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Unit Tests for Ontologies

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In software engineering, the notion of unit testing was successfully introduced and applied. Unit tests are easy manageable tests for small parts of a program – single units. They proved especially useful to capture unwanted changes and side effects during the maintenance of a program, and they grow with the evolution of the program. Ontologies behave quite differently than program units. As there is no information hiding in ontology engineering, and thus no black box components, at first the idea of unit testing for ontologies seems not applicable. In this paper we motivate the need for unit testing, describe the adaptation to the unit testing approach, and give use cases and examples.
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Unit tests for ontologies
Denny Vrandeˇci´c1, Aldo Gangemi2
1denny@aifb.uni-karlsruhe.de
Institute AIFB, University of Karlsruhe, Germany
2aldo.gangemi@istc.cnr.it
LOA Laboratory of Applied Ontology, Rome, Italy
Abstract. In software engineering, the notion of unit testing was suc-
cessfully introduced and applied. Unit tests are easy manageable tests
for small parts of a program – single units. They proved especially useful
to capture unwanted changes and side effects during the maintenance of
a program, and they grow with the evolution of the program.
Ontologies behave quite differently than program units. As there is no
information hiding in ontology engineering, and thus no black box com-
ponents, at first the idea of unit testing for ontologies seems not appli-
cable. In this paper we motivate the need for unit testing, describe the
adaptation to the unit testing approach, and give use cases and examples.
1 Introduction
In software engineering, the idea of unit testing [1] was introduced to counter
the complexities of modern software engineering efforts. Unit tests are meant
to facilitate the development of program modules or units, and to ensure the
interplay of such units in the combined system. It results in more loosely coupled
code, that is easier to refactor and simpler to integrate, and that has a formalized
documentation (although not necessarily complete). Unit tests can be added
incrementally during the maintenance of a piece of software, in order to not
accidentally stumble upon and old bug and hunt it down repeatedly.
Unit tests are not complete test suites: there are several types of errors that
unit tests will not catch, including errors that result from the integration of the
units to the complete system, performance problems, and, naturally, errors that
were not expected when writing the unit tests.
Unit tests in software engineering became popularized with the object ori-
ented language Smalltalk, and still to this today remain focused on languages
with strong possibilities to create smaller units of code. They are based on several
decomposition techniques, most important of all information hiding.
Ontologies are different. As of now, no form of information hiding or interfaces
are available – and it remains an open research issue in the field of ontology
modularization how this will be taken care of.
In this paper we will take a look at the benefits of unit testing applied to
ontologies, i.e. their possibilities to facilitate regression tests, to provide a test
framework that can grow incrementally during the maintenance and evolution
phase of the ontology, and that is reasonably simple to use. In order for the unit
testing for ontologies to be useful, they need to be reasonably easy to use and
mantain. This will depend heavily on the given implementation (which is un-
derway). The task of this paper is to investigate different ideas that are inspired
by the idea of unit testing, and to work out the intuitions of how these ideas
could be used in the context of the ontology lifecycle. Especially in the enterprise
application of ontologies, some easy to use form of ontology evaluation will be
required in order to let ontology based technologies become more widespread.
We will show a number of ideas and examples of how this goal can be achieved.
The paper will first show a typical use case, as encountered in a project
setting in Section 2. We will then discuss five different approaches, that all are
inspired by the unit testing frameworks in software engineering: first we look
at the idea of design by contract, i.e. of stating what statements should and
should not derive from an ontology being developed or maintained, either as
explicit ontology statements or as competency questions using a query language
(Sections 3 and 4). Then we investigate the relationship of heavy- to lightweight
ontologies, and how they can interplay with regards to ontology evaluation in
Section 5. Autoepistemic operators lend themselves also to be used in the testing
of ontologies, especially with regards to their (relative) completeness, since they
are a great way to formalize the introspection of ontologies (Section 6). We
also regard a common error in ontology modelling with description logics based
language, and try to turn this error into our favour in Section 7, before we discuss
related work and give an outlook on possible further work and open issues.
For this work, the term ontologies refers to web ontologies as defined by
the OWL DL standard [15]. This means that the ontologies are a variant based
on the description logics SH OIN (D), and, especially, that ontologies mean to
encompass both the so called TBox, where the vocabulary of the ontology is
defined (which some call the whole ontology), and the ABox, where facts using
the vocabulary defined are stated (which some call the knowledge base).
2 Motivation
In the SEKT project1, one of the case studies aims at providing an intelligent
FAQ system to help newly appointed judges in Spain [2]. The system depends on
an ontology for finding the best answers and to find references to existing cases
in order to provide the judge with further background information. The applied
ontology is built and maintained by legal experts with almost no experience in
formal knowledge representation [4].
As the ontology evolved and got refined (and thus changed), the legal experts
noticed that some of their changes had undesired side effects. To give a simplified
example, consider the class hierarchy depicted in Figure 1. Let’s take for granted
that this ontology has been used for a while already, before someone notices that
not every academic needs necessarily be a member of an university. So Academic
1http://www.sekt-project.com
2
Lecturer
Professor
Academic
University member
Person
Secretary
Lecturer
Professor
Academic
University member
Person
Secretary
Fig. 1. Example class hierarchy
becomes a direct subclass of Person, instead of University member. But due to
this change, also Professor is no subclass of University member any more (a
change that maybe was hidden from the ontology engineer, as the ontology
development environment may not have displayed the subclasses of Academic).
The resulting ontology remains perfectly satisfiable. But a tool, that, for
example, creates a web page for all members of the university may now skip the
professors, since they are not classified as university members any more – an
error that would only become apparent in the use of the tool much later and will
be potentially hard to track down to that particular ontology change operation.
Unit testing for ontologies can discover such problems, and a few other ones
as well, as we will see in the following sections.
3 Affirming derived knowledge
We create two test ontologies T+(called the positive test ontology) and T
(the negative test ontology), and define that an ontology O, in order to fulfil the
constraints imposed by the test ontologies, needs to fulfil the following conditions:
each axiom A+
1...A+
nT+must be derivable from O, i.e.
O|=A+
iA+
iT+
and each axiom A
1...A
nTmust not be derivable from O, i.e.
O6|=A
iA
iT
Note that T+trivially fulfils the first condition if Ois not satisfiable, whereas
an empty ontology trivially fulfils the second condition. So it is not hard to
come up with ontologies that fulfil the conditions, which shows that unit tests
are not meant to be complete formalizations of the requirements of an ontology,
but rather helpful indicators towards possible errors or omissions in the tested
ontologies. Note also that Tcould be unsatisfiable, i.e. there are two sets of
axioms (both subsets of Tthat contradict each other. This still makes sense,
as it means that Omust not make a decision about the truth of either of these
3
sets (thus formalizing the requirement that Omust be agnostic towards certain
statements).
To come back to our previous example in Section 2 a simple test ontology
T+that consists of the single axiom Professor vUniversitymember would have
been sufficient to discover the problem described. So after the discovered error,
this statement is added to the test ontology, and now this same error will be
detected by running the unit tests.
The test ontologies are meant to be created and grown during the mainte-
nance of the ontology. Every time an error is encountered in the usage of the
ontology, the error is formalized and added to the appropriate ontology (like
in the example above). Experienced ontology engineers may add appropriate
axioms in order to anticipate and counter possible errors in maintenance.
In software engineering it is often the case, that the initial development of a
program is done by a higher skilled, better trained, and more consistent team,
whereas the maintenance is then performed by a less expensive group, with less
experienced members, that change more frequently. So in software engineering,
the more experienced developers often anticipate frequent errors that can happen
during maintenance, and create unit tests accordingly in order to put appropriate
constraints on the future evolution of the software. We expect a similar devel-
opment in ontology engineering and maintenance, as soon as ontologies become
more common components of information systems. The framework proposed in
this paper offers the same possibilities to an ontology engineer.
Why should an ontology engineer not just add the axioms from T+to O,
and ¬A
ifor each A
iin T? There are several reasons: 1) not every axiom
A
ican be negated. For example, the simple statement R(a, b) stating a relation
Rbetween the individuals aand bcan not be negated in OWL DL. 2) adding
such axioms increases redundancy in the ontology, and thus makes it harder
to edit. 3) the axioms may potentially increase reasoning complexity, or else
use language constructs that are not meant to be used within the ontology, for
whatever reason. 4) as stated above, the axioms in Tmay be contradictory.
5) Finally, due to the open world assumption, O6|=A
iA
iTis not the
same as O|=¬A
iA
iT, so that the negative test ontology can actually
not be simulated with the means of OWL DL.
4 Formalized competency questions
Competency questions, as defined by some methodologies for ontology engineer-
ing (like OTK [17] or Methontology [6]), describe what kind of knowledge the
resulting ontology is supposed to answer. These questions can always be formal-
ized in a query language (or else the ontology will actually not be able to answer
the given competency question, and thus will not meet the given requirements).
Formalizing the queries, instead of writing them down in natural language, and
formalizing the expected answers as well, allows for a system that automati-
cally checks if the ontology meets the requirements stated with the competency
questions.
4
We consider this approach especially useful not for the maintenance of the
system, but rather for its initial build, in order to define the extent of the on-
tology. Note that competency questions usually are just exemplary questions –
answering all competency questions does not mean that the ontology is complete.
Also note that sometimes, although the question is formalizable, the answer does
not necessarily need to be known at the time of writing the question. This is es-
pecially true for dynamic ontologies, i.e. ontologies that reflect properties of the
world that keep changing often (like the song the user of the system is listening
to at query time). In that case we can define some checks if the answer is sensible
or even possible (like that the answer indeed needs to be a song). Often these
further checks will not go beyond the abilities defined by the other approaches
to unit testing in this paper.
5 Expressive consistency checks
Ontologies in information systems often need to fulfil the requirement of allowing
reasoners to quickly answer queries with regards to the ontology. Light weight
ontologies usually fulfil this task best. Also, many of the more complex con-
structors of OWL DL often do not add further information, but rather are used
to restrict possible models. This is useful in many applications, like ontology
mapping and alignment, or information integration from different sources.
For example, a minimal cardinality constraint will, due to the open world
assumption, hardly ever lead to any inferred statements in an OWL DL ontology
(this can only become the case if range of the minimal cardinality restricted
relation is a class consisting of nominals). Nevertheless the statement can be
useful as an indicator for tools that want to offer a user interface to the ontology,
or for mapping algorithms that can take this information into account.
Further expressive constraints on the ontology, like disjointness of classes, can
be used to check the ontology for consistency at the beginning of the usage, but
after this has been checked, a light weight version of the ontology, that potentially
enables reasoners to derive answers with a better response time, could be used
instead.
Also, for these pre-use consistency checks, more expressive logical formalisms
could be used, like reasoning over the ontology metamodel [13, 3], using SWRL [11],
or using the transformation of the ontology to a logic programming language like
datalog [8] and then add further integrity constraints to that resulting program
(that may easily go far beyond the expressivity available in the original ontology
language: with a logic programming language it would be easy to state that,
by company policy, a supervisor is required to have a higher income than the
persons reporting to her – which is impossible in OWL DL).
Formally, we introduce a test ontology TCfor an ontology O, that includes
the high axiomatization of the terms used in O, and check for the satisfiability
of the merged ontology OTC. In the case of using the logic programming
translation, we merge (concatenate) the translation of the ontology to datalog
5
(LP(O)) with the test program TC
LP, and test the resulting program for violation
of the integrity constraints.
Let us consider an example ontology Ox:
tradesStocks(Jim,MegaCorp)
CEO(MegaCorp,Jack)
bestBuddy(Jim, J ack)
bestBuddy vhasNoSecrets
This example ontology is equivalent to the translated logic program LP(Ox):
tradesStocks(Jim,MegaCorp).
CEO(MegaCorp,Jack).
bestBuddy(Jim, J ack).
hasNoSecrets(X, Y ) : bestBuddy(X, Y ).
The test program TC
LP (that checks for insider trading) may consist of the
following line, a single integrity constraint:
:hasNoSecrets(X, Y ),tradesStocks(Y, C),CEO(X, C ).
Evaluating the program should now raise a violated integrity constraint. We
could also name the integrity constraints (by putting insiderT rading into its
head and then explicitly evaluate insiderTrading to see if it evaluates to true
or false. We also could use the head insiderTrading(Y) and then query for the
same head, to get a list of people who actually do the insider trading (and thus
uncover problems in the program much faster).
6 Use of autoepistemic operators
In [7] an extension of OWL DL with autoepistemic operators is described. Espe-
cially the K-operator can be useful to check an ontology not only with regards to
its consistent usage, but also with regards to some explicitly defined understand-
ing of completeness. In a geographic ontology, we may define that every country
has a capital, Country v ∃capital.City. But stating the existence of a country
without stating its capital will not lead to an error in the ontology, because the
reasoner (correctly) assumes, that the knowledge is not complete. Using the K-
and Aoperators instead, we would define that KCountry v ∃Acapital.ACity,
i.e. for every known country the capital must also be known (i.e. either stated
explicitly or inferrable) in the ontology, or else the ontology will be not satisfiable
(the example follows ex. 3.3 in [5]). Thus we are able to state what should be
known, and a satisfiability check will check if, indeed this knowledge is present.
On the Semantic Web, such a formalism will prove of great value, as it allows
to simply discard data that does not adhere to a certain understanding of com-
pleteness. For example, a crawler may gather event data on the Semantic Web.
But instead of simply collecting all instances of event, it may decide to only
accept events that have a start and an end date, a location, a contact email,
and a classification with regards to a certain term hierarchy. Although this will
decrease the recall of the crawler, the data will be of a higher quality, i.e. of a
bigger value, as it can be sorted, displayed, and actually used by calendars, map
tools, and email clients in order to support the user.
6
The formalisation and semantics of autoepistemic operators for the usage in
web ontologies is described in [7], and thus will not be repeated here.
7 Domain and ranges as constraints
Users often complain that their intuitive usage of relation domain and ranges
contradict their actual semantics. They expect domain and ranges to be used like
constraints, i.e. if they say that brideOf is a relation with the domain Woman
and one applies it to John, who is a Man, instead of getting an inconsistency
John will be classified as a Woman by the reasoner (for the sake of the example,
we take it for granted that Man and Woman are not disjoint). In the following
we will try to use this error to the benefit of the user.
As the domain and range declarations in the ontology will usually render
these checks trivially true, we need to remove them first from the ontology.
Therefore we take an ontology, and delete all domain and range declarations that
are to be understood as constraints (in the example in the previous paragraph,
we would remove the declaration of brideOf ’s domain as Woman). Now we check
for all instantiations of the removed domain or range declaration’s relation if the
subject (in case of a removed domain declaration) or the object (in case of a
removed range declaration) indeed gets classified with the supposed class (in the
example, we ask if John is indeed a Woman).
Note that these removals may have further implications on the ontology’s
inferred statements, depending on the further axioms of the ontology, and its
planned usage. Experiments need to be performed to be able to judge the de-
scribed approach with regards to its impact on the inferred knowledge in real
world scenarios. This approach actually will not necessarily highlight errors, but
only indicate possible places for errors. It will probably make more sense to in-
troduce a new relation that let us define constraints for relations, and then to
check these explicitly. We expect to learn from the planned experiments how to
exactly bring this approach to use.
8 Related work
A Prot´eg´e Plug-In implementing an OWL Unit Test framework2exists, that
allows to perform what we have described with T+testing for affirming derived
knowledge in Section 3.
In [16] the theory and practice of ontology evolution is discussed. Ontology
change operations and ontology evolution strategies are introduced. Based on
this, [9] extends this work for OWL DL ontologies, and investigates the evo-
lution of ontologies with regards to consistency, implemented in the so called
evOWLution framework. As the theoretical work allows generic and user defined
consistency checks, the ideas presented here could be regarded as a number of
2http://www.co-ode.org/downloads/owlunittest/
7
ways to formalize further aspects of the ontology, and enable more expressive
consistency checks beyond simple logical satisfiability.
Some parts of the presented ideas – especially the test ontologies in Section 3
and the consistency check against heavy weight descriptions in Section 5 – may
often lead to unsatisfiable ontologies when the unit testing uncover problems. In
this case, research done in debugging [14] and revising [12], especially evolving
ontologies [10], will provide the tools and techniques to actually resolve the
problems.
9 Outlook
The approaches described in this paper address problems in ontology engineering
and maintenance that have been discovered during the work with ontologies
within the SEKT case studies. As they often reminded us of problems that
occurred in software engineering, a solution that was successfully introduced to
software engineering was examined – unit testing. Although the notion of unit
testing needed to be changed, it inspired a slew of possible approaches, that
have been described in this paper. Also, examples for these approaches have
been given to illustrate how they can be used within the lifecycle of an ontology.
As of now, we are working on an implementation of the presented ideas in
order to experimentally verify their usefulness. Although we have shown that sev-
eral problems we have encountered can be solved with the presented approaches,
it is unclear if the idea behind them is simple enough to be understood by non-
experts in ontology engineering. Also it needs to be investigated, how often
certain classes of problems appear in real world ontologies, and which of the
ideas presented here are most effective to counter these problems.
Like in software engineering, we do not expect unit tests to cover the whole
field of ontology evaluation. But we expect it to become (and remain) an impor-
tant building block within an encompassing framework, that will cover regression
tests and (relative) completeness, and help to indicate further errors in the initial
development, and especially further maintenance of an ontology.
We expect modularization of ontologies and networked ontology to become
more important in the next generation of web ontology based technologies. Unit
testing provides a framework to formalize requirements about ontologies. We
expect the approaches described in this paper, and maybe further similar ap-
proaches, to become much more investigated and discussed in the close future.
Acknowledgements
Research reported in this paper was supported by the IST Programme of the Eu-
ropean Community under the SEKT project, Semantically Enabled Knowledge
Technologies (IST-1-506826-IP, http://www.sekt-project.com). We want to
thank our colleagues for fruitful discussions, especially Stephan Grimm, Boris
Motik, Peter Haase, Sudhir Agarwal, Jos Lehmann, and Malvina Nissim.
This publication reflects the authors’ view.
8
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... They called it "Competency question-driven approach for ontology testing". Note that previously, [24] introduced the dynamic (unit) testing approach for ontologies too. ...
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... As approach to ontology evaluation we took into account two aspects: (i) data-driven (Brank et al., 2005), to represent real situations, to validate BiGe-Onto, we instantiated concepts and relations using data from GBIF and OBIS, and (ii) ontology testing (Vrandečić and Gangemi, 2006), to answer the competence questions formulated by domain experts. Below, each of the proposed steps is described in detail. ...
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