Computer Science ›› 2016, Vol. 43 ›› Issue (5): 42-46.doi: 10.11896/j.issn.1002-137X.2016.05.007

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Descriptions for Ontologies Based on Category Theory

YU Shan-shan, SU Jin-dian and YI Fa-ling   

  • Online:2018-12-01 Published:2018-12-01

Abstract: To solve the inconsistence problems brought by various ontology languages when describing ontologies,a description method for ontologies based on category theory was proposed by taking full advantages of abstractness and graphical expressions of category theory.The category theoretical definitions for ontology,ontology mapping and onto-logy instanilization were presented,where each ontology is described as an object of a category,each morphism between ontologies is described as the a homomorphism between objects of a category,and the instanlization of ontologies is described as a functor between two categories.After that,the notions of colimit and pushout were used to describe the merging of ontologies.And some interesting properties for ontology merging were proved from the viewpoints of category theory.

Key words: Ontology,Category theory,Ontology description,Ontology merging,Ontology alignment

[1] Awodey S.Category Theory[M].Oxford University Press,2006:265-290
[2] Hitzler P,Krtzsch M,Ehrig M,et al.What is Ontology Merging? - a Category Theoretic Perspective Using Pushouts[C]∥Proc.First International Workshop on Contexts and Ontologies:Theory,Practice and Applications(C&O).AAAI Press,2005:104-107
[3] Yu Shan-shan,Li Shi-xian,Su Jin-dian.Hylomorphisms with Parameters and Its Associated Calculational Laws [J].Journal of Computer Research and Development,2012,50(3):502-618(in Chinese) 余珊珊,李师贤,苏锦钿.一种带参数的Hylomorphisms及其计算律[J].计算机研究与发展,2012,50(3):502-618
[4] Yu Shan-shan,Li Shi-xian,Su Jin-dian.Final Coalgebraic Se-mantics for Behavioral Equality of Objects[J].Computer Science,2012,39(2):182-190(in Chinese) 余珊珊,李师贤,苏锦钿.对象行为等价的终结共代数语义[J].计算机科学,2012,39(2):182-190
[5] Yu Shan-shan,Li Shi-xian,Su Jin-dian.Formal Semantics of Object Oriented Methods Based on Coalgebras[J].Computer Science,2011,38(8):142-146(in Chinese) 余珊珊,李师贤,苏锦钿.一种基于共代数的面向对象形式语义[J].计算机科学,2011,38(8):142-146
[6] Su Jin-dian,Yu Shan-shan.Bialgebraic Structures of AbstractData Types and its Calculational Laws[J].Journal of Computer Research and Development,2012,49(8):1787-1803(in Chinese) 苏锦钿,余珊珊.抽象数据类型的双代数结构及其计算定律[J].计算机研究与发展,2012,49(8):1787-1803
[7] Su Jin-dian,Yu Shan-shan.Corecursive operations with parameters and the associated calculational laws [J].Journal of Computer Research and Development,2013,50(12):2672-2690(in Chinese) 苏锦钿,余珊珊.带参数的共递归操作及其计算定律[J].计算机研究与发展,2013,50(12):2672-2690
[8] Healy M J.Category Theory as a Mathematics for Formalizing Ontologies[M]∥Theory and Applications of Ontology:Computer Applications.2010:487-510
[9] Zhang Yuan,Li Shi-xian.Research on Formal Categorical On-tologies[J].Computer Science,2006,33(9):1-3(in Chinese) 章远,李师贤.基于范畴论的形式化本体研究[J].计算机科学,2006,33(9):1-3
[10] Ye Dan-dan,Wang Hai-tao.Web Ontology Description Research Based on Category Theory[J].Journal of Changchun University of Science and Technology(Natual Science Edition),2011,4(3):146-148,151(in Chinese) 叶丹丹,汪海涛.基于范畴论的Web本体论描述研究[J].长春理工大学学报(自然科学版),2011,34(3):146-148,1
[11] Bench-Capon T J M,Malcolm G.Formalising Ontologies andTheir Relations[C]∥Proc.10th Database and Expert Systems Applications(DEXA’99).1999:250-259
[12] Zimmermann A,Krtzsch M,Euzenat J,et al.Formalizing Ontology Alignment and its Operations with Category Theory[C]∥Proc.of the Fourth International Conference(FOIS 2006).2006:277-288
[13] Abbas M A,Berio G.Creating Ontologies Using Ontology Mappings:Compatible and Incompatible Ontology Mappings[C]∥Proc.Web Intelligence/IAT Workshops.2013:143-146
[14] Goguen J.Three Perspectives on Information Integration[C]∥Semantic Interoperability and Integration,Dagstuhl Seminar Proceedings 04391.2005
[15] Kent R E.Semantic Integration in the Information Flow Framework[C]∥Semantic Interoperability and Integration,Dagstuhl Seminar Proceedings 04391.2005
[16] Cafezeiro I,Haeusler E H.Semantic Interoperability via Category Theory[C]∥26th International Conference on Conceptual Modelling-ER Auckland.New Zealand,2007:197-202
[17] Pierce B.Basic Category Theory for Computer Scientists[M].The MIT Press,1991
[18] Bench-Capon T J M,Malcolm G.Formalising Ontologies andTheir Relations[C]∥Proc.10th Database and Expert Systems Applications(DEXA’99).1999:250-259
[19] Kalfoglou Y,Schorlemmer M.Ontology Mapping:the State of the Art[J].Knowl.Eng.Rev.,2003,18(1):1-31
[20] Lucanu D.A Logical Foundation for the OWL Languages[C]∥Proc.First International Symposium on Leveraging Applications of Formal Methods(ISoLA 2004) VolumeTR-2004-6.2004:135-142

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