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: jevermann@mun.ca

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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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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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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A UML and OWL description of Bunges upper-level ontology model 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.

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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.

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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.

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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.

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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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