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January 1, 1958Transactions of the American Mathematical SocietyOpen Access

Algebraic analysis of many valued logics

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CCC. C. ChangYunnan Normal University

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Implication

Theoretical analysis introduces MV-algebras corresponding to many-valued propositional calculus, establishing algebraic foundations for non-classical logics.

Key Points

To develop an algebraic theory of systems (termed MV-algebras) naturally corresponding to many-valued propositional calculus and to explore proofs of logical completeness using algebraic structures.
Axiomatized MV-algebras as algebraic structures $(A, +, \cdot, \sim, 0, 1)$ that generalize two-valued Boolean algebras to infinite-valued systems.
Analyzed the arithmetic, ideal structure, and representation theory of MV-algebras by adapting techniques from the Boolean prime ideal theorem.
Demonstrated that every Boolean algebra is an MV-algebra, whereas the converse does not hold.
Obtained partial success in duplicating classical completeness results for infinite-valued logic via MV-algebraic structural properties.

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C. C. Chang (1958) studied this question.

synapsesocial.com/papers/6ab1e64cd0a6f86827c4685d https://doi.org/10.1090/s0002-9947-1958-0094302-9

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Implication

Theoretical analysis introduces MV-algebras corresponding to many-valued propositional calculus, establishing algebraic foundations for non-classical logics.

Algebraic analysis of many valued logics

Discussion

Member takes

Implication

Key Points

Cite This Study

Algebraic analysis of many valued logics

Discussion

Member takes

Implication

Key Points

Cite This Study

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