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Re: [ontolog-forum] Category theory and ontologies

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Obrst, Leo J." <lobrst@xxxxxxxxx>
Date: Fri, 11 Jul 2014 19:05:59 +0000
Message-id: <FDFBC56B2482EE48850DB651ADF7FEB035223878@xxxxxxxxxxxxxxxxxx>

And of course, Till Mossakowski and others are using Goguen’s theory of institutions for ontology mapping, including in the current OntoIOp effort: http://about.ontohub.org/ontoiop.html.


Kutz, Oliver, Till Mossakowski, Dominik Lücke. 2010. Carnap, Goguen, and the Hyperontologies - Logical Pluralism and Heterogeneous Structuring in Ontology Design. In Logica Univeralis, 4 (2), pp. 255–333. http://www.informatik.uni-bremen.de/~till/papers/Hyperontology.pdf.


Goguen, Joseph; Rod Burstall. 1992. Institutions: Abstract model theory for specification and programming,  in Journal of the ACM, 39, No. 1, Jan. 1992, pages 95-146.


From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Obrst, Leo J.
Sent: Friday, July 11, 2014 2:56 PM
To: [ontolog-forum]
Subject: [ontolog-forum] Category theory and ontologies


For the historical record:


Probably folks tend to forget Robert Kent's original contributions at the IEEE-SUO list/standards effort on category theory with respect to ontologies. He used Barwise & Seligman’s Information Flow Theory [1] (itself an application of category theory) to develop the Information Flow Framework (IFF) meta-ontology. I don’t think that much of Kent’s IFF is online these days, but here are a couple of references: [2, 3]. Other related references include [4-7], among others.


[1] Barwise, Jon; Seligman, Jerry. 1997.  Information Flow: The Logic of Distributed Systems. Cambridge University Press, Cambridge, UK.

[2] Kent, Robert E. 2006. The Information Flow Framework: New Architecture. International Category Theory Conference (CT 2006), White Point, Nova Scotia, June 25 – July 1, 2006. A version at (2011): http://arxiv.org/abs/1109.0983.

[3] Kent, Robert E. 2011. A KIF Formalization for the IFF Category Theory Ontology. Paper presented at the Standard Upper Ontology workshop of the 17th International Joint Conference on Artificial Intelligence (IJCAI-01), August, 2001, Seattle, Washington. http://arxiv.org/ftp/arxiv/papers/1109/1109.0333.pdf.

[4] Markus Kr¨otzsch, Pascal Hitzler, Marc Ehrig, York Sure. 2005. Category Theory in Ontology Research: Concrete Gain from an Abstract Approach. http://www.aifb.kit.edu/web/Techreport893.

[5] Kalfoglou, Y. and M. Schorlemmer. 2003. Ontology Mapping: The State of the Art. The Knowledge Engineering Review. Volume 18,  Issue 1  (January 2003), pp. 1 – 31.

[6] Kalfoglou & Scholemmer. 2011. The information flow approach to ontology-based semantic alignment. In: TAO – Theory and Applications of Ontology, Volume 2: Computer Applications, Michael Healy, Achilles Kameas, Roberto Poli, eds.

[7] Healy, M. 2011. Category theory as a mathematics for formalizing ontologies. In: TAO – Theory and Applications of Ontology, Volume 2: Computer Applications, Michael Healy, Achilles Kameas, Roberto Poli, eds.




Dr. Leo Obrst        The MITRE Corporation, Information Semantics

lobrst@xxxxxxxxx     Information Technology Tech Center, CCG

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