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2004•Journal of Mathematical Research and ExpositionRequires access

On Implication Algebras Based on Lattices and Their Dual Algebras

Zhu Yi-quan

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Abstract

This paper gives out that the relationship among lattice implication algebras, MV algebras, R0 algebras and other implication algebras based on lattices, and their dual algebras are established. Those results describe the characterizations of interior structures of those algebras, and also offer a new way for further researching lattice-valued logic systems from the semantics.

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What this paper is about

This paper gives out that the relationship among lattice implication algebras, MV algebras, R0 algebras and other implication algebras based on lattices, and their dual algebras are established. Those results describe the characterizations of interior structures of those algebras, and also offer a new way for further researching lattice-valued logic systems from the semantics.

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Available abstract

This paper gives out that the relationship among lattice implication algebras, MV algebras, R0 algebras and other implication algebras based on lattices, and their dual algebras are established. Those results describe the characterizations of interior structures of those algebras, and also offer a new way for further researching lattice-valued logic systems from the semantics.

Key concepts: Mathematics, Dual (grammatical number), Interior algebra, Lattice (music), Nest algebra, Non-associative algebra, Jordan algebra, Pure mathematics

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