A completeness theorem for a functionally complete Łukasiewicz logic
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2025
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Uniwersytet Mikołaja Kopernika
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Aranda, V. (2025) “A Completeness Theorem for a Functionally Complete Łukasiewicz Logic”, Logic and Logical Philosophy, pp. 1–12. doi: 10.12775/LLP.2025.014.
Abstract
Radzki has recently claimed the incompleteness of the axioms given by Słupecki for the functionally complete Ł3: some of its tautologies are not provable. In this paper, we provide a new axiom system for this logic (choosing a variant with two propositional constants and the Łukasiewicz implication as primitive symbols) and prove a Completeness Theorem.