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2011•Unpublished venueRequires access

MP logical algebra

Jianping Yan

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Abstract

In this paper, we define a logical algebra named MP-algebra and discuss its algebraic properties. We find that MP algebra not only takes Boole algebra, MV-algebra and R0algebra as its special examples but also holds the subdirect representation theorem same as that of on Boole algebra, MV algebra and R0algebra. We also explore the basic properties of implication operation of MP-algebra. We prove that an MP-algebra is also a residuated lattice with many good properties. The conclusions we got show that MP-algebra is a well-structure logic algebra when it is taken as the logic truth degree set.

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What this paper is about

In this paper, we define a logical algebra named MP-algebra and discuss its algebraic properties. We find that MP algebra not only takes Boole algebra, MV-algebra and R0algebra as its special examples but also holds the subdirect representation theorem same as that of on Boole algebra, MV algebra and R0algebra. We also explore the basic properties of implication operation of MP-algebra. We prove that an MP-algebra is also a residuated lattice with many good properties. The conclusions we got show that MP-algebra is a well-structure logic algebra when it is taken as the logic truth degree set.

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Available abstract

In this paper, we define a logical algebra named MP-algebra and discuss its algebraic properties. We find that MP algebra not only takes Boole algebra, MV-algebra and R0algebra as its special examples but also holds the subdirect representation theorem same as that of on Boole algebra, MV algebra and R0algebra. We also explore the basic properties of implication operation of MP-algebra. We prove that an MP-algebra is also a residuated lattice with many good properties. The conclusions we got show that MP-algebra is a well-structure logic algebra when it is taken as the logic truth degree set.

Key concepts: Algebra over a field, Cellular algebra, Algebra representation, Division algebra, Filtered algebra, Boolean algebra, Subalgebra, Algebraic structure

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