论文标题
对否定逻辑及其模态伴侣的研究
A Study of Subminimal Logics of Negation and their Modal Companions
论文作者
论文摘要
我们研究了由约翰逊（Johansson）最少逻辑的语言产生的命题逻辑系统，并通过削弱对否定操作员的要求而获得。我们将他们的语义作为邻里语义的一种变体。我们使用二元性和完整性结果表明，有许多超级逻辑。我们还为过滤的模型理论和代数定义提供了最小逻辑的定义，并表明它们彼此双重。这些结构确保命题最小逻辑具有有限的模型属性。最后，我们针对某些相关的smini依系统定义并研究了具有非正态模态算子的双模式伴侣，并为这些双模式伴侣提供无限的公理。
We study propositional logical systems arising from the language of Johansson's minimal logic and obtained by weakening the requirements for the negation operator. We present their semantics as a variant of neighbourhood semantics. We use duality and completeness results to show that there are uncountably many subminimal logics. We also give model-theoretic and algebraic definitions of filtration for minimal logic and show that they are dual to each other. These constructions ensure that the propositional minimal logic has the finite model property. Finally, we define and investigate bi-modal companions with non-normal modal operators for some relevant subminimal systems, and give infinite axiomatizations for these bi-modal companions.
