论文标题
较高的维命题演算
The higher dimensional propositional calculus
论文作者
论文摘要
在最近的研究中，目前的一些作者介绍了n维布尔代数及其相应的命题逻辑NCL的概念，将布尔命题积分概括为n> = 2 = 2完全对称的真实值。本文为NCL提供了声音和完整的序列演算，名为NLK。我们提供了两个完整性证明：一种句法和一个语义。前者意味着NLK享有可接纳性的属性。后者依赖于基于公式和布尔超滤器的Lindenbaum代数的经典证明的N- ARY案例的概括。
In recent research, some of the present authors introduced the concept of an n-dimensional Boolean algebra and its corresponding propositional logic nCL, generalising the Boolean propositional calculus to n>= 2 perfectly symmetric truth values. This paper presents a sound and complete sequent calculus for nCL, named nLK. We provide two proofs of completeness: one syntactic and one semantic. The former implies as a corollary that nLK enjoys the cut admissibility property. The latter relies on the generalisation to the n-ary case of the classical proof based on the Lindenbaum algebra of formulas and Boolean ultrafilters.
