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

Modalities for an Allegorical Conceptual Data Model

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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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

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

AMA Style

Zieliński B, Maślanka P, Sobieski Ś. Modalities for an Allegorical Conceptual Data Model. Axioms. 2014; 3(2):260-279.

Chicago/Turabian Style

Zieliński, Bartosz; Maślanka, Paweł; Sobieski, Ścibor. 2014. "Modalities for an Allegorical Conceptual Data Model." Axioms 3, no. 2: 260-279.

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