**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32920

##### Merging and Comparing Ontologies Generically

**Authors:**
Xiuzhan Guo,
Arthur Berrill,
Ajinkya Kulkarni,
Kostya Belezko,
Min Luo

**Abstract:**

Ontology operations, e.g., aligning and merging, were studied and implemented extensively in different settings, such as, categorical operations, relation algebras, typed graph grammars, with different concerns. However, aligning and merging operations in the settings share some generic properties, e.g., idempotence, commutativity, associativity, and representativity, which are defined on an ontology merging system, given by a nonempty set of the ontologies concerned, a binary relation on the set of the ontologies modeling ontology aligning, and a partial binary operation on the set of the ontologies modeling ontology merging. Given an ontology repository, a finite subset of the set of the ontologies, its merging closure is the smallest subset of the set of the ontologies, which contains the repository and is closed with respect to merging. If idempotence, commutativity, associativity, and representativity properties are satisfied, then both the set of the ontologies and the merging closure of the ontology repository are partially ordered naturally by merging, the merging closure of the ontology repository is finite and can be computed, compared, and sorted efficiently, including sorting, selecting, and querying some specific elements, e.g., maximal ontologies and minimal ontologies. An ontology Valignment pair is a pair of ontology homomorphisms with a common domain. We also show that the ontology merging system, given by ontology V-alignment pairs and pushouts, satisfies idempotence, commutativity, associativity, and representativity properties so that the merging system is partially ordered and the merging closure of a given repository with respect to pushouts can be computed efficiently.

**Keywords:**
Ontology aligning,
ontology merging,
merging system,
poset,
merging closure,
ontology V-alignment pair,
ontology
homomorphism,
ontology V-alignment pair homomorphism,
pushout.

**References:**

[1] J. Euzenat and P. Shvaiko, Ontology Matching, 2nd ed. Springer, 2013.

[2] A. Zimmermann, M. Krotzsch, J. Euzenat, and P. Hitzler, “Formalizing ontology alignment and its operations with category theory,” in Proc. 4th International Conference on Formal Ontology in Information Systems (FOIS). Baltimore, USA: IOS Press, 2006, pp. 277–288.

[3] P. Hitzler, M. Kr¨otzsch, M. Ehrig, and Y. Sure, “What is ontology merging? - A category theoretical perspective using pushouts,” in Proceedings of the First International Workshop on Contexts and Ontologies: Theory, Practice and Applications (C&0). Workshop at the 20th National Conference on Artificial Intelligence AAAI-05. Pittsburgh, Pennsylvania, Jul. 2005.

[4] C. Antunes and M. Abel, “Ontologies in category theory: A search for meaningful morphisms,” in SEMINAR ON ONTOLOGY RESEARCH IN BRAZIL, PROCEEDINGS. S˜ao Paulo, 2018.

[5] I. Cafezeiro and E. H. Haeusler, “Semantic interoperability via category theory,” in Proceedings of the 26th International Conference on Conceptual Modeling. Auckland, New Zealand, 2007, pp. 197–202.

[6] M. Codescu, T. Mossakowski, and O. Kutz, “A categorical approach to ontology alignment,” in Proceedings of the 9th International Workshop on Ontology Matching collocated with the 13th International Semantic Web Conference (ISWC 2014). Riva del Garda, Trentino, Italy, 2014.

[7] M. Codescu, T. Mossakowski, and O. Kutz, “A categorical approach to networks of aligned ontologies,” Journal on Data Semantics, vol. 6, no. 4, pp. 155–197, 2017.

[8] L. Hu and J. Wang, “Geo-ontology integration based on category theory,” in International Conference On Computer Design and Applications. Qinhuangdao, 2010, V1-5–V1-8.

[9] N. Kibret, W. Edmonson, and S. Gebreyohannes, “Category theoretic based formalization of the verifiable design process,” in IEEE International Systems Conference (SysCon). Orlando, FL, USA, 2019, pp. 1–8.

[10] M. Mendonca, J. Aguilar, and N. Perozo, “Application of category theory,” Ing´enierie des syst`emes d’information, vol. 23, no. 2, 2018, pp. 11–38.

[11] J. Euzenat, “Algebras of ontology alignment relations,” In Sheth A. et al. ed. International Semantic Web Conference - ISWC 2008, Lecture Notes in Computer Science, Vol. 5318. Berlin, Heidelberg: Springer, 2008, pp. 387–402.

[12] M. Mahfoudh, L. Thiry, G. Forestier, and M. Hassenforder, “Algebraic graph transformations for merging ontologies,” in Model & Data Engineering, 4th International Conference, MEDI 2014. Larnaca, Cyprus, Sep. 2014, pp. 154–168.

[13] M. Mahfoudh, G. Forestier, and M. Hassenforder, “A benchmark for ontologies merging assessment,” in Proc. of the International Conference on Knowledge Science, Engineering and Management (KSEM). 2016, pp. 555–566.

[14] K. Sun, Y. Zhu, P. Pan, Z. Hou, D. Wang, W. Li, and J. Song, “Geospatial data ontology: the semantic foundation of geospatial data integration and sharing,” Big Earth Data, vol. 3, no. 3, pp. 269–296, 2019.

[15] O. Benjelloun, D. Garcia-Molina, D. Menestrina, Q. Su, S. E. Wang, and J. Widom, “Swoosh: A generic approach to entity resolution,” The VLDB Journal, vol. 18, no. 1, pp. 255–276, 2009.

[16] A. Maedche and S. Staab, “Ontology learning for the semantic web,” IEEE Intelligent systems, vol. 16, no. 2, pp. 72–79, 2001.

[17] H. Mitsch, “A natural partial order for semigroups,” Proceedings of the American Mathematical Society, vol. 97, no. 3, pp. 384–388, 1986.

[18] C. Daskalakis, R. M. Karp, E. Mossel, S. J. Riesenfeld, and E. Verbin, “Sorting and selection in posets,” SIAM Journal on Computing, vol. 40, no. 3, pp. 392–401, 2011.

[19] A. de Luca and S. Varricchio, Finiteness and regularity in semigroups and formal languages. Springer Science & Business Media, 2012.

[20] M. Morse and G. A. Hedlund, “Unending chess, symbolic dynamics and a problem in semigroups,” Duke Math. J., vol. 11, no. 1, pp. 1–7, 1944.

[21] T. C. Brown and E. Lazerson, “On finitely generated idempotent semigroups,” Semigroup Forum, vol. 78, no. 1, pp. 183–186, 2009.

[22] J. Ad´amek, H. Herrlich, and G. E. Strecker, Abstract and Concrete Categories: The Joy of Cats. Dover Publications, 2009.

[23] S. Mac Lane, Categories for the Working Mathematician, 2nd ed. Berlin: Springer Verlag, 1997.