Conceptual Modelling Languages

Abstract

Tutkimuksessa "Conceptual modelling languages" tarkastellaan käsitteellisessa mallintamisessa käytettäviä ns. mallinnuskieliä, niiden ilmaisuvoimaa ja soveltuvuutta mallinnustehtäviin.

Käsitteellinen mallintaminen tarkoittaa kohdealueen kuvaamista ja esittämistä käsitekaaviona. Standardijärjestö ISOn työryhmän suosituksen mukaisesti käsitekaaviossa tulisi olla vain kohteen käsitteellisesti relevantti sisältö ilman tekniseen tiedon esittämiseen liittyviä seikkoja. Käsitekaavio tulee kuitenkin ilmaista jollain (formaalilla) kielellä, jotta sen perusteella voidaan esim. laatia tietokoneohjelmisto tai tietokanta. Tällaista ns. ulkoistettua käsitekaaviota tarkasteltaessa on oleellista että formalismin semantiikka, ts. siinä käytettävien symbolien merkitys, on tarkkaan kiinnitetty. Muussa tapauksessa on vaikeaa sanoa onko kuvaamisessa tai implementaatiossa tapahtunut virheitä.

Jotkut formalismit, intensionaaliset mallintamiskielet, ovat suuntautuneet erityisesti kohdealueen käsitteiden ja niiden välisten suhteiden esittämiseen. Toinen, perinteisempi lähestymistapa (ekstensionaaliset kielet) käyttää kuvaamiseen enemmän logiikkaa ja joukko-oppia. Tutkimuksessa vertaillaan molemmille lähestymistavoille perustuvia kieliä ja osoitetaan niiden etuja ja rajoituksia. Esitämme myös joitakin menetelmiä erään intensionaalisen mallintamiskielen kaavioiden kääntämiseksi tunnetulle IFO-formalismille.

Tutkimuksen pääasialliset tulokset ja hyödynnettävyys liittyvät käsitekielten evaluointiin ja esitettyihin parannuksiin, jotka tarkentavat kielten semantiikkaa.

Conceptual modelling is needed to form a description of the domain of application at hand. In order to express the result of conceptual modelling, we need a modelling language. First order predicate logic (FOPL) or its variants (like Horn-clauses and Description Logics) and extensions (second order logics) can form a backbone of such a language, but some criteria is needed to define the fruitfulness or suitability of a modelling language, given the modelling task. The modelling language together with its methodology constitute a modelling perspective.

Many accounts of conceptual modelling emphasise an intensional perspective. This means that the starting point in conceptual modelling is the contents of the concepts that subsist in the domain of application (as opposed to ``things'' in the domain of application -- they belong to the extensions of these concepts). If an intensional perspective is used, it should be visible in the modelling language as well; therefore we divide modelling languages into intensional and extensional languages, and ``hybrid'' languages that combine some aspects of these two.

First order predicate logic has often been used as an example of a language with a well established extensional semantics. We examine FOPL as a modelling language in connection with Sowa's Conceptual Graphs (CGs). It can be demonstrated that a limited version of the language of CGs is equal (in expressive power) to that of FOPL with unary and binary predicates. However, contrary to the claims of proponents of CGs, CG presentations are not necessarily easier to read or understand than the same presentations expressed in FOPL (as can be demonstrated by comparing ``typical'' but complex FOPL formulas and their CG counterparts).

Kauppi's concept calculus is based on concepts and the relation of intensional containment. An approach where a modelling language is based completely on concept calculus is presented in this thesis. This approach has the advantage that the user can apply the operations of the calculus when designing a conceptual schema of the domain of application. However, this sort of modelling can be restrictive and impractical in many cases, since it enforces rather strict concept structures. CONCEPT D, a modelling language, can be seen as a less restrictive alternative.

Using CONCEPT D, the modeller reports the results of the modelling task in the form of concept diagrams. But we often need to ask ``is this concept diagram correct'' or ``does it correspond well to the domain of application''. Without semantics (which connects the diagrams to something extra-linguistic) we can only answer these questions on the basis of our intuitions. We address these questions from two different angles. First we demonstrate how to map (simplified) CONCEPT D concept diagrams into IFO schemata that have well-defined semantics.

Then we study what kind of semantical theory (e.g. possible world semantics, situation semantics, HIT-semantics) would capture the features that we want to express in concept diagrams. CONCEPT D has been rarely used in applications where it would be important to make a distinction between, for example,prime number less than one and round square, but is has the capability of making these distinctions. Therefore, it seems that it needs semantics ``fine-grained'' enough. Finally, we discuss, based on the previous chapters, on what premises HIT-semantics would serve as the semantical background of conceptual modelling.