In order to prove the validity of logical rules, one has to assume these rules in the metalogic. However, rule-circular ‘justifications’ are demonstrably without epistemic value (sec. 1). Is a non-circular justification of a logical system possible? This question attains particular importance in view of lasting controversies about classical versus non-classical logics. In this paper the question is answered positively, based on meaning-preserving translations between logical systems. It is demonstrated that major systems of non-classical logic, including multi-valued, paraconsistent, intuitionistic and quantum logics, can be translated into classical logic by introducing additional intensional operators into the language (sec. 2–5). Based on this result it is argued that classical logic is representationally optimal. In sec. 6 it is investigated whether non-classical logics can be likewise representationally optimal. The answer is predominantly negative but partially positive. Nevertheless the situation is not symmetric, because classical logic has important ceteris paribus advantages as a unifying metalogic.

为了证明逻辑规则的有效性，人们必须在元逻辑中假设这些规则。然而，规则循环的“理由”显然没有认知价值（第 1 节）。逻辑系统的非循环证明是否可能？鉴于关于经典逻辑与非经典逻辑的持久争论，这个问题变得特别重要。在本文中，基于逻辑系统之间的意义保留翻译，这个问题得到了肯定的回答。它证明了非经典逻辑的主要系统，包括多值逻辑、超一致性逻辑、直觉逻辑和量子逻辑，可以通过在语言中引入额外的内涵算子来翻译成经典逻辑（第 2-5 节）。基于这个结果，有人认为经典逻辑是表示最优的。秒。6 研究非经典逻辑是否同样可以在表示上是最优的。答案主要是否定的，但部分是肯定的。然而情况并不是对称的，因为经典逻辑作为统一元逻辑具有重要的其他条件不变的优势。