Many-valued logics and Suszko's thesis revisited

Studia Logica 60 (2):299-309 (1998)
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Abstract

Suszko's Thesis maintains that many-valued logics do not exist at all. In order to support it, R. Suszko offered a method for providing any structural abstract logic with a complete set of bivaluations. G. Malinowski challenged Suszko's Thesis by constructing a new class of logics (called q-logics by him) for which Suszko's method fails. He argued that the key for logical two-valuedness was the "bivalent" partition of the Lindenbaum bundle associated with all structural abstract logics, while his q-logics were generated by "trivalent" matrices. This paper will show that contrary to these intuitions, logical two-valuedness has more to do with the geometrical properties of the deduction relation of a logical structure than with the algebraic properties embedded on it.

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References found in this work

Abolition of the Fregean Axiom.Roman Suszko - 1975 - Lecture Notes in Mathematics 453:169-239.
Remarks on Lukasiewicz's three-valued logic.Roman Suszko - 1975 - Bulletin of the Section of Logic 4 (3):87-90.
An Interpretation of Many-Valued Logic.Alasdair Urquhart - 1973 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 19 (7):111-114.
Remarks on Sentential Logics.R. Suszko - 1975 - Journal of Symbolic Logic 40 (4):603-604.

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