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...

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Detalhes bibliográficos
Autor: Aranda Utrero, Víctor
Tipo de documento: artigo
Data de publicação:2025
País:España
Recursos:Universidad Complutense de Madrid (UCM)
Repositório:Docta Complutense
Idioma:inglês
OAI Identifier:oai:docta.ucm.es:20.500.14352/123833
Acesso em linha:https://hdl.handle.net/20.500.14352/123833
Access Level:Acceso aberto
Palavra-chave:164
Many-valued logics
Three-valued logics
Propositional logic
Non-classical logics
Fuzzy logic
Lógica (Filosofía)
1102.08 Lógica Matemática
1102.05 Sistemas Formales
1102.12 Cálculo Proposicional
Descrição
Resumo: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.