Journal of Symbolic Logic

Rational Pavelka Predicate Logic is a Conservative Extension of Lukasiewicz Predicate Logic

Petr Hajek, Jeff Paris, and John Shepherdson

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Abstract

Rational Pavelka logic extends Lukasiewicz infinitely valued logic $by adding truth constants \bar{r} for rationals in [0, 1].$ 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.

Article information

Source
J. Symbolic Logic, Volume 65, Issue 2 (2000), 669-682.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183746068

Mathematical Reviews number (MathSciNet)
MR1771076

Zentralblatt MATH identifier
0971.03025

JSTOR
links.jstor.org

Citation

Hajek, Petr; Paris, Jeff; Shepherdson, John. Rational Pavelka Predicate Logic is a Conservative Extension of Lukasiewicz Predicate Logic. J. Symbolic Logic 65 (2000), no. 2, 669--682. https://projecteuclid.org/euclid.jsl/1183746068


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