Rational Pavelka Predicate Logic is a Conservative Extension of Lukasiewicz 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 $by adding truth constants \bar{r} for rationals in [0, 1].$ 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.

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Jeffrey Paris
University of Manchester

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