Abstract and concrete categories
Abstract and concrete categories
Basic category theory for computer scientists
Basic category theory for computer scientists
Institutions: abstract model theory for specification and programming
Journal of the ACM (JACM)
Information flow: the logic of distributed systems
Information flow: the logic of distributed systems
Maintaining knowledge about temporal intervals
Communications of the ACM
Information-Flow-Based Ontology Mapping
On the Move to Meaningful Internet Systems, 2002 - DOA/CoopIS/ODBASE 2002 Confederated International Conferences DOA, CoopIS and ODBASE 2002
A survey of approaches to automatic schema matching
The VLDB Journal — The International Journal on Very Large Data Bases
A survey of schema-based matching approaches
Journal on Data Semantics IV
Logical properties of foundational relations in bio-ontologies
Artificial Intelligence in Medicine
Semantic interoperability via category theory
ER '07 Tutorials, posters, panels and industrial contributions at the 26th international conference on Conceptual modeling - Volume 83
Institutionalising ontology-based semantic integration
Applied Ontology
Acquiring advanced properties in ontology mapping
Proceedings of the 2nd PhD workshop on Information and knowledge management
Algebras of Ontology Alignment Relations
ISWC '08 Proceedings of the 7th International Conference on The Semantic Web
Semantic Interoperability between Functional Ontologies
Proceedings of the 2007 conference on Databases and Information Systems IV: Selected Papers from the Seventh International Baltic Conference DB&IS'2006
Conservativity in Structured Ontologies
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
Managing requirement volatility in an ontology-driven clinical LIMS using category theory
International Journal of Telemedicine and Applications - Special issue on electronic health
Modular Ontologies for Architectural Design
Proceedings of the 2009 conference on Formal Ontologies Meet Industry
HOM: an approach to calculating semantic similarity utilizing relations between ontologies
AIRS'08 Proceedings of the 4th Asia information retrieval conference on Information retrieval technology
Towards a Functional Approach to Modular Ontologies using Institutions
Proceedings of the 2010 conference on Modular Ontologies: Proceedings of the Fourth International Workshop (WoMO 2010)
Dealing with matching variability of semantic web data using contexts
CAiSE'10 Proceedings of the 22nd international conference on Advanced information systems engineering
Three semantics for distributed systems and their relations with alignment composition
ISWC'06 Proceedings of the 5th international conference on The Semantic Web
Impact of using relationships between ontologies to enhance the ontology search results
ESWC'12 Proceedings of the 9th international conference on The Semantic Web: research and applications
Institutionalising ontology-based semantic integration
Applied Ontology
Ontological modelling of form and function for architectural design
Applied Ontology
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An ontology alignment is the expression of relations between different ontologies. In order to view alignments independently from the language expressing ontologies and from the techniques used for finding the alignments, we use a category-theoretical model in which ontologies are the objects. We introduce a categorical structure, called V-alignment, made of a pair of morphisms with a common domain having the ontologies as codomain. This structure serves to design an algebra that describes formally what are ontology merging, alignment composition, union and intersection using categorical constructions. This enables combining alignments of various provenance. Although the desirable properties of this algebra make such abstract manipulation of V-alignments very simple, it is practically not well fitted for expressing complex alignments: expressing subsumption between entities of two different ontologies demands the definition of non-standard categories of ontologies. We consider two approaches to solve this problem. The first one extends the notion of V-alignments to a more complex structure called W-alignments: a formalization of alignments relying on “bridge axioms.” The second one relies on an elaborate concrete category of ontologies that offers high expressive power. We show that these two extensions have different advantages that may be exploited in different contexts (viz., merging, composing, joining or meeting): the first one efficiently processes ontology merging thanks to the possible use of categorical institution theory, while the second one benefits from the simplicity of the algebra of V-alignments.