The aim of this breakout session was to chart the landscape of existing approaches
for representing mappings between heterogeneous models, identify common
ideas and formulate research questions to be addressed in the future. In the
session, the discussion mainly concerned three aspects: The nature of mappings,
existing proposals for mappings and open research questions

Breakout Sessions

Stuckenschmidt, Heiner

Uschold, Michael

Dagstuhl Research Online Publication Server

Representation of Semantic MappingsResults from the Breakout SessionHeiner Stuckenschmidt1, Mike Uschold21Vrije Universiteit Amsterdam2Boeing Phantom Works, SeattleThe aim of this breakout session was to chart the landscape of existing ap-proaches for representing mappings between heterogeneous models, identify com-mon ideas and formulate research questions to be addressed in the future. In thesession, the discussion mainly concerned three aspects: The nature of mappings,existing proposals for mappings and open research questions.1 The Nature of MappingsWhen talking about the nature of mappings it quickly turned out that the natureof mappings is not understood well enough to come up with a definition of whata mapping is. Instead, a number of questions about the nature of mappings wereformulated that illustrate the design space of mapping approaches.What do Mappings define ? The first question to be answered about a mappingis the way it establishes a relation between two models. The basic distinctionthat can be made here is between operational and declarative specifications ofrelations. Operational approaches describe the procedure of translating elementsfrom one model into the other. An example of an operational specification is theuse of re-write rules. Declarative specifications define constraints on the jointinterpretation of the two models. This is normally done in terms of logical axiomsthat contain elements from different models.What do Mappings preserve ? It is normally assumed that mappings preserve the’meaning’ of of the two models in the sense that the semantic relation betweenthe intended interpretations of connected elements is the one specified in themapping. A problem with this assumption is that it is virtually impossible toverify this property. Instead, there are a number of verifiable formal propertiesthat mappings can be required to satisfy. Examples of such formal propertiesare the satisfiability of the overall model, preservation of possible inferences orthe preservation of answers to queries. Often such properties can only be statedrelative to a given application context, such as a set of queries to be answeredor a set of tasks to be solved.What do Mappings connect ? There are many different kinds of models thatwe might want to connect with semantic mappings (database schemas, thesauri,ontologies, ...) and even more languages for representing these models. Given thisDagstuhl Seminar Proceedings 04391Semantic Interoperability and Integrationhttp://drops.dagstuhl.de/opus/volltexte/2005/53variety, it is not clear what mappings should actually connect. The most generalapproach is to define mappings between arbitrary statements in the languagesused in the connected models. This is not always feasible as complexity issuesmight make it necessary to restrict the kinds of statements that can be mappedto a subset of the language. A general question is also whether it makes sense atall to make mappings language dependent. An alternative is to specify mappingsindependent of a particular logic – this can be achieved by defining mappingsbetween the signatures of models – or even independent of the representationsyntax by mapping between identifiers independent of what kind of element theyrepresent.How are Mappings organized ? The final question is how mappings are orga-nized. They can either be part of a given model or specified independently. Inthis case the question is how to distinguish between mappings and other ele-ments in the models. Mappings can be uni- or bidirectional. Further it has tobe defined whether a set of mappings is normative or whether it is possible tohave different sets of mappings according to different applications, viewpoints ordifferent matchers.2 Available Tools and TechnologiesAnother question is about the availability of mapping technology that is availablefor use today. This question is not only of great practical relevance, but is alsonecessary to identify open problem and set a research agenda.2.1 OWL and RelativesAn obvious choice is to first look at current developments in the area of the se-mantic web, where mapping between semantic models is one of the most pressingproblems. The Web Ontology Language (OWL) indeed contains a number of el-ements that can be used to define semantic relations between elements fromdifferent models. It is possible, for example to state that two instances relations,or concepts are the same or different or to define a concept to be more specificor more general than a concept in another model. This can be sufficient for somepurposes, but there are also shortcomings of the direct use of OWL constructs fordefining mappings. One of the short comings is that OWL constructs are limitedto defining abstract relations, but they cannot be used to define transformationson data. This gap will probably be closed by the introduction of the semanticweb rule language which is currently under development. Another problem withthe way OWL treats mappings in that it takes an ’all or nothing’ approach tothe import of external axioms. In particular, mapped concepts are only treateda simple names unless the corresponding ontology is imported. Importing anontology, however, leaves no control over which statements are important andwhich not. This can be a problem when trying to map models with a high degreeof heterogeneity because it is likely that the overall model will be inconsistent.2The recently proposed C-OWL language offers a solution to this problem by in-troducing explicit mappings between OWL models. The mappings are stored inseparate files thus keeping the mapped ontologies independent. A special seman-tics for mapping rules allows the selective use of external knowledge and evenallows to use information from ontologies that are inconsistent with one another.Another shortcoming that is currently not addressed in any of the approaches isthe inability to define the strength of mappings.2.2 Other ApproachesOver the excitement connected with Semantic Web technologies, the wide rangeof other existing mapping technologies is in danger of being ignored. Neverthe-less, there are a number of mapping languages that have been used in application.Many of these languages have their origin in the database community. Examplesof such languages are:– datalog– F-Logic– DLRBesides these database-related technologies there are a number of approachesthat use general first order logic axioms or other expressive knowledge repre-sentation languages such as KIF or LOOM. We can observe that all of theseapproaches are more or less subsets of first order logic, however, we have to ac-knowledge that mappings do not necessarily have to be specified in logic. Thereare also transformation languages such as XSLT are available for specifying se-mantic mappings.3 Open Problems and Research DirectionsWhile languages for representing semantic models have been studied intensivelyin the past, work on mappings is in a very preliminary stage. Existing proposalsfor mapping languages have a number of serious limitations. We identified anumber of challenging topics that should addressed in future research.Language Heterogeneity Despite the tendency of standardizing languages forrepresenting semantic models, one of the most pressing problems is still thetranslation between models encoded in different languages. The challenge is toprovide translations with guaranteed formal properties. First results have beenachieved in this direction using theory of institutions that describes differentlogics in a uniform way.The Nature of Semantic Relations Most existing mapping approach use a verylimited set of semantic relations that can hold between elements from different3models. In particular implication and equivalence are frequently used. Many re-alistic setting, however, demand for richer relations such as inconsistency, effect-cause relations or overlap. Very limited work exists on approaches for measuringthe degree of relatedness specified by a mapping. This is in particular importantwhen mappings are created by automatic mapping tools. A very specific problemwith respect to semantic relations is the definition of semantic relations betweenmodels that describe the domain of interest at different levels of abstraction.Mappings as first Class Citizen A general observation about the state of the artof mapping representations is that mappings are not yet considered to be firstclass entities in semantic models. While most approaches agree on elements suchas concepts relations and instances, mappings are not yet an agreed elementof semantic modelling. Our conclusion is that this attitude has to change. Inorder to make advancements in mapping technologies, we need specialized toolsthat support the creation and maintenance of mappings. Important operationson mappings such as reasoning about, retrieving and composing mappings arecurrently not supported.A Framework for Comparing Mappings A very concrete research task is to designa common framework for comparing existing mapping approaches. It is probablynot possible to find a framework that us sufficiently concrete and still coversall possible approaches. A promising restriction is to only consider declarativemappings. As mentioned above, most of these approaches are related to firstorder logic, we can hope to find a logical framework that captures most existingapproaches.4

Representation of Semantic Mappings

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Representation of Semantic Mappings

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