Classical Logic withnTruth Values as a Symmetric Many-Valued Logic

We introduce Boolean-like algebras of dimension n (nBAs) having n constants e(1), ... , 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 nBAs share many remarkable properties with the variety of Boolean algebras and with primal varieties. The nBA 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, nCL, and this embedding preserves validity. We define a confluent and terminating first-order rewriting system for deciding validity in nCL, and, via the embeddings, in all the finite tabular logics.