A consequence relation is strongly classical if it has all the theorems and entailments of classical logic as well as the usual meta-rules (such as Conditional Proof). A consequence relation is weakly classical if it has all the theorems and entailments of classical logic but lacks the usual meta-rules. The most familiar example of a weakly classical consequence relation comes from a simple supervaluational approach to modelling vague language. This approach is formally equivalent to an account of logical consequence according to which \(\alpha _1, \ldots , \alpha _n\) entails \(\beta \) just in case \(\Box \alpha _1, \ldots , \Box \alpha _n\) entails \(\Box \beta \) in the modal logic S5. This raises a natural question: If we start with a different underlying modal logic, can we generate a strongly classical logic? This paper explores this question. In particular, it discusses four related technical issues: (1) Which base modal logics generate strongly classical logics and which generate weakly classical logics? (2) Which base logics generate themselves? (3) How can we directly characterize the logic generated from a given base logic? (4) Given a logic that can be generated, which base logics generate it? The answers to these questions have philosophical interest. They can help us to determine whether there is a plausible supervaluational approach to modelling vague language that yields the usual meta-rules. They can also help us to determine the feasibility of other philosophical projects that rely on an analogous formalism, such as the project of defining logical consequence in terms of the preservation of an epistemic status.

如果结果关系具有经典逻辑的所有定理和蕴涵以及通常的元规则（例如条件证明），则它是强经典的。如果结果关系具有经典逻辑的所有定理和蕴涵，但缺乏通常的元规则，则它是弱经典关系。弱经典结果关系最熟悉的例子来自于对模糊语言进行建模的简单超评价方法。这种方法在形式上相当于对逻辑结果的解释，根据该逻辑，\(\alpha _1, \ldots , \alpha _n\)必然包含\(\beta \)以防万一\(\Box \alpha _1, \ldots , \模态逻辑 S5 中的Box \alpha _n\)蕴含\(\Box \beta \) 。这就提出了一个自然的问题：如果我们从不同的底层模态逻辑开始，我们可以生成强经典逻辑吗？本文探讨了这个问题。特别是，它讨论了四个相关的技术问题：（1）哪些基本模态逻辑生成强经典逻辑，哪些生成弱经典逻辑？(2) 哪些基本逻辑是自己生成的？(3) 我们如何直接表征从给定的基本逻辑生成的逻辑？(4) 给定一个可以生成的逻辑，哪些基本逻辑生成它？这些问题的答案具有哲学意义。它们可以帮助我们确定是否存在一种合理的超评估方法来对模糊语言进行建模，从而产生通常的元规则。它们还可以帮助我们确定其他依赖于类似形式主义的哲学项目的可行性，例如根据保存认知状态来定义逻辑结果的项目。