基于有限格蕴涵代数的格值命题逻辑语法系统
Syntactic System of Lattice-Valued Propositional Logic Based on Finite Lattice Implication Algebra
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摘要: 以有限格蕴涵代数为真值域,建立了基于有限格蕴涵代数的格值命题逻辑系统;采用公理化的方法,给 出了该系统在A水平上的语法导出、证明和协调性等基本定义,并证明了系统的可靠性定理、协调性定理、弱完 备性定理和弱演绎定理.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.
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Key words:
- many-valued logic /
- logic algebra /
- lattice implication algebra
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