descriptionPublicationkeyboard_double_arrow_right Article 01 Jun 2000 English Publisher:Cambridge University Press (CUP)Journal:Journal of Symbolic Logic, volume 65, pages 669-682 (issn: 0022-4812, eissn: 1943-5886,

Authors: John C. Shepherdson; Petr Hájek; Jeff B. Paris;

doi: 10.2307/2586560

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

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Abstract

AbstractRational 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.

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Keywords

Łukasiewicz predicate logic, product logic, Many-valued logic, infinitely valued predicate logic, rational Pavelka predicate logic, conservative extension

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