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Partially ordered monads for monadic topologies, Kleene algebras and rough sets
Umeå University, Faculty of Science and Technology, Department of Computing Science.
Department of Applied Mathematics, University of Málaga, Málaga, Spain.
Scheibenbergstraße 37, D-12685 Berlin, Germany.
2009 (English)In: Electronical Notes in Theoretical Computer Science, ISSN 1571-0661, Vol. 225, 67-81 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we will show that partially ordered monads contain sufficient structure for modelling monadic topologies, rough sets and Kleene algebras. Convergence represented by extension structures over partially ordered monads includes notions of regularity and compactness. A compactification theory can be developed. Rough sets [Z. Pawlak, Rough sets, Int. J. Computer and Information Sciences 5 (1982) 341356] are modelled in a generalized setting with set functors. Further, we show how partially ordered monads can be used in order to obtain monad based examples of Kleene algebras building upon a wide range of set functors far beyond just strings [S. C. Kleene, Representation of events in nerve nets and finite automata, In: Automata Studies (Eds. C. E. Shannon, J. McCarthy), Princeton University Press, 1956, 3-41] and relations [A. Tarski, On the calculus of relations, J. Symbolic Logic 6 (1941), 65-106].

Place, publisher, year, edition, pages
Elsevier, 2009. Vol. 225, 67-81 p.
Keyword [en]
Partially ordered monads, Monadic topologies, Rough sets, Kleene algebras
National Category
Computer Science
URN: urn:nbn:se:umu:diva-80625DOI: 10.1016/j.entcs.2008.12.067OAI: diva2:650525
Proceedings of the Irish Conference on the Mathematical Foundations of Computer Science and Information Technology (MFCSIT 2006), Cork, Ireland, 1–5 August 2006
Available from: 2013-09-22 Created: 2013-09-22 Last updated: 2014-01-30Bibliographically approved

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