好奇的邻里逻辑逻辑
1Università di Padova, Padua, Italy.
概括
我们为邻里模型引入了一个新的好奇模式逻辑,为语句和问题提供了一个新的条件运算符. 这种逻辑被证明是健全的,完整的,可决定的,在表达力上匹配双相似性.
科学领域:
- 逻辑和形式方法的逻辑和形式方法.
- 理论计算机科学 理论计算机科学
- 语言的哲学语言的哲学
背景情况:
- 模态逻辑提供了关于各种形式的必要性和可能性的推理框架.
- 社区模型为模态逻辑提供了替代的语义,重点是可访问世界的集合.
- 探究语义丰富了传统语义,在陈述旁边加入了问题.
研究的目的:
- 为社区模型量身定制的一种新的探究性模式逻辑进行介绍和调查.
- 定义和分析一个好奇的严格条件运算符和相关的邻里定量器.
- 建立所提出逻辑的表达力,公理化和可决定性.
主要方法:
- 开发一种新的模态逻辑,使用一个好奇的严格条件运算符 () 和邻近量化器 (, ).
- 在邻近模型中证明逻辑的表达力等价性与双相似性.
- 在邻近修改下对语言碎片及其不变性属性的研究.
- 通过有限模型属性构建一个健全和完整的公理化,并证明可决定性.
主要成果:
- 逻辑的表达力与邻近模型中的双相似性相匹配.
- 询问条件 (
) 不能从邻近量化器 ( , ) 中定义,突出了嵌入式问题的不可或缺性. - 为逻辑提供了健全和完整的公理化,包括特定的类.
- 可决定性是通过有限模型属性建立的.
结论:
- 开发的探究模态逻辑为推理邻近模型提供了一个强大的框架,整合了陈述和问题.
- 逻辑的属性,包括其表达力和可决定性,使其成为正式语义和理论计算机科学的宝贵工具.
- 这项研究阐明了好奇语义,邻近模型和标准模态逻辑概念之间的关系.
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