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Axioms 2014, 3(2), 260-279; doi:10.3390/axioms3020260

Modalities for an Allegorical Conceptual Data Model

Department of Computer Science, Faculty of Physics and Applied Informatics,University of Łódź ul. Pomorska nr 149/153, 90-236 Łódź, Poland
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Received: 27 February 2014 / Revised: 12 May 2014 / Accepted: 13 May 2014 / Published: 30 May 2014
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Abstract

Allegories are enriched categories generalizing a category of sets and binary relations. In this paper, we extend a new, recently-introduced conceptual data model based on allegories by adding support for modal operators and developing a modal interpretation of the model in any allegory satisfying certain additional (but natural) axioms. The possibility of using different allegories allows us to transparently use alternative logical frameworks, such as fuzzy relations. Mathematically, our work demonstrates how to enrich with modal operators and to give a many world semantics to an abstract algebraic logic framework. We also give some examples of applications of the modal extension.
Keywords: allegories; data modeling; modal logic allegories; data modeling; modal logic
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Zieliński, B.; Maślanka, P.; Sobieski, Ś. Modalities for an Allegorical Conceptual Data Model. Axioms 2014, 3, 260-279.

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