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

Published online by Cambridge University Press:  12 March 2014

Petr Hájek ,
Jeff Paris  and
John Shepherdson
Petr Hájek
Affiliation:
Institute of Computer Science, Academy of Sciences, 18207 Prague, Czech Republic, E-mail: hajek@uivt.cas.cz
Jeff Paris
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL, UK, E-mail: jeff@ma.man.ac.uk
John Shepherdson
Affiliation:
Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK, E-mail: john.shepherdson@bris.ac.uk
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Abstract

Rational Pavelka logic extends Łukasiewicz 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 Łukasiewicz logic. We also give a counterexample to a soundness theorem of Belluce and Chang published in 1963.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 2 , June 2000 , pp. 669 - 682
Copyright
Copyright © Association for Symbolic Logic 2000

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