support integrated use of models, the language and construct descriptions and their representation mappings into the common ontology are not enough. UEML must also offer ways to identify and manage correspondences among language constructs and among model elements. In addition to supporting integrated use of models, identifying and managing correspondences can also help validating the representation mapping and eliminating ontology redundancy.
Construct correspondence refers to whether constructs refer to distinct, related, overlapping or identical states of affairs in the problem domain. The UEML work has so far considered three kinds of correspondence, described as follows:
- Equality: Occurs when two or more constructs represent the same state of affairs, as under "Language Description". If two constructs are equal, one can replace the other, e.g., during model-to-model translation.
- Containment: Occurs when the state of affairs represented by one construct has the state of affairs represented by another as a part. When one construct contains several others, the former may have to be replaced by the others during model-to-model translation.
- Generalisation: Occurs when one modelling construct represents a state of affairs that generalises the state of affairs represented by another construct. If one construct generalises another, the general construct can replace the special one in a model-to-model translation (with loss of information), but the inverse replacement may not be appropriate.
Of course these kinds of simple correspondences are not independent. Equal constructs will trivially contain and generalise one another. There are also complex correspondences, such as when one construct represents a state of affairs that generalises a part of the state of affairs represented by another, thus combining containment and generalisation. There are also overlapping constructs, each of which contains part, but not all, of the other. A complete typology of correspondence kinds and how they combine stills needs to be worked out.
The three kinds of correspondences between constructs can be precisely formulated in terms of the ontology classes, properties, states and transformations onto which the constructs have been mapped: The constructs are equal if they are mapped onto the exact same concepts in the ontology and these concepts also play the exact same roles in relation to one another. A construct contains another if the ontology concepts represented by the former form a superset of the concepts represented by the latter and if the relationship roles match too. Finally, one construct generalises another if the ontology concepts represented by the former generalise the concepts represented by the latter and if their relationship roles match.
Hence we can identify correspondences with different degrees of precision. It is possible to only take into account how each construct is mapped onto ontology concepts, ignoring which relationships between concepts that each construct represents. More precise correspondences can be identified by taking into account both ontology concepts and the relationships between them, but ignoring the roles that concepts may play in the relationships. Most precisely, both ontology concepts, the relationships between them and the roles played in relationships can be taken into account.
Specific techniques for integrated model use, such as consistency checking, automatic update reflection and model-to-model translation across languages, still have to be developed for UEML and implemented in UEMLBase?. As a preparation, work is in progress on deriving measures of correspondence between pairs of modelling constructs. The measures are inspired by measures used to compare objects in the areas of classification theory and knowledge engineering (Lin, 1998), (Rodręguez & Egenhofer, 2003), (Blanchard, Kuntz, Harzallah & Briand, 2006).
Correspondence measures may be useful for validating the representation mappings and the common ontology. Correspondence measures derived automatically from the common ontology can be compared to expert estimates of the same correspondences. Deviations indicate either that the representation mapping is wrong for a construct or that the common ontology is not optimally organised. The two can also occur together, when the representation mapping is wrong because there are concepts missing from the common ontology. Another ontology problem that can be detected is missing relationships between ontology concepts, e.g., a missing generalisation relationship from a sub- to a superclass. If left undetected, missing relationships can lead to redundancies in the common ontology when the subclass is added again as a specialisation of the superclass. In this way, correspondence measures can also aid eliminating ontology redundancy.
Correspondence measures may also be useful as high-level guides for model-to-model translation and similar cross-language services. The representation mappings and common ontology provide the details for how to translate between modelling constructs belonging to different languages, as soon as the pair of modelling constructs to translate between have been decided. But it offers less help with selecting which constructs in one language to translate into which other constructs in the other one in the first place. The correspondence measures potentially aid this language-level issue by indicating, for each construct in a language, which constructs in the other language are most suitable as targets for, e.g., translation, leaving the final choice to the model manager. When the language-level construct-to-construct correspondences have been established in this way, the representation mapping and common ontology will support the detailed construct-level mappings.
References
- Blanchard E., Kuntz P., Harzallah M. and Briand H. (2006). A tree-based similarity for evaluating concept proximities in an ontology. In Proceedings of 10th conference of the International. Federation of Classification Society. Springer, pp.311.
- Lin D. (1998). An information-theoretic definition of similarity. In Proceedings of the 15th international conference on machine learning. Morgan Kaufmann, pp. 296304.
- Rodręguez M., Egenhofer M (2003). Determining semantic similarity among entity classes from different ontologies. IEEE Transactions on Knowledge and Data Engineering, 15(2), pp. 442456.