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Ittlormation Modelling attd Knowk:dge Bases XVII 321

Y. Kiyoki et ul (Eds )IOS Press, 2006A 2006 The outhors All rights resert,etl

Concept Theory in the Context of Information Systems

Jari Palomiiki- & Momir Radidevii**

* Massey University, Department of lnformation SystemsPrivate Bag 756, Wellington, New Zcaland

E-mai l : J .J .Palornaki@ rnassey.ac. l lz** Waiariki Institute of Technology, School of Business and Computing

Private Bag 3028, Rotorua, New ZealandE-mail : Mornir.Racliccvr c(f waiariki.ac.nz

Abstract: ln this paper the role and the proper p lace of a concept theory in the context of

informat ion systc l rs is proposed We def ine the basic model l ing s i tuat ion consist ing ofobjects to be moclel lec l , a tnodel ler , i .e. a person who is rnodel l ing, a r roclc l , and thc

relationships between these. We continue this process by describing an iuforuatiot.t

systern l lav ing descr ibcd infbrmat ion systems ws consider a conceptual rnodel l ingprocess, the goal of which is to develop a conceptual scherna of the dor-nain of

application. In this contcxt the place of a concept theory is tbund as the foundation fbr all

conceptuaI model l ing

Ke1,t1'urr1.t. Concept, concept theory, conccptual rnodelling, iuformation systcns, systcnt.

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1. Introduction

In this paper the role and the proper placc of a concept theory in the contcxt ofinformation systems is proposed. Firstly, we define the basic nTodclling situationconsisting of objects to be modelled, a modeller, a model, and relationships betweenthese. Secondly, we dcscribe an information systcm as an instance of basic modcllingsituation. Thirdly, having described information systems we consider a conceptualmodell ing process, the goal of which is to develop a conceptual schema of the domainof application. Lastly, wc consider a concept thcory and its role in conceptualmodell ing.

2. Basic Modelling Situation

Modelling starts when for some special purposes something is to bc modelled. Thiscreates a basic modell ing situation, which consists of l) objects to be modelled,2) amodeller, who is doing the modelling, 3) a model, which is to bc a rcsult of themodclling, and 4) different relationships between these. Thc basic modelling situationis then a three-place relation: M(object(:r), modellerfv), modcl(z)), which is to be read:"an object,,r is modelled by ), us t."

Tlre objects to bc modelled form the ob.ject domain, i.e. the universc of discoursc. Theobjects in the object domain do not have necessarily to be concrete things in spaceand time of which we are to have immediate sense perception, but can as well beabstract objects consisting e.g. expert's knowledge. Moreovcr, the objects to be

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322 J. Paktnttiki ud M RaditjeviLl / Concept Theory m ilrc Conte.rt rl Infbrnqtiotl Sy.stems

modelled do not have to exist before the model of it is created. This situation happens,for example, when designing or planning something.

A^m.odeller is the subject_of a modelling situation. In most cases a modeller consistsof the group of persons having different expertises. The most importunt task for amodeller is to consider those features of the objects to be modellea ritrict are relevantfor the purpose of modelling.

A model is a result of an abstraction that ildomain. Abstraction is an epistemologicalobjects in the object domain is separakprocesses connected with creating a modelthe objects into classes on the basis of somrarrlvlng at some general notion from the instances, axiomatisation, i.e. by giving thebasic propositions (truths) from which we can deduce other propositions (truths) theresult of which is called an axiom system, etc.

Modelling relations consist of logical and epistemological relationships between themodeller, model, and obiect domain.

3. Information System

J.

actually a rindicate thrZwass 199

In informatcapturing cconcerningor transfonwith the asrperformed Iinterplays raschema in rrbe used as a

An informatisense. An lryto achievein/brmationphysical layrhardware anc

Figure l. Basic Modelline Situation

of Infurnntial Sl5:,sn1s

ted. This sifuation happens,

il cases a modeller consistsmost important task for a

lodelled which are relevant

:nt the objects in the objectiome relevant aspect of thetlso other epistemologicalrlassification, i.e. grouping)Berttes, generalization, i. e.atisation, i.e. by giving thegr propositions (truths) the

,]

lrelationships between theL

to an informationcomponents

toward a common(3) outputs,

A system mayOutputs are the, vur . vqryu lo o tv [ l tE

The outputs of onethe work: it

and outputs with itsTo adopt itself to

a portion of

J. Palotrtti.ki artrl M Radi(evi( / Concept T-heory in the Context of htlbrnation S1ts1sn1j ) L )

actually a special kind of input. lt is used as a control mechanism within the system toindicate the difference between the goals and actual performance of a system, (see e.g.Zwass 1998, Whitten et al. 2001).

Figure 2. System.

ln information system inputs are of two kinds: firstly, they are result of gathering andcapturing data to be stored in databases and, secondly, they consist of queriesconcerning the data stored in databases. Information processing involves convertingor transforming queries into valuable information, and it can be done manually orwith the assistance of a computer. Processing performed by a computer is actuallyperformed by the computer's central Processing Unit (cpU) which, in doing that,interplays with databases and a conceptual schema, sometimes also called the logicalschema in relational data models. Resulting information, as an answer to a query, maybe used as a feedback to make changes to input or procesSing activities.

nfoma o Sy m

Figure 3. Information System l.

An information system is not isolated from its environment, and so it has also a largersense. An inJormation system is a set of people, data, and processes that work togetherto achieve the common goal of information management. A computer-basedinformation system includes also hardware, which consists of everything in thephysical layer, and software, which consists of systems programs that control thehardware and application programs used to produce the required information.

thus, a feedback is

) l + J' Palonuiki and M- Raditevit / co,t:ept Tie.ry itt the Context .J Inlurmatir, systents

Figure 4. Information System 2.

4. Conceptual Model and Conceptual Modelling

In the construction of the conceptual schema at least the forlowing four principleswould serve as guidelines (van Griethuysen 19g2, Kangassalo 19g3, rtarjoma a tsoll:

In ord,need imodelland U.accoullto realconcepas well

Let us I"concep

modellirmodellirls conceone. lndetermir

5. Col

A concrbetweenoperatiotexampleunlversaentities rneutral tabilities,withoutabstract r

of Infomutiar Syttenrs

g

lsising concepts which areconceptual model of it bythis process is presented inual description of the datadata representing a certainon ofthat data is describedIthe object domain, in turn,rich generates a database offunctionalities as well.

; following four principlesalo 1983, Marjomaa 1997):

;h only conceptual aspectsconceptual schema.ant aspects of the domain

lnceptual schemata should

iitual schemata should be

pnt aspects of the domainitual. The principle 3. isp to the principle 4. The

I representing conceptual

[e modelling process, andI why the principle 4. mayfyone is familiar with the

l. Pakmtiki and M. Radiievi( / Concept Theory in the Context of lnlbrntation St,stems 325

In order to express the result of conceptual modelling as a concepfual schema, weneed a modelling language. The three most popular notations for informationmodelling are Object-Role Modelling (ORM), Entify-Relationship (ER) diagrams,and Unified Modelling Language (UML), (see e.g. Halpin 2001). However, manyaccounts ofconceptual modelling emphasise an intensional aspect concept as opposedto real world things in the domain of objects, which belong to the extensions of thoseconcepts. This means that intensionality should be visible in the modelling languageas wef l, (Kangassalo 1992193).

Figure 5. Conceptual Modelling l.

Let us note that there are two different inquires each having a right to the name"conceptual modelling". The first one is when we are actually doing conceptualmodelling, and the second one is when we are describing the process of conceptualmodelling. The first one is more basic, since in the second one conceptual modellingis conceptually modelled, and hence, it has different ontological status than the firstone. ln any given discussion, it is easy to fall into confusion through failure todetermine to which of the two inquiries the discussion is intended to belons.

5. Concepts and Concept Theory

A conceptual model is composed of particular concepts and particular relationsbetween them. A concept theory, in turn, is studying concepts and the relations andoperations between them in general. There are numerous theories of concepts, forexample, concepts can be thought of as any of the following: supersensible entities asuniversals, meanings, abstract objects, definitions, or predicates and relations; mentalentities or states as composite images, ideas, thoughts, conceptions, or innate ideas;neutral entities joining e.g. words, thoughts, and things; human or animal skills orabilities, etc. (see e.g. Weitz 1988). In order to condense this great number of theorieswithout sacrificing too many of their indispensable properlies, the following moreabstract classifications can be made:

326 J Ptlonttikian,M'Racriievi'/Cow:eptTheoryitttheConrett,f,tformatktts),stens

I' The entity theories oJ concepts, according to which concepts are entities such as- ideas, images, thought, abstract objects, etc.2. The dispositional

.rh"!:-i.": o.f ioncepts, according to which concepts areunderstood to be the abilities or skills io do somethiig, "rp""iutty

the ability touse language correctly.

we may go even further. one of the major doctrines of both the entity and thedispositional theories of concepts is that a .on."pt, in order to be a concept, must becharac-terised by a de,finite sef of necessury und sufficient criteria. This is called aclo,sed concept, and the requirement that air concepts are to be closed is called theclosttre principle of concepts. Thus we have abstracted the particular conceptions ofconcepts to the point where there are just concepts, and whatever form these take,they must satisfl, the closure principle of concepts. The advantage of this approach isthat developing a concept theory ii does not confine us to any partrcular theory ofconcepts with its specific accompanying restrictions una,p".iui"h'*a.t..irti...

Relations between concepts enable us to establish conceptual structures. The mostessential relation between concepts is the intensional containment relation, which isbased on the intensions of conce.pts,-(see Kauppi 1967, Kangas saro 1992/93. palomiiki1994)' Another important relation between concepts is th"e conceptual containmentrelation between concepts, which is based on the conceptual constit'uents of concepts,and is thus a different relation than the intensional containmeni, (palomiiki 1997,2003).

In current literature, the relations between concepts are mostly based on the settheoretical relations between the extensions of concepts. For example, according toNebel & Smolka (1990), the conceptual intersection of the ,orr."'t, of .man, and'woman' is the empty-concept, and their conceptual union is the concept of .adult,.

However, intensionally. the common concept which contains both the concepts of'man' and :l -y:-"i':,

and so is their iniensional ,on."ptuut-*tersection, is rhe, and the concept in which they both areptual union, is the concept of ,androgyne,,, formal concept analysis (Ganter A Wltters of sets of attributes and sets of thinss.

the hierarchicar order, is then defi ned o, ;H"J|i f;:":'.",1ff:ffi:iffi ::J',##between a set of things (or u r"t of attributes).of the concepts. fhe resultingconceptual structure forms a complete rattice, and is called u "on""pt

lattice. Thus,although they are talking about concepts, they are dealing with them only in terms ofextensional set theory, not intensional concepi theory.

one of the crucial differences between extensionality and intensionality is that inextensionality a collection is determined by its elements, whereas in rntensionality acollection is determined by a concept, a property, an attribute, etc. Now intensionalnotions (e.g. concepts) are not strictiy formai notions, and it would be misleading totake these as subjects of study for logic only, since logic is concerned with the formsof propositions as distinct from their contents. perhaps only par-t of the theory ofintensionality which can be called formal is pure modai logic'and its possible worldssemantic. However, in concept theories based on possible-worlds semannc, (see e.g.

Hintikkare defiworlds,more elbeing rpresenticontenn

Thus, theidea of thfor all corconcept tlultimately

Conclus

In this painformaticconslstlngmodel, arinformaticconcepfuathe objectand creatrepresentsthe founda

AcknowledgKawakuchiBases, Kriplcontext ofin

tnfonnation Systems

cepts are entities such as

to which concepts are, especially the ability to

both the entity and theto be a concept, must becriteria. This is called al be closed is called theparticular conceptions ofhatever form these take,ntage of this approach isany parlicular theory ofial characteristics.

ral structures. The mostnment relation, which isssalo I 992193, Palomrikiconcepfual containment

constituents of concepts,nment, (Palomlki 1997,

nostly based on the set'r example. according toI concepts of 'man' ands the concept ol"adult '.ns both the concepts ofrtual intersection, is thein which they both areconcept of 'androgyne',

rnalysis (Ganter & Wille:utes and sets of things,)etween concepts, calledteoretical subset relationconcepts. The resultinga concept lattice. Thus,th them only in terms of

intensionality is that inrereas in intensionality aLte, etc. Now intensionalwould be misleading tooncemed with the formsly part of the theory of; and its possible worldsorlds semantic, (see e.g.

J. Palomtiki tutd M. RarLitevil / Concept Theory in tlrc Corilert o.f lrtlorntutirnt Systents 327

Hintikka 1969, Montague 1974, Palomiiki l99l,Matena 1998), intensional notionsare defined as (possibly partial, but indeed set-theoretical) functions from the possibleworlds to extensions in those worlds. In these approaches intensional notions are oncemore either reduced to extensional set-theoretic constnrcts in diversity of worlds or asbeing non-logical notions left unexplained. So, when developing an adequatepresentation of a concept theory it has to take into account both formal (logic) andcontentual (epistemic) aspects of concepts and their relationships.

_- : t::Ll

Figure 6. Conceptual Modelling 2.

Thus, the foundation of conceptual modelling is based on a concept theory, where theidea of the concept of a concept and the relations between concepts seryes as the basisfor all conceptual modelling, and all conceptual structures are ultimately reducible toconcept theory, which is to be understood in the similar way as "all mathematics isultimately reducible to set theory".

Conclusion

In this paper the role and the proper place of a concept theory in the context ofinformation systems was proposed. First, we defined the basic modelling situationconsisting of objects to be rnodelled, a modeller, i.e. a person who is modelling, amodel, and the relationships between these. In this context we described aninformation system. Having described information systems we were consideringconceptual modelling process, the goal of which is to develop a conceptual schema ofthe object domain. A conceptual schema is a physical part of an information system,and creating a conceptual schema presupposes a conceptual model, which itrepresents and is based on. In this context the place ofa concept theory was found asthe foundational basis for all conceptual modelling.

Acknowledgement: This paper was inspired by the "simple" question put forward by Professor EijiKawakuchi at the l2'n European-Japanese Conference on Information Modelling and KnowledgeBases, Krippen, Germany, 27.-30.05.2002, which concerned the status of a concept theory in thecontext of information systems.

328 J. Palomciki uruL M. Radiievit / Concept T'heory irt the C1ntext ol InJormatirtn Systerns

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