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
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- 2.
- 3.
\(\mathbb Set\) is the category having sets as objects and functions as arrows.
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\(\mathbb Cat\) 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.
That is, with the same objects as the original category.
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- 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.
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.
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 \(\mathcal {O}\).
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We thank Thomas Schneider for discussions and feedback.
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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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