We introduce Boolean-like algebras of dimension n (\(n{\mathrm {BA}}\)s) having n constants \({{{\mathsf {e}}}}_1,\ldots ,{{{\mathsf {e}}}}_n\), and an \((n+1)\)-ary operation q (a “generalised if-then-else”) that induces a decomposition of the algebra into n factors through the so-called n-central elements. Varieties of \(n{\mathrm {BA}}\)s share many remarkable properties with the variety of Boolean algebras and with primal varieties. The \(n{\mathrm {BA}}\)s provide the algebraic framework for generalising the classical propositional calculus to the case of n–perfectly symmetric–truth-values. Every finite-valued tabular logic can be embedded into such a n-valued propositional logic, \(n{\mathrm {CL}}\), and this embedding preserves validity. We define a confluent and terminating first-order rewriting system for deciding validity in \(n{\mathrm {CL}}\), and, via the embeddings, in all the finite tabular logics.

我们引入具有n 个常数的n维类布尔代数( \(n{\mathrm {BA}}\) s) \({{{\mathsf {e}}}}_1,\ldots ,{{{\mathsf {e}}}}_n\)和一个\((n+1)\)元运算q （一个“广义的 if-then-else”），它通过 so-将代数分解为n 个因子称为n 个中心元素。\ (n{\mathrm {BA}}\)的变体与布尔代数的变体和原始变体具有许多显着的性质。\(n{\mathrm {BA}}\)提供了将经典命题演算推广到n的情况的代数框架– 完全对称 – 真值。每个有限值表格逻辑都可以嵌入到这样一个n值命题逻辑\(n{\mathrm {CL}}\)中，并且这种嵌入保持有效性。我们定义了一个融合和终止的一阶重写系统来决定\(n{\mathrm {CL}}\)中的有效性，并且通过嵌入，在所有有限表格逻辑中。