Rational Pavelka predicate logic is a conservative extension of łukasiewicz predicate logic

Journal of Symbolic Logic 65 (2):669-682 (2000)
Rational Pavelka logic extends Lukasiewicz infinitely valued logic by adding truth constants r̄ for rationals in [0, 1]. We show that this is a conservative extension. We note that this shows that provability degree can be defined in Lukasiewicz logic. We also give a counterexample to a soundness theorem of Belluce and Chang published in 1963
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DOI 10.2307/2586560
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References found in this work BETA
On Fuzzy Logic III. Semantical Completeness of Some Many-Valued Propositional Calculi.Jan Pavelka - 1979 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 25 (25-29):447-464.
Fuzzy Logic and Arithmetical Hierarchy, II.Petr Hájek - 1997 - Studia Logica 58 (1):129-141.

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Citations of this work BETA
Omitting Uncountable Types and the Strength of [0,1]-Valued Logics.Xavier Caicedo & José Iovino - 2014 - Annals of Pure and Applied Logic 165 (6):1169-1200.
A Note on the Notion of Truth in Fuzzy Logic.Petr Hájek & John Shepherdson - 2001 - Annals of Pure and Applied Logic 109 (1-2):65-69.
Omitting Types for Infinitary -Valued Logic.Christopher J. Eagle - 2014 - Annals of Pure and Applied Logic 165 (3):913-932.

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