A geometric proof of the completeness of the Łukasiewicz calculus

DOI10.2307/2275851zbMath0837.03018OpenAlexW1966763988MaRDI QIDQ4842633

Giovanni Panti

Publication date: 13 May 1996

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2275851

zbMATH Keywords

toric varietiesfree algebracompletenessnormal formsMV-algebrasvaluationsinfinite-valued logicpiecewise linear functions\(n\)-cubeLindenbaum algebraequational calculusMcNaughton theorem

Mathematics Subject Classification ID

Many-valued logic (03B50)

Related Items (19)

On normal forms in Łukasiewicz logic ⋮ Geometry of Robinson consistency in Łukasiewicz logic ⋮ A characterization of truth-functions in the nilpotent minimum logic ⋮ The Lebesgue state of a unital abelian lattice-ordered group ⋮ Bernoulli automorphisms of finitely generated free MV-algebras ⋮ Invariant Measures in Free MV-Algebras ⋮ Free Łukasiewicz implication algebras ⋮ A characterization of MV-algebras free over finite distributive lattices ⋮ Unnamed Item ⋮ A discrete representation of free MV-algebras ⋮ Decidable and undecidable prime theories in infinite-valued logic ⋮ Functorial representation theorems for MV\(_\Delta\) algebras with additional operators ⋮ Finite axiomatizability in Łukasiewicz logic ⋮ Faithful and Invariant Conditional Probability in Łukasiewicz Logic ⋮ Varieties of MV-algebras ⋮ The complexity of McNaughton functions of one variable ⋮ Semiring and Semimodule Issues in MV-Algebras ⋮ Lattice-ordered Abelian groups and Schauder bases of unimodular fans ⋮ Geometrical methods in Wajsberg hoops

Cites Work

• Interpretation of AF \(C^*\)-algebras in Łukasiewicz sentential calculus
• A constructive proof of McNaughton's theorem in infinite-valued logic
• A theorem about infinite-valued sentential logic

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