Syntactic System of Lattice-Valued Propositional Logic
Based on Finite Lattice Implication Algebra

MAJun; GAO Ya; QINKe-yun; XUYang

Volume 17 Issue 1

Feb. 2004

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Journal of Southwest Jiaotong University > 2004 > 17(1): 90-94.

MAJun, GAO Ya, QINKe-yun, XUYang. Syntactic System of Lattice-Valued Propositional LogicBased on Finite Lattice Implication Algebra[J]. Journal of Southwest Jiaotong University, 2004, 17(1): 90-94.

Citation:

MAJun, GAO Ya, QINKe-yun, XUYang. Syntactic System of Lattice-Valued Propositional Logic Based on Finite Lattice Implication Algebra[J]. Journal of Southwest Jiaotong University, 2004, 17(1): 90-94.

MAJun, GAO Ya, QINKe-yun, XUYang. Syntactic System of Lattice-Valued Propositional LogicBased on Finite Lattice Implication Algebra[J]. Journal of Southwest Jiaotong University, 2004, 17(1): 90-94.

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Syntactic System of Lattice-Valued Propositional Logic Based on Finite Lattice Implication Algebra

Publish Date: 25 Feb 2004

Abstract

Abstract

By taking finite lattice implication algebra as a truth-value field, a syntactic system of lattice- valued propositional logic based on finite lattice implication algebra was proposed. The basic definitions of syntactic implies, proof and consistency of the system on levelAwere given axiomatically. Finally, the soundness theorem, consistency theorem, weak complete theorem andweak deduction theoremof the system were proved.
- many-valued logic,
- logic algebra,
- lattice implication algebra