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  • 1.
    Eklund, Patrik
    et al.
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Galán, M.A.
    Department of Applied Mathematics, University of Málaga, Málaga, Spain.
    Gähler, Werner
    Scheibenbergstraße 37, D-12685 Berlin, Germany.
    Partially ordered monads for monadic topologies, Kleene algebras and rough sets2009In: Electronical Notes in Theoretical Computer Science, ISSN 1571-0661, E-ISSN 1571-0661, Vol. 225, p. 67-81Article in journal (Refereed)
    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].

  • 2.
    Eklund, Patrik
    et al.
    Åbo Akademi University, Dept. Computer Science, Åbo, Finland.
    Galán, M.A.
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Medina, J.
    Ojeda Aciego, M.
    Valverde, A.
    A categorical approach to unication of generalised terms2002In: Electronical Notes in Theoretical Computer Science, ISSN 1571-0661, E-ISSN 1571-0661, Vol. 66, no 5, p. 41-45Article in journal (Refereed)
    Abstract [en]

    Unification of generalised terms in a many-valued setting involves considerations for equalities in the sense of similarity degrees between operators and thus similarities between terms. Further, allowing for substitutions of variables with powersets of terms requires ‘flattening’ operators for handling composition of variable substitutions. These techniques are available when using powerset functors composed with the term functor so that this composition of functors is extendable to a monad. In this paper we provide a framework for unification of such generalised terms.

  • 3.
    Eklund, Patrik
    et al.
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Galán, M.A.
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Medina, J.
    Ojeda Aciego, M.
    Valverde, A.
    A graphical approach to monad composition2001In: Electronical Notes in Theoretical Computer Science, ISSN 1571-0661, E-ISSN 1571-0661, Vol. 40, p. 145-160Article in journal (Refereed)
    Abstract [en]

    In this paper we show how composite expressions involving natural transformations can be pictorially represented in order to provide graphical proof support for providing monad compositions. Examples are drawn using powerset monads composed with the term monad.

  • 4.
    Nieves, Juan Carlos
    et al.
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Marcial-Romero, José Raymundo
    Preface2015In: Electronical Notes in Theoretical Computer Science, ISSN 1571-0661, E-ISSN 1571-0661, Vol. 315, no 9, p. 1-2Article in journal (Other academic)
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