
the corpus or data of the domain knowledge
provides a measure of the fit between them; and
highlights the terms that are present/absent in
ontology and corpus. Context level evaluation
approach takes into account the larger collection of
ontologies as a reference for evaluation of particular
ontology (Supekar, 2005). The library of ontologies
or the context for evaluation provided by the
ONTOLOGICAL ERRORS - Inconsistency, Incompleteness and Redundancy
knowledge engineer acts as reference to follow.
Other approaches of ontology evaluation would be
to observe the results of application or task where
this ontology is being used. Prozel and Malanka
(2004) proposed the task-based approach for
ontology evaluation but could not be so much
effective, as ontology acts only a backbone and
several other issues of task itself can generate bad
results. Burton-Jones (2004) defined a semiotic
metrics based on different criteria for ontology
assessment for syntactic and lexical/vocabulary
evaluation. Likewise Fox el al. (1998) made a set of
parameters but these are more useful for manual
assessment of quality of ontology. These ontology
evaluation approaches are useful in different
applications, scenarios and environments (2005) and
the choice of a suitable methodology should be
adopted according to the purpose of evaluation and
where that ontology is used.
Ontology driven architecture has revolutionized the
inference system by allowing interoperability
between heterogeneous multi-vendors systems. We
have identified that accurate ontologies free from
errors enable more interoperability, improve the
accuracy of ontology mapping and merging and
lessen human intervention during this process. We
have discussed existing ontological errors, and
identified newer types of errors present in
ontologies. We have concluded that without
identification and removal of these errors the most
desirable goal of ontology mapping and merging
could not be achieved. We have integrated the
overall work about ontology evaluation based on
design principles and anomalies under one
framework. This framework acts as control
mechanism that helps ontologist to build accurate
ontologies that serve best for the desired
applications, provide better reasoning support, lessen
user intervention in efficient ontology merging and
combined use of independently developed online
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