论文标题
积极的逻辑
Positive logics
论文作者
论文摘要
Lindström的定理将一阶逻辑描述为满足紧凑型定理和向下löwenheim-Skolem定理的最大逻辑。如果我们不假定逻辑在否定下是关闭的，那么一阶逻辑具有明显的扩展，其中有两个模型理论属性，即存在的二阶逻辑。我们表明，存在的二阶逻辑具有完整的适当扩展家庭，满足了紧凑的定理和向下的löwenheim-skolem定理。此外，我们表明，在无否定逻辑的背景下，正面逻辑，正如我们所说的那样，一阶逻辑没有最大的延伸，其紧凑型定理和向下的löwenheim-skolem定理。
Lindström's Theorem characterizes first order logic as the maximal logic satisfying the Compactness Theorem and the Downward Löwenheim-Skolem Theorem. If we do not assume that logics are closed under negation, there is an obvious extension of first order logic with the two model theoretic properties mentioned, namely existential second order logic. We show that existential second order logic has a whole family of proper extensions satisfying the Compactness Theorem and the Downward Löwenheim-Skolem Theorem. Furthermore, we show that in the context of negationless logics, positive logics, as we call them, there is no strongest extension of first order logic with the Compactness Theorem and the Downward Löwenheim-Skolem Theorem.
