不一定是这样：消极模态的基本认知系统
It ain't necessarily so: Basic sequent systems for negative modalities
摘要：
我们期待在非经典的否定和相应的调整连接词从模态的观点，在完整的分配格，并应用一个非常一般的机制，以提供足够的分析证明系统的逻辑是基于它们。在通常的模态语义学中定义非经典否定自动地允许人们将等价公式视为同义的，并且对对位规则的全局版本有一个自然的理由。从这个角度来看，我们的研究提供了一个特别有用的环境中，消极模态和他们的同伴可以用来处理不一致和不确定性。在研究了基于任意框架的模态逻辑之后，我们将结果推广到了序列框架、自反框架、函数框架和对称框架。在每一种情况下，我们也调查何时以及如何经典否定可能从而被定义。
英文摘要：
We look at non-classical negations and their corresponding adjustment connectives from a modal viewpoint, over complete distributive lattices, and apply a very general mechanism in order to offer adequate analytic proof systems to logics that are based on them. Defining non-classical negations within usual modal semantics automatically allows one to treat equivalent formulas as synonymous, and to have a natural justification for a global version of the contraposition rule. From that perspective, our study offers a particularly useful environment in which negative modalities and their companions may be used for dealing with inconsistency and indeterminacy. After investigating modal logics based on arbitrary frames, we extend the results to serial frames, reflexive frames, functional frames, and symmetric frames. In each case we also investigate when and how classical negation may thereby be defined.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
