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dc.contributor.authorZielinski, Bartosz
dc.contributor.authorMaślanka, Paweł
dc.contributor.authorSobieski, Ścibor
dc.description.abstractAllegories 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.pl_PL
dc.description.sponsorshipWe would like to thank the reviewers for their helpful suggestions.pl_PL
dc.publisherMDPI AGpl_PL
dc.rightsUznanie autorstwa 3.0 Polska*
dc.subjectdata modelingpl_PL
dc.subjectmodal logicpl_PL
dc.titleModalities for an Allegorical Conceptual Data Modelpl_PL
dc.contributor.authorAffiliationUniversity of Łódź, Faculty of Physics and Applied Informaticspl_PL
dc.referencesFreyd, P.; Scedrov, A. Categories, Allegories; North-Holland Mathematical Library; Elsevier Science: New York, NY, USA, 1990pl_PL
dc.referencesTarski, A.; Givant, S. A Formalization of Set Theory Without Variables; Number t. 41 in A Formalization of Set Theory without Variables; American Mathematical Society: Providence, RI, USA, 1987pl_PL
dc.referencesLippe, E.; Hofstede, A. A Category Theory Approach to Conceptual Data Modeling; University of Nijmegen, Computing Science Institute: Tartu, Estonia, 1994pl_PL
dc.referencesPiessens, F.; Steegmans, E. Selective attribute elimination for categorical data specifications. In Algebraic Methodology and Software Technology; Johnson, M., Ed.; Lecture Notes in Computer Science; Springer: Berlin/Heidelberg, Germany, 1997; Volume 1349, pp. 424–436pl_PL
dc.referencesRosebrugh, R.; Wood, R.J. Relational databases and indexed categories. In Proceedings of the International Category Theory Meeting, CMS Conference Proceedings, Montreal, QC, Canada, 23–30 June 1991; American Mathematical Society: Providence, RI, USA, 1992; Volume 13, pp. 391–407pl_PL
dc.referencesJohnson, M.; Rosebrugh, R. Sketch data models, relational schema and data specifications. Electron. Notes Theor. Comput. Sci. 2002, 61, 51–63pl_PL
dc.referencesDiskin, Z.; Kadish, B. Algebraic Graph-Oriented = Category Theory Based—Manifesto of Categorizing Database Theory; Technical Report for Laboratory for Database Design; Frame Inform Systems: Riga, Latvia, 1995pl_PL
dc.referencesDiskin, Z. Formalizing graphical schemas for conceptual modeling: Sketch-based Logic vs. heuristic pictures. In Proceedings of the 10th International Congress of Logic, Methodology and Philosophy of Science, Florence, Italy, 9–25 August 1995; pp. 40–41pl_PL
dc.referencesDiskin, Z. Generalised Sketches as an Algebraic Graph-Based Framework for Semantic Modeling and Database Design; University of Latvia: Riga, Latvia, 1997pl_PL
dc.referencesSpivak, D.I. Simplicial Databases. CoRR 2009, abs/0904.2012pl_PL
dc.referencesZielinski, B.; Maslanka, P.; Sobieski, S. Allegories for database modeling. In Model and Data Engineering; Cuzzocrea, A., Maabout, S., Eds.; Lecture Notes in Computer Science; Springer: Berlin/Heidelberg, Germany, 2013; Volume 8216, pp. 278–289pl_PL
dc.referencesJohnson, M.; Rosebrugh, R. Fibrations and universal view updatability. Theor. Comput. Sci. 2007, 388, 109–129pl_PL
dc.referencesJohnson, M.; Rosebrugh, R.; Wood, R.J. Lenses, fibrations and universal translations. Math. Struct. Comput. Sci. 2012, 22, 25–42pl_PL
dc.referencesJohnson, M.; Kasangian, S. A relational model of incomplete data without nulls. In Proceedings of the Sixteenth Symposium on Computing: The Australasian Theory (CATS ’10), Brisbane, Australia, 18–21 January 2010; Australian Computer Society, Inc.: Darlinghurst, Australia, 2010; Volume 109, pp. 89–94pl_PL
dc.referencesBarr, M.; Wells, C. Category Theory for Computing Science; Prentice-Hall International Series in Computer Science; Prentice Hall: Upper Saddle River, NJ, USA, 1995pl_PL
dc.referencesDavey, B.; Priestley, H. Introduction to Lattices and Order; Cambridge Mathematical Text Books; Cambridge University Press: Cambridge, UK, 2002pl_PL
dc.referencesWinter, M. Products in categories of relations. J. Log. Algebr. Program. 2008, 76, 145–159, Relations and Kleene Algebras in Computer Sciencepl_PL
dc.referencesRosenfeld, A. An Introduction to Algebraic Structures; Holden-Day: San Francisco, CA, USA, 1968pl_PL
dc.referencesBlackburn, P.; van Benthem, J.; Wolter, F. Handbook of Modal Logic; Studies in Logic and Practical Reasoning; Elsevier Science: New York, NY, USA, 2006pl_PL
dc.referencesBlackburn, P.; de Rijke, M.; Venema, Y. Modal Logic; Cambridge Tracts in Theoretical Computer Science; Cambridge University Press: Cambridge, UK, 2002pl_PL
dc.referencesDiaconescu, R.; Stefaneas, P. Ultraproducts and possible worlds semantics in institutions. Theor. Comput. Sci. 2007, 379, 210–230pl_PL
dc.referencesGoguen, J.; Burstall, R. Introducing institutions. In Logics of Programs; Clarke, E., Kozen, D., Eds.; Lecture Notes in Computer Science; Springer: Berlin/Heidelberg, Germany, 1984; Volume 164, pp. 221–256pl_PL

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