潜直觉逻辑及其模式伴侣:一个嵌套的方法
1Institute of Logic and Computation, TU Wien, Vienna, Austria.
概括
这项研究为潜直觉和模态逻辑引入了新的嵌套计算. 它提供了Gödel-McKinsey-Tarski嵌入的语法证明,并证明了古典逻辑的保守性.
科学领域:
- 逻辑 逻辑 逻辑 逻辑
- 证明理论证明理论
- 模式逻辑 模式逻辑
背景情况:
- 潜直觉主义逻辑是直觉主义逻辑的较弱碎片.
- 模态逻辑扩展了古典或直觉逻辑的模态运算符.
- 嵌套计算器为逻辑系统提供了一个结构化的框架.
研究的目的:
- 为潜直觉系统引入新的嵌套计算.
- 在S4模态立方体内开发模态逻辑的嵌套计算.
- 为戈德尔-麦金西-塔斯基嵌入提供纯语法证明.
主要方法:
- 开发了专门的嵌套计算器.
- 理论证明技术的应用.
- 在嵌套系统中分析模式运营商规则.
主要成果:
- 建立了哥德尔-麦肯锡-塔斯基嵌入的纯语法证明.
- 嵌入保留了衍生结构和高度.
- 对于古典逻辑对一个弱的潜直觉系统的保守性结果是得到的.
结论:
- 引入的嵌套计算器为研究潜直觉和模式逻辑提供了一个强大的工具.
- 语法证明为戈德尔-麦肯锡-塔斯基嵌入提供了新的见解.
- 保守性结果突出了古典逻辑和潜直觉逻辑之间的关系.
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