论文标题
从2个时间和线性嵌套序列到正常模态逻辑的自然扣除
From 2-sequents and Linear Nested Sequents to Natural Deduction for Normal Modal Logics
论文作者
论文摘要
我们扩展到自然扣除线性嵌套序列和2个时期的方法。公式装饰有空间坐标，该配方允许以自然推论的原始精神制定形式系统 - 每个连接的介绍和一个消除规则，没有其他（结构）规则，没有明确的参考，即对预期的Kripke模型的可访问性关系。我们为正常模态逻辑提供从K到S4的系统。对于系统的直觉版本，我们定义了降低证明并证明了证明归一化，从而获得了一致性的句法证明。对于逻辑K和K4，我们使用存在谓词（Scott之后）来制定声音扣除规则。
We extend to natural deduction the approach of Linear Nested Sequents and of 2-sequents. Formulas are decorated with a spatial coordinate, which allows a formulation of formal systems in the original spirit of natural deduction -- only one introduction and one elimination rule per connective, no additional (structural) rule, no explicit reference to the accessibility relation of the intended Kripke models. We give systems for the normal modal logics from K to S4. For the intuitionistic versions of the systems, we define proof reduction, and prove proof normalization, thus obtaining a syntactical proof of consistency. For logics K and K4 we use existence predicates (following Scott) for formulating sound deduction rules.
