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The Distributed Ontology, Modeling and Specification Language – DOL

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The Road to Universal Logic

Part of the book series: Studies in Universal Logic ((SUL))

Abstract

There is a diversity of ontology languages in use, among them \(\mathsf{OWL}\), RDF, OBO, Common Logic, and F-logic. Related languages such as UML class diagrams, entity-relationship diagrams and object role modeling provide bridges from ontology modeling to applications, e.g., in software engineering and databases. Also in model-driven engineering, there is a diversity of diagrams: UML consists of 15 different diagram types, and SysML provides further types. Finally, in software and hardware specification, a variety of formalisms are in use, like Z, VDM, first-order logic, temporal logic etc.

Another diversity appears at the level of ontology, model and specification modularity and relations among ontologies, specifications, and models. There is ontology matching and alignment, module extraction, interpolation, ontologies linked by bridges, interpretation and refinement, and combination of ontologies, models and specifications.

The distributed ontology, modeling and specification language (DOL) aims at providing a unified metalanguage for handling this diversity. In particular, DOL provides constructs for (1) ‘‘as-is’’ use of ontologies, models, and specifications (OMS) formulated in a specific ontology, modeling or specification language, (2) OMS formalized in heterogeneous logics, (3) modular OMS, (4) mappings between OMS, and (5) networks of OMS. This chapter sketches the design of the DOL language. DOL has been submitted as a proposal within the OntoIOp (ontology, model, specification integration and interoperability) standardisation activity of the object management Group (OMG).

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Notes

  1. 1.

    DOL has formerly been standardized within ISO/TC 37/SC 3. The OntoIOp (ontology, modeling and specification integration and interoperability) activity is now being continued at OMG, see the project page at http://ontoiop.org.

  2. 2.

    See http://ifipwg13.informatik.uni-bremen.de

  3. 3.

    The languages that we call ‘‘basic’’ OMS languages here are usually limited to one logic and do not provide meta-theoretical constructs.

  4. 4.

    \(\mathbb{S}et\) is the category having all sets as objects and functions as arrows.

  5. 5.

    \(\mathbb{C}at\) is the category of categories and functors. Strictly speaking, \(\mathbb{C}at\) is not a category but only a so-called quasicategory, which is a category that lives in a higher set-theoretic universe.

  6. 6.

    That is, with the same objects as the original category.

  7. 7.

    Note that extension, union, translation, reference, qualification and combination are defined for flattenable and elusive OMS, while interpolate/forget and extract are only defined for flattenable OMS.

  8. 8.

    This is a mathematically abstracted version of DOL. In reality, signatures are represented by symbol sets, and signature morphisms by symbol maps. The details of passing from symbol sets (resp. maps) to signatures (resp. signature morphisms) are left out here. Also, we have left out OMS bridges, since their design is still being discussed.

  9. 9.

    The theory of O, written, \(\mathbf{Th}(O)\), is the closure of \(\mathbf{Ax}(O)\) under logical entailment. Note, however, that throughout the text we use ‘‘theory’’ also more informally as denoting some set of axioms in a particular signature and logic.

  10. 10.

    I is normally determined by the context of the enclosing library and passed around as an additional parameter of the semantics. For simplicity, here we let I become part of the basic OMS.

  11. 11.

    Note that not all OMS can be downloaded by dereferencing their IRIs. Implementing a catalogue mechanism in DOL-aware applications might remedy this problem.

  12. 12.

    Some of the following listings abbreviate IRIs using prefixes but omit the prefix bindings for readability.

  13. 13.

    While owl:same as is borrowed from the vocabulary of \(\mathsf{OWL}\), it is commonly used in the RDF logic to link to resources in external graphs, which should be treated as if their IRI were the same as the subject’s IRI.

  14. 14.

    We assume that GALEN is available as an OWL ontology.

  15. 15.

    If this smallest signature does not exist, the semantics is undefined.

  16. 16.

    Interpolants need not always exist, and even if they do, tools might only be able to approximate them.

  17. 17.

    In practice, one looks for a finite subset that still is logically equivalent to this set. Note that \(\Updelta^{\bullet}\) is the set of logical consequences of \(\Updelta\), i.e. \(\Updelta^{\bullet}=\mathbf{Th}(\Updelta)\).

  18. 18.

    If the smallest such subtheory does not exist, the semantics is undefined. In [22], it is shown that it does exist in usual institutions.

  19. 19.

    Note that the resulting module can still contain symbols from \(\Upsigma\), because the resulting signature may be enlarged.

  20. 20.

    Note that BioPortal’s [40] mappings are correspondences in the sense of the Alignment API and hence of DOL. BioPortal only allows users to collect correspondences, but not to group them into alignments. In a sense, for each pair of ontologies, all BioPortal users contribute to a big alignment between these.

  21. 21.

    Ontohub’s sources are freely available at https://github.com/ontohub/ontohub.

  22. 22.

    Some (but only few) of DOL’s features are still being implemented at the time of the writing of this chapter.

  23. 23.

    ‘‘Linked data’’ is a set of best practises for publishing structured data on the Web in a machine-friendly way [1]. DOL and Ontohub conform with linked data.

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Acknowledgment

The development of DOL is supported by the German Research Foundation (DFG), Project I1-[OntoSpace] of the SFB/TR 8 ‘‘Spatial Cognition.’’ The project COINVENT acknowledges the financial support of the Future and Emerging Technologies (FET) programme within the Seventh Framework Programme for Research of the European Commission, under FET-Open Grant number: 611553. The authors would like to thank the OntoIOp working group for their valuable input, particularly Michael Grüninger, Maria Keet, Christoph Lange, and Peter Yim. We also want to thank Yazmin Angelica Ibañez, Thomas Schneider and Carsten Lutz for valuable input on interpolation and module extraction.

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Authors and Affiliations

  1. Institute of Knowledge and Language Engineering, Otto-von-Guericke-University Magdeburg, Magdeburg, Germany

    Till Mossakowski, Mihai Codescu & Fabian Neuhaus

  2. KRDB Research Centre for Knowledge and Data, Free University of Bozen-Bolzano, Bozen-Bolzano, Italy

    Oliver Kutz

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  1. Till Mossakowski
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Correspondence to Till Mossakowski .

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  1. City University of New York, New York, New York, USA

    Arnold Koslow

  2. Federal University of Santa Catarina, Florianópolis, Santa Catarina, Brazil

    Arthur Buchsbaum

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Mossakowski, T., Codescu, M., Neuhaus, F., Kutz, O. (2015). The Distributed Ontology, Modeling and Specification Language – DOL. In: Koslow, A., Buchsbaum, A. (eds) The Road to Universal Logic. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-15368-1_21

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