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  1.  26
    Boolean Deductive Systems of BL-Algebras.Esko Turunen - 2001 - Archive for Mathematical Logic 40 (6):467-473.
    BL-algebras rise as Lindenbaum algebras from many valued logic introduced by Hájek [2]. In this paper Boolean ds and implicative ds of BL-algebras are defined and studied. The following is proved to be equivalent: (i) a ds D is implicative, (ii) D is Boolean, (iii) L/D is a Boolean algebra. Moreover, a BL-algebra L contains a proper Boolean ds iff L is bipartite. Local BL-algebras, too, are characterized. These results generalize some theorems presented in [4], [5], [6] for MV-algebras which (...)
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  2.  1
    Mathematics Behind Fuzzy Logic.Esko Turunen - 1999 - Physica-Verlag Heidelberg.
    Many results in fuzzy logic depend on the mathematical structure the truth value set obeys. In this textbook the algebraic foundations of many-valued and fuzzy reasoning are introduced. The book is self-contained, thus no previous knowledge in algebra or in logic is required. It contains 134 exercises with complete answers, and can therefore be used as teaching material at universities for both undergraduated and post-graduated courses. Chapter 1 starts from such basic concepts as order, lattice, equivalence and residuated lattice. It (...)
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  3.  23
    Well‐Defined Fuzzy Sentential Logic.Esko Turunen - 1995 - Mathematical Logic Quarterly 41 (2):236-248.
    A many-valued sentential logic with truth values in an injective MV-algebra is introduced and the axiomatizability of this logic is proved. The paper develops some ideas of Goguen and generalizes the results of Pavelka on the unit interval. The proof for completeness is purely algebraic. A corollary of the Completeness Theorem is that fuzzy logic on the unit interval is semantically complete if and only if the algebra of the truth values is a complete MV-algebra. In the well-defined fuzzy sentential (...)
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  4.  7
    Hyper-Archimedean BL-Algebras Are MV-Algebras.Esko Turunen - 2007 - Mathematical Logic Quarterly 53 (2):170-175.
    Generalizations of Boolean elements of a BL-algebra L are studied. By utilizing the MV-center MV(L) of L, it is reproved that an element x L is Boolean iff x x * = 1. L is called semi-Boolean if for all x L, x * is Boolean. An MV-algebra L is semi-Boolean iff L is a Boolean algebra. A BL-algebra L is semi-Boolean iff L is an SBL-algebra. A BL-algebra L is called hyper-Archimedean if for all x L, xn is Boolean (...)
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  5.  10
    A Note on Pavelka's Fuzzy Logic.Esko Turunen - 1991 - Mathematical Logic Quarterly 37 (2‐4):39-40.
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  6.  29
    A Note on Pavelka's Fuzzy Logic.Esko Turunen - 1991 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 37 (2-4):39-40.
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