In recent work, the authors introduced the notion of n-dimensional Boolean algebra and the corresponding propositional logic nCL. In this paper, we introduce a sequent calculus for nCL and we show its soundness and completeness. Completeness relies on the generalisation to the n-ary case of the classical proof based on the Lindenbaum algebra of formulas and on Boolean ultrafilters.

翻译：在近期工作中，作者引入了 n 维布尔代数概念及其对应的命题逻辑 nCL。本文提出 nCL 的相继式演算，并证明其可靠性与完备性。完备性的证明依赖于经典证明方法向 n 元情形的推广，该方法基于公式的 Lindenbaum 代数与布尔超滤子。