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Softw Syst Model (2009) 8:235249DOI
10.1007/s10270-008-0082-3
REGULAR PAPER
A UML and OWL description of Bunges upper-level ontology
model
Joerg Evermann
Received: 25 February 2006 / Revised: 28 September 2007 /
Accepted: 23 January 2008 / Published online: 5 March 2008
Springer-Verlag 2008
Abstract A prominent high-level ontology is that proposedby
Mario Bunge. While it has been extensively used forresearch in IS
analysis and conceptual modelling, it has notbeen employed in the
more formal settings of semantic webresearch. We claim that its
specification in natural languageis the key inhibitor to its wider
use. Consequently, this paperoffers a description of this ontology
in open, standardizedknowledge representation formats. The ontology
is descri-bed both in UML and OWL in order to address needs of
bothsemantic web and conceptual modelling communities.
1 Introduction
Ontologies play an increasingly important role in informa-tion
systems (IS) research and practice. Two different unders-tandings
of the term ontology have evolved. Research inthe areas of
ontology-driven information systems (ODIS) [1]and the semantic web
[2,3] uses the term ontology withoutnecessarily implying a firm
commitment to the existence of aparticular set of entities in
reality [46]. In this research area,ontologies are descriptions of
shared conceptualizations ofapplication domains [7], they are
constructed as needed [8],and engineered to fit a particular
problem [4,911]. There,domain specific ontologies can be integrated
by referringto concepts in upper-level ontologies. The upper-level
onto-logies in this research area, such as SUMO [12] and Cyc[1315],
are specified in formal knowledge representationlanguages, such as
KIF, DAML, or OWL. The current stan-dard ontology language OWL [16]
is based on the formalism
Communicated by Prof. Heinrich Hussmann.
J. Evermann (B)Memorial University of Newfoundland, St. Johns,
Canadae-mail: [email protected]
of description logics [1719], which allows reasoning
andinference. Specifically, the OWL-DL subset is restricted tothe
SHOIQ description logic to guarantee efficient reaso-ning [20].
In contrast, in conceptual modelling research [2154] , theterm
ontology is used in its original philosophical sense,understood as
meta-physics or the philosophy of existence[55]; an ontology is a
fundamental, domain-independentphilosophical position, a commitment
to the existence of cer-tain entities in external reality.Research
in this area has drawnprimarily on the ontological work by Mario
Bunge [56,57].In contrast to upper-level ontologies for the
semantic weband ODIS, and other philosophically-based ontologies
suchas GFO/GOL [3942] and Dolce [43], this ontology has notbeen
specified in a formal ontology description language, butis defined
in natural language with some formal descriptionin set theoretic
terms.
1.1 Problem statement
Both areas, semantic web applications and conceptualmodelling
research, can benefit from the availability of awell-developed and
well-known high-level ontology, suchas that of Bunge. However, the
current representation formhinders the application andwide-spread
use of Bunges onto-logy in both the semantic web and the conceptual
modellingresearch areas. To overcome this limitation, this paper
pre-sents a new representation of Bunges ontology in a
standar-dized and open format that can benefit both communities.The
objective of the paper is to develop a UML model andan OWL model of
this ontology.
It is not the aim of the paper to argue for or against
theadoption of a particular ontology. The focus of this paperon
Bunges ontology does not dispute the validity of otherontologies or
imply the superiority of Bunges ontology.
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236 J. Evermann
Instead, the argument is one about the usefulness of
thisresearch to the community of researchers and practitionersusing
this ontology:
Bunges ontology has been widely used in the IS
researchliterature to compare and evaluate conceptual
modellinglanguages, clarify the notion of data quality, and
informobject-oriented modelling principles [2138,4454,5864] . This
research has been using informal argumentationeven though the
potential for more rigorous and formaldiscussion has been
recognized [48,65].
Other upper-level ontologies in IS, such as SUMO [12],Cyc
[1315], GFO/GOL [3942] and Dolce [43] arealready expressed using
modern ontology or knowledgedescription languages such as DAML, KIF
or OWL.Bunges ontology is not. Given the research interest inthis
ontology, especially in conceptual modelling, a UMLand OWL
description is useful.
Note that while UML is not a formal language in the sensethat
fix-point, model-theoretic or operational semantics aredefined for
it, it is less ambiguous than a natural languagerepresentation.
1.2 Expected benefits
In conceptual modelling, UML is the de-facto standarddescription
language. Providing a description of Bungesontology in UML makes it
available to be used with esta-blished modelling, model conversion,
model exchange, andmodel repository tools.1 The availability of
these tools foruse with Bunges ontology can in turn promote the use
andadoption of this ontology. Furthermore, availability of
aUMLdescription of Bunges ontology allows research on concep-tual
modelling languages to employ meta-model based com-parisons to
other ontologies or models [48,65] and supportsthe derivation of
modelling guidelines and rules [31].
The Web Ontology Language (OWL) [16] is an acceptedstandard to
express semanticweb ontologies, either in its abs-tract syntax
form, or in anXML-based exchange syntax form.A large number of
domain ontologies have been developed inOWL and DAML, a precursor
to OWL.2 The availability ofupper-level ontologies in a semantic
web language can helpwith the integration of disparate domain
ontologies in thesemantic web context. For example, two large-scale
domainontologies, TOVE [11] and the AIAI Enterprise Ontology[66],
describe the same domain, albeit based on differentfoundations.
Formally relating concepts of both to concepts
1 e.g. IBM Rational Rose, Visual-Paradigm, Poseidon-UML,
Magic-Draw.2
http://www.daml.org/ontologies/,http://knowledgeweb.semanticweb.org/o2i/ontology_repository.php.
in Bunges ontology enables interoperability. For
example,primitive action in TOVE may be equivalent to an eventin
Bunges ontology, and activity in the AIAI EnterpriseOntology may
also be equivalent to an event in Bungesontology. An ontology
reasoner could exploit these equi-valences and derive
inter-ontology inferences based on thecombined knowledge base of
TOVE and the AIAI EnterpriseOntology.
Moreover, an OWL description makes Bunges ontologyavailable to
be used with established ontology tools and tech-nologies, e.g. for
ontology alignment, reasoning, editing andontology repositories
[2,67,68]. In turn, the availability ofthese tools can promote the
use and adoption of Bungesontology, as tool availability is an
important quality aspect[69,70].
Finally, the availability of Bunges ontology in an onto-logy
description language as well as a conceptual modellinglanguage
brings us closer towards the goal of ontology drivenIS development
[1]:Domain ontologies could be transformedto domain conceptual
models, which can then, as part of anMDA (model driven
architecture) process, be transformed tocode. Existing ontologies
may be harnessed as conceptualmodels. In turn, existing conceptual
models may be levera-ged for the development of domain
ontologies.
The remainder of this paper proceeds as follows. Section 2offers
a discussion of related work. Our solution approach ispresented in
Sect. 3, followed by a description of developinga UML model of
Bunges ontology in Sect. 4. Subsequently,Sect. 5 presents a brief
description of a UML to OWL trans-lation approach and its
application to the UML model ofBunges ontology. The paper discusses
the challenges andlimitations of this work (Sect. 6) before
concluding (Sect. 7).
2 Related work
An extended Entity-Relationship (eER) model of Bungesontology
had been developed previously [48], but with seve-ral
limitations.
1. The model in [48] is not reported to have been
intersub-jectively validated.
2. The eER language dialect chosen is not widely knownor
used.
3. OWL and UML are the current de-facto standards forontology
description and conceptual modelling, respec-tively. A description
of the model as an ERmodel makesit difficult to e.g. compare this
model to models of UMLor ebXML, both of which are specified as UML
models.Comparisons to such software design and processmodel-ling
languages have been shown to be theoreticallyimportant and useful
[23,27,35,71].
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A UML and OWL description of Bunges upper-level ontology model
237
4. Most importantly from a pragmatic perspective, themodel
developed in [48] is not available in a format thatallows further
use: The CASE tool with which it is gene-rated uses a proprietary,
binary format.
5. The model described in [48] is based on a limited
scopederivative of Bunges ontology, while the present effortis
based directly on Bunges work [56,57].
The research by Bera and colleagues brings togetherBunges
ontology and OWL [21,22]. They view OWL asan ontology, rather than
an ontology language, and assignreal-world meaning to its
constructs by mapping them toconcepts of Bunges ontology. They
propose modelling rulesand add concepts to OWL such as event, and
state. Addingsuch concepts to OWL is not problematic when OWL is
vie-wed as an ontology, rather than as a formal description
logicthat requires formal semantics and inference rules for thenew
concepts [1820]. In contrast, the present work viewsOWL as the
logical formalism it is intended to be, a meansfor describing
ontologies. Consequently, no real-world mea-ning is required for
OWL, only for the ontologies describedin OWL.
Under the auspices of the Object Management Group(OMG), which
coordinates modelling and meta-modellingstandards such as Corba and
UML, a working group on onto-logies has been formed. The product of
this working group isthe Ontology Definition Metamodel
Specification [72]. Thisis a specification of the OWL ontology
language in termsof the MOF (meta-object facility), in essence a
definition ofOWL inUML. It isnot a specification of a particular
ontologyin UML and OWL, as developed in this paper.
Work on other ontologies and ontology languages has ledto
profiles for UML to guide and support conceptual model-lers. For
example, Guizzardi and colleagues [73] have deve-loped a profile
for UML based on GOL [74], and Djuric [75]has proposed a UML
profile based on description logics. Theproposal in Sect. 4.3
develops an analogous UML profilebased on Bunges ontology.
Finally, the close relationship between OWL and UMLhas been
expressed in [76], where the ability to reason withUML class
diagrams is explored by translating UML classdiagrams to OWL. Sect.
5 makes use of this work. Such atranslation is also implemented by
the UML storage backendfor the Protege ontology editor.3
3 Solution approach
As formal ontology and conceptual modelling research canboth
benefit from the same ontology, albeit using different
3 http://protege.cim3.net/cgi-bin/wiki.pl?UMLBackendMapping
(lastaccess on 25 Sept. 2007).
representation languages, there are three alternative
app-roaches:
1. Developing and maintaining separate UML and OWLmodels of
Bunges ontology has the advantage that bothmodels can be developed
tomake full use of the expressi-veness of each language. However,
the modelling wouldrequire twice the initial effort, the models
would not beidentical and may not even be consistent, and
increasingeffort must be expended to maintain the models.
2. Developing and maintaining an OWL model and auto-matically
deriving a UMLmodel reduces modelling andmaintenance effort. On the
other hand, the modellingcapabilities of UML cannot be fully
exploited, as themodel would be limited to the expressiveness of
OWL.
3. Developing and maintaining a UML model and automa-tically
derive an OWL model has the same benefits anddrawbacks as the
second alternative.
In this paper, we have chosen the last option for the follo-wing
reasons.
We aim to guarantee a single model in both languages.This, and
the associated effort, rules out the first approach.
While each language (UML and OWL) offers languageconstructs not
available in the other (Sect. 5), the UMLconstructs that cannot
easily be mapped to OWLconstructs [72,76] are not critical to
describing Bungesontology.4
UML has been successfully used not only for conceptualmodelling
but also for ontology modelling [75,76,78].
Pragmatically, UML is more widely used than OWL andhas the more
mature modelling tool support.
Bunges ontology is mainly used in conceptual model-ling research
where UML is the prominent descriptionlanguage.
The diagram in Fig. 1 summarizes the chosen approach.An
interpretation of Bunges ontological writings [56,57]leads to a
graphical UML model (Sect. 4), which is expor-ted in the
standardized XMI (XML Model Interchange) for-mat. From the UML and
OWL standards, and based partiallyon existing research, an XSL
transformation is developedand applied to the XMI model, yielding
an OWL descriptionof Bunges ontology (Sect. 5). Only one model (the
UMLmodel) of Bunges ontology needs to be created and
main-tained.
4 While UML class diagrams can be supplemented with the
objectconstraint languageOCL (Object Constraint Language) [77],
thiswouldprohibit the use of the ontology in the semantic web
context, as OCLis full first order logic, so that efficient
reasoning abilities cannot beguaranteed.
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238 J. Evermann
UML Standard OWL Standard
XSLT
Interpretation
OWL ModelBunges
OntologyGraphical
UML ModelXMI Model
InterpretationAutomatic
Export
AutomaticTransformation
Fig. 1 From Bunges writings to an OWL model
4 Development of a UML model of Bunges ontology
The translation of a text or description from one languageor
representation form to another requires its interpretationand
understanding. Consequently, we choose a hermeneuticapproach for
the development of the UMLmodel of Bungesontology.Hermeneutics is
an interpretation technique to iden-tify the meaning of a text. It
was pioneered by Gadamer [79]and Ricoeur [80], and is well accepted
in IS research (e.g.[8184]).
Hermeneutics is a dialectic process, using a cycle thatiterates
over repeated interpretations of a text before differentbackgrounds
of understanding. Originally this hermeneuticcycle was conceived of
as a process that relates the meaningof parts of a text to the
meaning of the whole text, and viceversa. More generally, every
time the reader interprets a textin light of a different
understanding, be it causedby adifferentsense of the holistic
meaning or otherwise, the reader in turngains a different
understanding of the text. This change inthe understanding of the
reader consequently changes thereaders interpretation of subsequent
readings of the text [79,80]. Interpretation of a text by a reader
is complete whenthe readers interpretation does not change from
previousreadings of a text. In terms of [79], this is the point of
fusionof horizons.
In the case of this research, knowing that Bunges work[56,57]
needs to be represented in UML or OWL, will(consciously or not)
invoke a different sense or readingof the text in the interpreter,
as for example, when comparingit to Kants work on categories. The
first iteration over thehermeneutic cycle begins with a naive
reading of Bungeswork, shaped only by the knowledge that a
representation inUML is the aim of the reading, and knowledge of
the model-ling capabilities of UML. Representing this naive
unders-tanding of Bunges writings in UML provides a
differentbackground to the next reading of the text. For example,
thisnext readingmay emphasize particularly unclear passages,
orpassages that appeared inconsistent when naively expressedin UML.
The interpretation of Bunges writings on ontology
was achieved by such an iterative process of developing aUML or
OWL model based on the detailed and critical rea-ding of
[56,57].
A rigorous and systematic procedurewas adopted for
eachiteration, as follows: during each iteration all definitions
andpostulates in [56,57] were examined as to whether they defi-ned
concepts within the scope of the study. If this was thecase, the
concepts were included in the model as UMLclasses. In this case,
further critical reading of related corol-laries and plain text
explanations in [56,57] was carried outto define the relationships
of the new concept with others.For every concept and relationship
added in this way, theremainder of Bunges writings were re-examined
to cross-validate and clarify the relationships within the text.
Onceall definitions in [56,57] were examined in this way,
anotheriteration of the hermeneutic cycle was begun.
The iterations continued until the understanding of theontology,
and the UML model based on that understanding,was not changed
during subsequent readings. The UMLmodel underwent a total of five
iterations, corresponding tofive critical readings of the text. Of
these, the second modeliterationwas done inOWL, rather thanUML, in
order to gaina better understanding of potential differences and
tradeoffsbetween UML and OWL modelling.
Scoping of the translation was determined by examiningthe
previous body of work that employs Bunges ontology[2138,4454,5864].
That body of work shows consen-sus on a certain subset of Bunges
writings as relevant forresearch and practice in IS. Because the
present researcheffort is aimed at delivering a useful result for
those resear-chers and practitioners, the scope of the present work
is res-tricted accordingly. Consequently, we omit topics such as
thestructure of space and time, possibility, and human and
socialsystems, as they have not been employed in previous work.
4.1 Validation
The resultingmodel was inter-subjectively validated by
threeindependent researchers in the semantic web and
conceptualmodelling community. All have published on Bunges
onto-logy and can be considered topic experts [21,22,24,65].
Theindependent validation, detailed in the following
paragraphs,highlighted different issues with the overall model
(Table 1).
The validation effort included the maintainer of the eERmodel.
The extent of this validation was a full day in per-son discussion
of both models, and a subsequent confe-rence call, in addition to
weekly email exchanges. Thefocus of the discussions was on the
modelling of states,attributes, and state functions, because the
largestdifferences were found there. As a result, both the UMLmodel
and the eER model, which had not originally
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A UML and OWL description of Bunges upper-level ontology model
239
Table 1 Definitions and postulates used from [56,57]
Section, definition orpostulate in [56]
Construct
Chapter 1 Individual
Definition 1.1 Composite individual
Definition 1.1 Simple individual
Definition 1.2 Individual part of relation
Definition 1.3, Postulate 1.2 World individual
Postulate 1.1, Corollary 1.1 Null individual
Postulate 1.5 Individual superposition
Postulate 1.5, Definition 1.10 Individual juxtaposition
Definitions 2.2, 2.5, 2.17,Chap. 2, Sects. 1.1 and 3
Property
Postulate 2.1 Property in general
Postulate 2.1 Individual property (property inparticular)
Definition 2.6, Definition 3.14 Class
Postulate 2.8 Basic property
Postulate 2.8, Corollary 2.1 Complex property
Definition 2.15 Property weight
Postulate 2.2, Chap. 2,Sect. 2.2
Mutual property
Postulate 2.2, Chap. 2,Sect. 2.2
Intrinsic property
Chapter 3, Sect. 5.1, p. 101f Binding mutual property
Chapter 3, Sect. 5.1, p. 101f Non-binding mutual property
Definition 2.16 Emergent property (gestaltproperty)
Definition 2.16 Resultant property (hereditaryproperty)
Chapter 2, Sect. 1.2 (esp. p. 60) Attribute
Definition 2.4 Property incompatibility
Definitions 2.7, 2.9, 2.10,Postulate 2.7
Property precedence as lawa
Definition 3.1 Thing
Definitions 3.1, 2.5, 2.17 Thing possesses properties
Definitions 3.3, 3.4,Postulate 3.2
Thing juxtaposition
Definition 3.4 Composite thing, composition,and part-of
relation
Definition 3.4 Basic thing
Postulate 3.2 Null thing
Postulate 3.3,Corollary 3.2
World
Definition 3.6, also p. 125 Domain
Definition 3.6 Co-domain
Definition 3.6 State function
Definition 3.6 Functional schema (model, modelthing)
Definition 3.7 Amount of structure
Definition 3.9 State (associated with functionalschema)
Definition 3.9 Value of total state function(defines state)
Table 1 continued
Section, definition orpostulate in [56]
Construct
Definition 3.9 Function value (assumed value ofstate
function)
Definitions 3.10, 2.7,Criterion 2.2 Law statement (restricts
statefunctions)
Definition 3.11 Lawful state
Definition 3.11 Lawful state space (defined by
lawstatements)
Chapter 3, p. 133f Conceivable state spaceb
Definition 3.17 Kind
Definitions 3.21, 3.22, 3.25 Natural kind (species).c
Chapter 3, Sect. 3.5 Basic law
Chapter 3, Sect. 3.5 Derived lawd
Definition 3.25 Natural genus
Definition 5.2 Change (w.r.t. a lawful statespace)
Definition 5.3 Qualitative change
Definition 5.3 Quantitative change
Definition 5.4, Principle 5.2 Event (ordered pair of states)
Definition 5.4 Event space
Definition 5.4 Composition of two events
Definition 5.6 Composite event(complex event)
Definition 5.8 Lawful transformation
Definition 5.9, Principle 5.3 Functional change(lawful
event)
Definition 5.9 Lawful event space
Definition 5.10 Composite functional event
Definition 5.11, Rule 6.1 Reference frame
Definition 5.11 Coordinatization
Definition 5.14 Relative rate of change
Definition 5.14 Relative extent of change
Definition 5.15 Global rate of change
Definition 5.15 Global extent of change
Definition 5.24, Definition 5.6 Process
Definition 5.26, Postulate 5.9 Process predecessorand
successor
Definition 5.27 History
Definitions 5.29, 5.31,Postulate 5.10, Criterion 5.1
Action
Definitions 5.30, 5.31 Interaction
Definitions 5.32, 5.33 Bond
Definition 5.33, [57] 1.5 Bondage (internal A-Structure)
Definition 5.35, [57] 1.1,Corollaries 5.14, 5.15
System
[57] Definition 1.2,Theorem 1.1
A-Composition
[57] Definition 1.2 A-Structure
[57] Definition 1.2 A-Environment
[57] Definitions 1.6, 1.7 Sub-system (nesting structure)
[57] Definition 1.8 Level
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240 J. Evermann
Table 1 continued
Section, definition orpostulate in [56]
Construct
[57] Definition 1.8 Level structure
[57] Definition 1.10 Input
[57] Definition 1.10 Output
aBunge uses the terms law and law statement synonymous in Chap.
2.A second definition of law statement in Chap. 3 (Definition 3.10)
is ofa different form than the one in Chap. 2, but with the same
content. Inthe present model, we distinguish law from law statement
and proposethat a law statement expresses or describes a lawbThe
conceivable state space was modelled even though it is notformally
defined in [56]. This allows us to introduce the idea that
statespaces are spanned by the co-domains of state functions of
functionalschemata. The lawful state space is a conceivable state
space that isconstrained by law statementscNote that natural kinds
are defined by laws. As laws relate properties,members of natural
kinds also possess certain properties. These arecalled
idiosyncratic properties (Definition 3.22)dNote that while the
distinction between basic and derived laws islogically,
methodologically and ontologically crucial [56], it is notformally
defined in [56]
been inter-subjectively validated, underwent
substantialrevisions.5 However, as the eER was obtained
primarilyfrom the comparatively brief description in [25],
ratherthan the full source [56,57], some differences remain(Tables
2 and 3).
Subsequent discussions with a second expert were basedon the
model resulting from the validation process withthe first expert.
This validation was conducted via mul-tiple telephone discussions
and email exchanges, andhighlighted two main issues of omission in
the UMLmodel. This expert reported approximately 8 hours oftime
spent on validating the model against Bunges work[56,57] over a two
week period. The focus was on therelationships between the
identified concepts and theirmultiplicities. The concept of
interaction was introdu-ced to the model as a result of this
validation. Minorclarification issues, dealing e.g. with synonymous
termi-nology, were also raised and addressed in the model.
Asub-sequently repeated validation by this expert of therevised
model yielded agreement on the entire model.
The validation with a third expert, based also on the resultof
the validation process with the first expert,
revealedinconsistencies in the modelling of co-domains and
theirrelationship to state spaces and state functions. Two
tele-phone discussionswith this expert led to clarifications
andminor changes in this area of the model. A minor errorin the
multiplicity of the association between events andstates was
corrected as a result of this validation. Overall,
5 The current version of the eER model is 5.1, last revised 15
Sept.2005.
Table 2 Elements in the eER model not in the UML model
Internal event Natural law Transformation law
External event Human law Conceivable event space
Stable state Well-defined event Corrective action
Unstable state Poorly defined event Value change
Time instant Known state Stability condition
History Predictable state
Table 3 Elements in the UML model not in the eER model
Individual Natural genus Domain
Individual juxtaposition Thing juxtaposition Co-domain
Individual superposition Null thing Qualitative change
World (individual) Property precedence Quantitative change
Composite individual Derived law Reference frameand
coordinatization
Simple individual Basic law Composite event
Null individual Functional schema Functional change
Natural kind State function ProcessBondage
this validation process revealed no significant problemareas in
the model.
A complete exposition of the developed model is beyondthe scope
of this paper, as Bunges writings consist of twobook volumes.6
Figure 2 shows the UML model in thePoseidon UMLCASE tool. The
complete model contains 65classes, 62 generalizations, and 79
associations.7 Table 1 listsall the concepts in the model and their
definitions in [56,57].The table is not intended as a discussion of
the ontology,but instead is intended to offer an indication of the
rigor andcompleteness of this research.
Table 2 shows the elements in the current eER modelthat are not
contained in the UML model of this research.Except for internal and
external events, and stable and uns-table states, these are
acknowledged by the eERmodel main-tainer not to be part of the
ontology as described in [56].Internal and external events, stable
and unstable states arenot formally defined in [56] and therefore
not included in theUML model.
Table 3 shows the elements in the current UML modelwhich are not
contained in the eER model. As shown inTable 1, they are formally
defined in [56]. This suggests
6 The complete model is available electronically at
http://www.mcs.vuw.ac.nz/~jevermann/Bunge/ and print copies are
available from theauthor.7 This compares to 76 entity types in the
current eER model. However,of these, more than 25 are redefined
relationship types, which are rela-tionship types as well as entity
types, similar to the concept of a UMLassociation class.
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241
Fig. 2 Bunge ontology model in the Poseidon UML tool
that the present UML model may be a more completerepresentation
of Bunges ontology than the eER model.
4.2 Excerpt of UML model
Figure 3 is an excerpt of the full model, showing states
andrelated concepts to offer an impression of the resulting
UMLmodel.8 This subsection briefly examines the derivation ofthe
model excerpt in Figs. 3 from [56].
Bunge introduces a functional schema in [56, Def. 3.6] asa
certain nonempty set M together with a finite sequence Fof
non-propositional functions on M , each of which repre-sents a
property. Therefore, we have modelled Functio-nalSchema as an
aggregate of StateFunction. Because theset is described as
nonempty, the lower multiplicity is 1.While Bunge makes no mention
of whether a state functioncan be part of multiple schemata, we
make the least restric-
8 A note on the specialization of associations in the model:
While thespecialization of associations may not be widely used, a
related tech-nique, subsetting of association-end properties, is
widely used by theOMG itself and applied to most associations in
the definition of theUML meta-model [85]. The specification
suggests that these can beused interchangeably: In the case of
associations, subsetting ends,,correlates positively with
specialization the association [85, p. 37],except in a special
case, which does not apply in this research: Thisview falls down
because it ignores the case of classifiers which, for wha-tever
reason, denote the empty set. [85, p. 37]. The paper, thereforeuses
specialization as a clearer alternative to subsetting.
tive assumption that the aggregation is a shared one,9
withmultiplicity 1..* on the FunctionalSchema end.
Any substantial property in general is representable as
apredicate (or propositional function) [56, Post. 2.1, p.
63].Therefore, the non-propositional functions of the
functionalschema represent individual properties. We shall call
them[the functions of a functional schema] state functions [56,p.
125].We represent the relationship between state functionsand
individual properties by means of an association bet-ween
StateFunction and IndividualProperty in Fig. 3. Bungeonly suggests
that each of which [the state functions] repre-sents a property
[56, Def. 3.6]. Hence, the multiplicity at theStateFunction end of
the association is not restricted and themultiplicity at the
IndividualProperty end is 1.
Propositional functions that represent properties in gene-ral
[56, Post. 2.1, p. 63] are called attributes: Such proposi-tional
functions will be called attributes [56, p. 62]. There-fore, we
associate Attribute and PropertyInGeneral in Fig. 3.The
multiplicities on the Attribute end of the association arenot
restricted, so that it is possible that a property in generalcan be
represented by multiple attributes, or not be represen-ted at all.
This is because the representation of properties byattributes is a
function : P 2A that assigns eachpropertyp a collection (p) 2A of
attributes [56, p. 60]. Because
9 As the precise semantics of shared aggregations are not
defined in[85], we characterize them in the terminology of [86] as
shareable andseparable.
123
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242 J. Evermann
Fig. 3 Excerpt from the UMLmodel of Bunges ontology
Individual PropertyProperty In General
Attribute
Property
0..1
*represents
Value
value+*
valueOf+
FunctionalSchema
+ AmountOfStructure :float
StateFunction
InSchema+
1..*
hasFunction+
1..*
*
ObservedAs
Domain
* *
State
*
*
1..*
FunctionValue
OfFunction+*
AssumedValue+ 1..*
ValueOfTotalStateFunction*
1..*
DefinedBy+
represents+
1..*
Co-Domain
*
*
*
represents
there are attributes with no ontic correlate [56, p. 60],
themultiplicity on the PropertyInGeneral end is 0..1.
Bunge states that any individual substantial property, ...,is
representable as the value of an attribute. [56, p. 63,Post. 2.1].
Consequently, we have associated IndividualPro-perty and Attribute.
Bunge does not mention whether attri-butes can represent multiple
individual properties. We makethe least restrictive assumption and
model a multiplicity of* on the IndividualProperty end of the
association.
Because every functional schema possesses a unique totalstate
function [56, Def. 3.9], we do not introduce a separateconcept.
Instead, the FunctionalSchema is associated
withValueOfTotalStateFunction. Because the total state functionmay
take on different values (e.g. at different times), themultiplicity
at the ValueOfTotalStateFunction end is *.
The total state function is defined as the set of all
statefunctions of a functional schema [56, Def. 3.9] and its
valueis said to represent the state of [56, p. 127, emphasis
added].Consequently, we have modelled ValueOfTotalStateFunc-tion as
a shared aggregation of multiple FunctionValue.Because Bunge does
not indicate whether a state functionvalue can be part of multiple
values of the total state func-tion, we make the least restrictive
assumption and assign amultiplicity of * to the
ValueOfTotalStateFunction end.
From the terminology its value is said to represent thestate
[56, p. 127] we assume an association between Stateand
ValueOfTotalStateFunction with multiplicities of 1 atboth ends.
Because a state is defined only in the context of a functio-nal
schema [56, Def. 3.9] the association between State
andFunctionalSchema is modelled with a 1 multiplicity at
theFunctionalSchema end and a 1..* multiplicity at the
Stateend.
A functional schema consists of . . . a list F . . . of
func-tions with ... unspecified co-domains Vi [56, p. 125].
Therefore, we have modelled the Co-Domain as anaggregation of
Value.
The amount of structure of a functional schema is definedin [56,
Def. 3.7] as a function of the rank and number of func-tions in a
functional schema [56, p. 122] and is representedas the attribute
AmountOfStructure of FunctionalSchema.
4.3 A UML profile for Bunges ontology
An immediate extension of the UML model is the definitionof an
ontological UML profile to annotate models, therebyproviding for an
ontological interpretation of the model ele-ments and also offering
guidance to the modeller [31]. TheUML profile for Bunges ontology
presented here is analo-gous to the work by Djuric [75] for a UML
profile for OWLand Guizzardi [73] for a UML profile for GOL.
UML 2.0 features a substantially revised definition ofthe
lightweight extension mechanisms. Profiles are spe-cializations of
packages and stereotypes are specializationof classes.
Consequently, the graphical depiction of profilesand stereotypes is
identical to that of packages and classes(Fig. 4a). This UML
revision makes it possible that a modelthat was developed on the M1
level (model-level) can be re-used as a model on theM2 level to
define profiles. In fact, theOMG suggests that a profile must
therefore be defined as aninterchangeable UML model [85, p. 633].
This is accom-plished syntactically by all classes being
specialized to ste-reotypes and all packages being specialized to
profiles. Thespecialization preserves generalization and
association rela-tionships, as well as features. This simple
syntactical step is apowerful way to define and create profiles
based on existing(M1) models. As required by the OMG [85, Sect.
18.1.2],the use of the profile is strictly an addition to the
UML
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A UML and OWL description of Bunges upper-level ontology model
243
Bunge
Property
[StructuralFeature]
IntrinsicProperty
[Property]
NaturalKind
[Class]
Kind
StructuralFeature
Class
Property
+definingProperty
2..*
1..*
(a)
Supplier
+Name+Number
(b)
Fig. 4 Using the UML model of Bunges ontology as a profile
2.0 meta-model and introduces only constraining, but
notcontradicting, semantics.
Specifically, this new profile definitionmechanism is usedhere
as a simple but powerful way to make use of the exten-sive research
work mapping UML constructs to elements ofBunges ontology
[23,28,29,31,35,60]. We illustrate usinga brief excerpt from the
developed UML model of Bungesontology. Packages in that model
become profiles (a speciali-zation of meta-class package) and
classes become stereo-types (a specialization of meta-class class).
The existingmappings from UML to Bunges ontology are used to
iden-tify those UMLmeta-classes that are extended by the
stereo-types. For example, the mapping in [35]:10,11
Natural kind UML-class Property UML-structural feature Intrinsic
property UML-property (attribute)
leads to the following extensions:
Stereotype NaturalKind extends meta-class Class Stereotype
Property extendsmeta-class StructuralFea-
ture
10 Previous research on mappings from UML to Bunges
ontology[23,28,29,31,35,60] used UML 1.x. In UML 2.0 the
definitions ofattributes, properties, structural features and
associations have changedsignificantly, so that we can only present
a rough sketch without revi-siting and updating the existing work,
which is beyond the scope ofthis paper. The excerpt presented here
is for illustration of the principleonly.11 For a different mapping
see earlier work in [28]. There, a UML classis mapped to a
functional schema and a UML attribute is mapped to astate
function.
Stereotype InstrinsicProperty extends meta-classProperty
Other ontological concepts in the UML model similarlybecome
stereotypes, with the existing research that mapsUML to concepts in
Bunges ontology serving as the foun-dation for these extensions. An
excerpt of such a profile isshown in Fig. 4a.12
The profile defined in thisway can then be applied to adornmodel
elements on the M1 level. For example, Fig. 4b showsa (M1) model of
some domain that indicates that Supplieris a natural kind and Name
and Number are intrinsicproperties.
Application of this profile requires the satisfaction of
theconstraints defined in the profile, such as multiplicities
ofassociations between stereotypes. However, these
profileconstraints are constraints in the originally developed
UMLmodel of Bunges ontology. For example, there exists aconstraint
that a natural kind is defined by two or more com-mon properties
among members of the kind. Applying theresulting profile
consequently requires that whenever a classis stereotyped as
NaturalKind, two ormore of its propertiesmust be stereotyped as
IntrinsicProperty.
Modelling constraints such as these can be
automaticallyenforced, due the fact that the ontological model is
availableto a CASE tool as a profile. Such
ontology-derivedmodellingsupport has been demonstrated to be
beneficial to IS deve-lopment projects [60,61]. Previous work has
derived onto-logical modelling rules based on Bunges ontology
[28,29],
12 The association with the filled arrow notation is the symbol
for anExtension in UML [85].
123
-
244 J. Evermann
and has proposed to describe these in the form of a UMLprofile
[31].However,while amethod to automatically derivemodelling
constraints from an ontology was proposed, thenatural language
description of Bunges ontology preventedits demonstration [31].
5 Towards a formal ontology
This section briefly describes the UML to OWL translationand its
application to the UML model of Bunges ontology.It begins by
examining previous research.
A representation of UML in description logics has beendeveloped
in [76] to explore reasoning on class diagrams.However, this work
does not consider specifics such as navi-gability of associations
and n-ary associations, nor does itconsider the inverse
representation of OWL in UML.
The UML storage backend plug-ins for the Protege onto-logy
editor also allows a translation from UML to OWL andvice versa, but
is more limited than what is presented here.13
Specifically, association classes, n-ary associations,
generali-zation of associations, association end navigability and
chan-geability are not supported for UML import to Protege.
The approach in [75] relies on an extension of UML calledthe
Ontology UML Profile (OUP) which allows annotationof UML models
with tagged values and stereotypes definedin this profile. This
allows, e.g. describing a UML class tobe a union of two other
classes. This approach is limitedin its applicability to newly
created UML models using thisstereotype. Existing UML models are
excluded, as they arenot annotated.
Finally, as part of the ODM specification [72], the OMGalso
proposes an informative, rather than normative,mappingfrom UML to
OWL and vice versa.
5.1 XMI to OWL translation with XSLT
The translation between UML and OWL is implemented asa set of
XSLT 1.0 style sheets (XML Style-Sheet LanguageTransformation) that
take anXMI (XMLModel Interchange)description of the UML model as
input. The inverse trans-lation is also implemented in a separate
XSLT. The XMI1.2 description (of UML 1.5) contains 5113 lines of
XMLcode. The XSLT transform contains 283 lines of code in
5templates. Run with the open source Saxon 8.4 XSLT pro-cessor14 it
creates an output file of 2761 lines of OWL XMLcode.
Table 4 shows the correspondences between concepts ofeach
language. This table is partially based on existing work
13
http://protege.cim3.net/cgi-bin/wiki.pl?UMLBackendMapping(last
access on 25 Sept. 2007).14 http://saxon.sourceforge.net/.
presented in [72,76], and agrees with the correspondencesbetween
UML and OWL established there. The mappingsare therefore not
validated further.
Themost important conclusion to be drawn from this tableis that
there are more OWL constructs that have no UMLequivalent, than UML
constructs without OWL equivalent.This supports the decision to
develop Bunges ontology inUML, rather than OWL, in order to
guarantee translatabilityto the other language.
Note 1 UML attributes can be of a data type that is a class
inthe model, thus having the same semantics as a uni-directionally
navigable association. If that is the case, theattribute should
instead be modelled as an association whenusing this
translation.
Note 2 UML associations can involve three or more partici-pant
classes,while object properties inOWL represent binarypredicates.
In contrast to [76] where these associations areomitted, but in
agreement with [72], we translate n-ary asso-ciations to OWL
classes. This is an accepted approximation,as it is difficult to
correctly represent the multiplicities fromthe syntactic
information only [8789].
Note 3 In agreement with [72,76] association classes are
notrepresented as associations (of which they are
specializa-tions), but as classes (of which they are also
specializations)that are connected by binary associations to the
classes thatparticipate in the association class.
Note 4 The OWL union of two classes is approximated inUML as two
generalizations: A = B C B A C A. Further, these two
generalizations are part of the samegeneralization set which is
covering. This approximationrests on the interpretation of
generalization as subsets, notas feature inheritance.
Note 5 TheOWL intersection of two classes is approximatedin UML
as two generalization: A = B C A B A C . This approximation rests
on the interpretation ofgeneralization as subsets, not as feature
inheritance.
Note 6 Object properties in OWL are uni-directional
whileassociations in UML are bi-directional, barring explicit
navi-gability constraints. Hence, onlywhen the inverse of
anOWLobject property exists, does the corresponding
associationbecome navigable in both directions. In turn, if an
associationis navigable in both ways, twoOWLproperties
aremodelled,inverse of each other, in agreement with [72].
Note 7 Class definition by enumeration in OWL cannot beexpressed
in UML, but the specified OWL instances canbe modelled as UML
objects of the corresponding UMLclasses. UML provides the
Enumeration and EnumerationLiteral meta-classes. Enumeration is a
subset of the meta-class DataType, a type whose instances are
identified only
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A UML and OWL description of Bunges upper-level ontology model
245
Table 4 Comparison of UMLand OWL constructs
UML OWL Note
Class Class
Attribute DatatypeProperty 1
Association ObjectProperty 2
AssociationClass Class and ObjectProperties 3
Generalization between Classes subClassOf
Generalization between Associations subPropertyOf
Multiplicities Cardinalities
(Generalization) UnionOf 4
(Generalization) IntersectionOf 5
ComplementOf
AssociationEnd isNavigable InverseOf 6
TransitiveProperty
SymmetricProperty
(Objects) OneOf (class definition by enumeration) 7
AssociationEnd participant ObjectProperty value constraint
allValuesFrom
ObjectProperty value constraint someValuesFrom
AssociationEnd changeability ObjectProperty value constraint
hasValue
Attribute typedFeature DatatypeProperty value constraint
allValuesFrom
DatatypeProperty value constraint someValuesFrom
Attribute changeability and initial value DatatypeProperty
constraint hasValue
Mutual generalization EquivalentClass 8
DisjointWith 9
Mutual generalization EquivalentProperty 10
(Multiplicity constraint) FunctionalProperty
SameAs
DifferentFrom 11
AllDifferent 11
Aggregation kind 12
by their value [85, p. 57]. Accordingly, an EnumerationLiteral
does not represent objects but data values [85, p. 64].Enumeration
and EnumerationLiteral can therefore not beused to define classes
by enumeration of instance objects.
Note 8 To express OWL class equivalence in UML, we usemutual
generalization: A B A B B A. Thisapproximation rests on the
interpretation of generalizationas subsets, not as feature
inheritance, and agrees with [72].Of note, while the OMG ODM
specification [72] endorsesthis expression, the OMGUML
specification [85] in contrastrequires that generalization
relationships be acyclic.
Note 9 Disjointness of classes in OWL does not need anexplicit
modelling construct in UML, as classes by defaultare interpreted as
disjoint [76].
Note 10 To express OWL object property equivalence inUML, we use
mutual generalization of associations, analo-gous to OWL class
equivalence, in agreement with [72]. Seealso Note 8 above.
Note 11 It is not necessary to express the fact that an
instanceis distinct from another, as this is the default assumption
inUML and conceptual modelling [76].
Note 12 UML defines two kinds of aggregation types
forassociations (shared and composite). Characteristics
ofaggregation are described in terms of dynamics, e.g. ins-tance
creation or deletion [86]. However, as OWL is limitedto static
representations of domains, these constructs offer noadditional
semantics to regular associations for purposes oftranslation to OWL
[76].
5.2 Using the OWL ontology
The generated OWL code was validated and confirmed to beOWL-DL
compliant.15 It can be imported into and
15 http://www.mygrid.org.uk/OWL/Validator.
123
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-
246 J. Evermann
Fig. 5 Bunge Ontology in Protege, using the Pellet reasoner for
consistency checking and concept hierarchy inference
maintained with the Protege ontology editor.16 Figure 5shows the
Bunge ontology in Protege 3.3, interfaced withthe Pellet
reasoner.
At this stage, the Bunge ontology becomes usable forformal
reasoning. The Bunge ontology is describable in thedescription
logicALHIN , i.e. attributive languageAL plusrole hierarchies H,
inverse or symmetric roles I, and num-ber restrictions N . In other
terminology, this is the descrip-tion logic SHIN , a subset of
SHIQ, where S = ALCand Q (quantifiers) subsumes N (number
restrictions) [1820]. Using the Pellet open source reasoner17 via
the DIG(Description Logics Implementation Group) interface
fromProtege, the Bunge ontology was checked for consistency,i.e.
concept satisfiability. All concepts were found to be
16 http:://protege.stanford.edu.17
http://pellet.owldl.com/download.
satisfiable. Further, the reasoner was used to infer theconcept
hierarchy, i.e. find the most specific super-conceptfor any
concept. No changes to the explicit concept hie-rarchy were found.
These results lend further confidenceto the validity of the UML to
OWL translation proposedabove.
As the Bunge ontology is a TBox (terminology) only,limited
practical reasoning can be performed. Concreteapplications require
instances of the concepts, i.e. an ABox(assertions), to be useful.
Besides being used to reason overinstances, another possible use
for the formalBungeontologyis in the integration of multiple domain
ontologies, as indica-ted in Sect. 1.2. Different domain ontologies
can specializethe same Bunge concepts and can then be used for
integratedreasoning across multiple application domains. For
example,medical diagnosis ontologies could be integrated with
drugeffects and treatment ontologies.
123
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A UML and OWL description of Bunges upper-level ontology model
247
6 Discussion, challenges, and future research
Information loss is inevitable when translating an
ontologydescription from a specification in natural language and
settheory, which is equivalent to full first order logic, to
therestricted languages of UML, used in conceptual modelling,and
OWL, used on the semantic web. This is an inevitabledrawback in the
absence of more expressive standards forsemantic web
ontologies.
On the UML side, one can make use of the ObjectConstraint
Language OCL, which is capable of expressingfirst order logic.
However, while OCL is well defined, littleto no tool support
exists. For example, most UMLmodellingtools simply store OCL
constraints as text, and the few exis-ting OCL parsers and
compilers (e.g. [90]) are not well inte-grated. Consequently, while
use of OCLwould allow a betterrepresentation of Bunges ontology,
the ontology would notbe more accessible to researchers or
practitioners. It wouldalso lead to two very distinct models, one
in OWL and ano-ther, much more expressive one, in UML/OCL. In the
inter-est of developing a single model, we have therefore
decidedagainst the use of OCL.
As the brief discussion in Sect. 5 shows, most of the
diffi-culties translating betweenUML andOWL arise when tryingto
translateOWLconstructswhich have no direct counterpartinUML, e.g.
EquivalentClass. In these cases, approximationshave been outlined
for a translation from OWL to UML. Thework presented in this paper
requires a translation only fromUML to OWL. Consequently, the
validity of the OWLmodelof Bunges ontology is not affected by these
approximations.
7 Conclusion
In summary,we have developed a validatedmodel ofBungesontology
in two important representation formats, UML andOWL, making this
widely-used ontology more accessible toresearchers in both the
conceptual modelling and semanticweb community.
In the future, we plan to use this representation of
Bungesontology as a foundation for formal and rigorous
research.Specifically, three important applications are currently
beingpursued. (1) The use of theUMLmodel in schema integrationto
e.g. compare Bunges ontology with enterprise models,such as ebXML.
(2) The use of the UMLmodel as a profile togenerate
ontologicalmodelling constraints. (3) The use of theOWL
representation in ontology integration in the semanticweb
context.
The intention of this research is to begin an ongoing com-munity
process. Through the use of open formats and opentoolswe hope to
ensure this effortwill be supported by contri-butions from the
research community. The ongoing evolutionof the ontology
representation by the community is supported
by a web site with discussion forums.18 The research com-munity
is invited to participate in a joint effort of creatingan accepted
consensus model of Bunges ontology in usefuland widely-used
representation formats.
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Author biography
Joerg Evermann is with theFaculty of Business Adminis-tration at
Memorial Universityof Newfoundland, Canada. Afterreceiving his PhD
in MIS fromTheSauder School ofBusiness atthe University of British
Colum-bia in Vancouver, Canada, hewas a faculty member with
theSchool of Information Manage-ment at Victoria University
ofWellington, New Zealand. Hisresearch interests are in mode-ling
and knowledge representa-tion, with a special focus oncognitive
issues.
123
http://www.aiai.ed.uk/project/pub/documents/1998/98-ker-ent-ontology.pshttp://www.aiai.ed.uk/project/pub/documents/1998/98-ker-ent-ontology.ps
0pt A UML and OWL description of Bunge's upper-level ontology
modelAbstract1 Introduction1.1 Problem statement1.2 Expected
benefits
2 Related work3 Solution approach4 Development of a UML model of
Bunge's ontology4.1 Validation4.2 Excerpt of UML model4.3 A UML
profile for Bunge's ontology
5 Towards a formal ontology5.1 XMI to OWL translation with
XSLT5.2 Using the OWL ontology
6 Discussion, challenges, and future research7 Conclusion
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