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

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Journal of Symbolic Logic 65 (2):669-682 (2000)
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Abstract

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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10.2307/2586560

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Jeffrey Paris
University of Manchester

Citations of this work

Omitting uncountable types and the strength of [0,1]-valued logics.Xavier Caicedo & José N. Iovino - 2014 - Annals of Pure and Applied Logic 165 (6):1169-1200.
Omitting types for infinitary [ 0, 1 ] -valued logic.Christopher J. Eagle - 2014 - Annals of Pure and Applied Logic 165 (3):913-932.
Mathematical fuzzy logics.Siegfried Gottwald - 2008 - Bulletin of Symbolic Logic 14 (2):210-239.

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References found in this work

Logic, Semantics, Metamathematics.Atwell Turquette - 1958 - Philosophical Review 67 (1):113.
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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