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Modularity of Ontologies in an Arbitrary Institution

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Logic, Rewriting, and Concurrency

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9200))

Abstract

The notion of module extraction has been studied extensively in the ontology community. The idea is to extract, from a large ontology, those axioms that are relevant to certain concepts of interest (formalised as a subsignature). The technical concept used for the definition of module extraction is that of inseparability, which is related to indistinguishability known from observational specifications.

Module extraction has been studied mainly for description logics and the Web Ontology Language \(\mathsf {OWL}\). In this work, we generalise previous definitions and results to an arbitrary inclusive institution. We reveal a small inaccuracy in the formal definition of inseparability, and show that some results hold in an arbitrary inclusive institution, while others require the institution to be weakly union-exact.

This work provides the basis for the treatment of module extraction within the institution-independent semantics of the distributed ontology, modeling and specification language (DOL), which is currently under submission to the Object Management Group (OMG).

T. Mossakowski This work has been partially supported by the Future and Emerging Technologies (FET) programme within the Seventh Framework Programme for Research of the European Commission, FET-Open Grant number: 611553, project COINVENT.

A. Tarlecki This work has been partially supported by the National Science Centre, grant 2013/11/B/ST6/01381.

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Notes

  1. 1.

    http://ihtsdo.org/snomed-ct/.

  2. 2.

    http://www.opengalen.org/.

  3. 3.

    \(\mathbb Set\) is the category having sets as objects and functions as arrows.

  4. 4.

    \(\mathbb Cat\) is the category of categories and functors. Strictly speaking, \(\mathbb Cat\) is a quasicategory (which is a category that lives in a higher set-theoretic universe).

  5. 5.

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

  6. 6.

    Even though we use the same term as in [9], since the overall idea is the same, on one hand, some of our assumptions here are weaker than in [9], and on the other hand, we require a bit more structure on the category of signatures.

  7. 7.

    That is, for any family of signatures \(\mathbb {S}\subseteq |\mathbf {Sign}|\),  \(\mathbf {Sen}(\bigcap \mathbb {S})=\bigcap _{\varSigma \in \mathbb {S}}\mathbf {Sen}(\varSigma )\).

  8. 8.

    That is, we have a model functor  \(\mathbf {Mod}:\mathbf {Sign}^{op}\rightarrow \mathbb {IC}at\), where \(\mathbb {IC}at\) is the (quasi)category of inclusive categories and inclusive functors.

  9. 9.

    This remains true even if \(\mathcal {I} \) varies over models of arbitrary signatures, which seems to be a widespread understanding in the ontology modularity community. Note that \(\mathcal {I} \models \,\mathcal {O}\) still entails that \(\mathcal {I} \) interprets at least the symbols occurring in \(\mathcal {O}\).

References

  1. Basin, D.A., Clavel, M., Meseguer, J.: Reflective metalogical frameworks. ACM Trans. Comput. Log. 5(3), 528–576 (2004)

    Article  MathSciNet  Google Scholar 

  2. Boronat, A., Knapp, A., Meseguer, J., Wirsing, M.: What Is a multi-modeling language? In: Corradini, A., Montanari, U. (eds.) WADT 2008. LNCS, vol. 5486, pp. 71–87. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  3. Cerioli, M., Meseguer, J.: May I borrow your logic? (transporting logical structures along maps). Theor. Comput. Sci. 173, 311–347 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  4. Clavel, M., Meseguer, J.: Reflection in conditional rewriting logic. Theor. Comput. Sci. 285(2), 245–288 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Diaconescu, R., Goguen, J.A., Stefaneas, P.: Logical support for modularisation. In: 2nd Workshop on Logical Environments, pp. 83–130. CUP, New York (1993)

    Google Scholar 

  6. Paul, D., Valentina, T., Luigi, I.: Ontology module extraction for ontology reuse: An ontology engineering perspective. In: Proceedings of the Sixteenth ACM Conference on Conference on Information and Knowledge Management, CIKM 2007, pp. 61–70, New York, NY, USA. ACM (2007)

    Google Scholar 

  7. Durán, F., Meseguer, J.: Structured theories and institutions. Theor. Comput. Sci. 309(1–3), 357–380 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. Goguen, J.A., Burstall, R.M.: Institutions: abstract model theory for specification and programming. J. Assoc. Comput. Mach. 39, 95–146 (1992). (Predecessor. LNCS 164, (221–256) (1984))

    Article  MathSciNet  MATH  Google Scholar 

  9. Goguen, J., Roşu, G.: Composing hidden information modules over inclusive institutions. In: Owe, O., Krogdahl, S., Lyche, T. (eds.) From Object-Orientation to Formal Methods. LNCS, vol. 2635, pp. 96–123. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  10. Kontchakov, R., Wolter, F., Zakharyaschev, M.: Logic-based ontology comparison and module extraction, with an application to DL-Lite. Artif. Intell. 174(15), 1093–1141 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Lucas, S., Meseguer, J.: Localized operational termination in general logics. In: De Nicola, R., Hennicker, R. (eds.) Wirsing Festschrift. LNCS, vol. 8950, pp. 91–114. Springer, Heidelberg (2015)

    Google Scholar 

  12. Martí-Oliet, N., Meseguer, J., Palomino, M.: Theoroidal maps as algebraic simulations. In: Fiadeiro, J.L., Mosses, P.D., Orejas, F. (eds.) WADT 2004. LNCS, vol. 3423, pp. 126–143. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  13. Meseguer, J.: General logics. In: Logic Colloquium 87, pp. 275–329. North Holland (1989)

    Google Scholar 

  14. Meseguer, J.: Membership algebra as a logical framework for equational specification. In: Presicce, F.P. (ed.) WADT 1997. LNCS, vol. 1376, pp. 18–61. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  15. Meseguer, J., Martí-Oliet, N.: From abstract data types to logical frameworks. In: Astesiano, E., Reggio, G., Tarlecki, A. (eds.) Recent Trends in Data Type Specification. LNCS, vol. 906, pp. 48–80. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  16. Mossakowski, T., Codescu, M., Neuhaus, F., Kutz, O.: The distributed ontology, modeling, and specification language - DOL. In: Koslow, A., Buchsbaum, A. (eds.) The Road to Universal Logic, volume II of Studies in Universal Logic, pp. 498–520. Springer, Switzerland (2015)

    Google Scholar 

  17. Mossakowski, T., Kutz, O., Codescu, M., Lange,C.: The distributed ontology, modeling and specification language. In: Del Vescovo, C.., Hahmann, T., Pearce, D., Walther, D. (eds.) WoMo 2013, CEUR-WS Online Proceedings, vol. 1081 (2013)

    Google Scholar 

  18. Mossakowski, T., Kutz, O., Lange, C.: Semantics of the distributed ontology language: institutes and institutions. In: Martí-Oliet, N., Palomino, M. (eds.) WADT 2012. LNCS, vol. 7841, pp. 212–230. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  19. Palomino, M., Meseguer, J., Martí-Oliet, N.: A categorical approach to simulations. In: Fiadeiro, J.L., Harman, N.A., Roggenbach, M., Rutten, J. (eds.) CALCO 2005. LNCS, vol. 3629, pp. 313–330. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  20. Sannella, D., Tarlecki, A.: Specifications in an arbitrary institution. Inf. Control 76, 165–210 (1988). (Earlier version in Proceedings, International Symposium on the Semantics of Data Types, LNCS, vol. 173. Springer (1984))

    MathSciNet  MATH  Google Scholar 

  21. Sannella, D., Tarlecki, A.: Foundations of Algebraic Specification and Formal Software Development. Monographs in Theoretical Computer Science. An EATCS Series. Springer, Berlin (2012)

    Book  MATH  Google Scholar 

  22. Santiago, S., Escobar, S., Meadows, C., Meseguer, J.: A formal definition of protocol indistinguishability and its verification using maude-NPA. In: Mauw, S., Jensen, C.D. (eds.) STM 2014. LNCS, vol. 8743, pp. 162–177. Springer, Heidelberg (2014)

    Google Scholar 

  23. Schneider, M., Rudolph, S., Sutcliffe, G.: Modeling in OWL 2 without restrictions. In: Rodriguez-Muro, M., Jupp, S., Srinivas, K. (eds.) Proceedings of the 10th International Workshop on OWL: Experiences and Directions (OWLED 2013) Co-located with 10th Extended Semantic Web Conference (ESWC 2013), Montpellier, France, 26–27 May 2013, CEUR Workshop Proceedings, vol. 1080. CEUR-WS.org (2013)

    Google Scholar 

  24. Schröder, L., Mossakowski, T., Tarlecki, A., Klin, B., Hoffman, P.: Amalgamation in the semantics of CASL. Theor. Comput. Sci. 331(1), 215–247 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  25. Seidenberg, J., Rector, A.L.: Web ontology segmentation: analysis, classification and use. In: Carr, L., De Roure, D., Iyengar, A., Goble, C.A., Dahlin, M. (eds.) Proceedings of the 15th international conference on World Wide Web, WWW 2006, pp. 13–22, Edinburgh, Scotland, UK, 23–26 May 2006. ACM (2006)

    Google Scholar 

  26. Stuckenschmidt, H., Klein, M.: Structure-based partitioning of large concept hierarchies. In: McIlraith, S.A., Plexousakis, D., van Harmelen, F. (eds.) ISWC 2004. LNCS, vol. 3298, pp. 289–303. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  27. Stuckenschmidt, H., Parent, C., Spaccapietra, S. (eds.): Modular Ontologies: Concepts, Theories and Techniques for Knowledge Modularization. LNCS, vol. 5445. Springer, Heidelberg (2009)

    MATH  Google Scholar 

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Acknowledgement

We thank Thomas Schneider for discussions and feedback.

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Bremen, Bremen, Germany

    Yazmin Angelica Ibañez

  2. Faculty of Computer Science, Otto-von-Guericke University of Magdeburg, Magdeburg, Germany

    Till Mossakowski

  3. Laboratory for Foundations of Computer Science, University of Edinburgh, Edinburgh, UK

    Donald Sannella

  4. Institute of Informatics, University of Warsaw, Warsaw, Poland

    Andrzej Tarlecki

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  1. Yazmin Angelica Ibañez
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Editors and Affiliations

  1. Universidad Complutense de Madrid, Madrid, Spain

    Narciso Martí-Oliet

  2. University of Oslo, Oslo, Norway

    Peter Csaba Ölveczky

  3. SRI International, Menlo Park, California, USA

    Carolyn Talcott

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Ibañez, Y.A., Mossakowski, T., Sannella, D., Tarlecki, A. (2015). Modularity of Ontologies in an Arbitrary Institution. In: Martí-Oliet, N., Ölveczky, P., Talcott, C. (eds) Logic, Rewriting, and Concurrency. Lecture Notes in Computer Science(), vol 9200. Springer, Cham. https://doi.org/10.1007/978-3-319-23165-5_17

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  • DOI: https://doi.org/10.1007/978-3-319-23165-5_17

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