1.  64
    Residuated Lattices Arising From Equivalence Relations on Boolean and Brouwerian Algebras.Thomas Vetterlein - 2008 - Mathematical Logic Quarterly 54 (4):350-367.
    Logics designed to deal with vague statements typically allow algebraic semantics such that propositions are interpreted by elements of residuated lattices. The structure of these algebras is in general still unknown, and in the cases that a detailed description is available, to understand its significance for logics can be difficult. So the question seems interesting under which circumstances residuated lattices arise from simpler algebras in some natural way. A possible construction is described in this paper.Namely, we consider pairs consisting of (...)
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  2.  29
    Partial Algebras for Łukasiewicz Logics and its Extensions.Thomas Vetterlein - 2005 - Archive for Mathematical Logic 44 (7):913-933.
    It is a well-known fact that MV-algebras, the algebraic counterpart of Łukasiewicz logic, correspond to a certain type of partial algebras: lattice-ordered effect algebras fulfilling the Riesz decomposition property. The latter are based on a partial, but cancellative addition, and we may construct from them the representing ℓ-groups in a straightforward manner. In this paper, we consider several logics differing from Łukasiewicz logics in that they contain further connectives: the PŁ-, PŁ'-, PŁ'△-, and ŁΠ-logics. For all their algebraic counterparts, we (...)
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  3.  31
    A Way to Interpret Łukasiewicz Logic and Basic Logic.Thomas Vetterlein - 2008 - Studia Logica 90 (3):407-423.
    Fuzzy logics are in most cases based on an ad-hoc decision about the interpretation of the conjunction. If they are useful or not can typically be found out only by testing them with example data. Why we should use a specific fuzzy logic can in general not be made plausible. Since the difficulties arise from the use of additional, unmotivated structure with which the set of truth values is endowed, the only way to base fuzzy logics on firm ground is (...)
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