A Completeness Theorem for a Functionally Complete Łukasiewicz Logic

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.

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Publication Details

Journal
Logic and Logical Philosophy
Published
2025-08-28
DOI
https://doi.org/10.12775/llp.2025.014
Primary Topic
Advanced Algebra and Logic
Type
article
Field-Weighted Citation Impact
0.00

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article

A Completeness Theorem for a Functionally Complete Łukasiewicz Logic

Víctor Aranda
Logic and Logical Philosophy
Advanced Algebra and Logic
article

A Completeness Theorem for a Functionally Complete Łukasiewicz Logic

Víctor Aranda
article en

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.

Logic and Logical Philosophy
Universidad Complutense de Madrid (ES)
European Regional Development Fund, Agencia Estatal de Investigación
Openalex Percentile: Top 75%
Advanced Algebra and Logic
DOIOpen Access PDFOpenAlex
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A Completeness Theorem for a Functionally Complete Łukasiewicz Logic — Víctor Aranda · Logic and Logical Philosophy (2025) | TGRS Research Map | TGRS