文章摘要
常逻辑公式与可定义性
Constant Logical Formulas and Definability
  
DOI:
中文关键词: 模态逻辑  直觉主义逻辑  框架类  可定义
英文关键词: modal logic  intuitionistic logic  frame class  definability
基金项目:国家社科基金青年项目(12CZX054)
作者单位
马明辉 西南大学 逻辑与智能研究中心重庆 400715 
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中文摘要:
      常逻辑公式是不含命题变元的逻辑公式,运用它们可以定义结构类。但反过来某些结构类却不能以常逻辑公式集定义。模态逻辑中一阶可定义的框架类可被常模态公式集定义的充分必要条件,是该框架类对满射互模拟象、不相交并封闭,并且它的补类对超滤扩张封闭。有穷传递框架类相对可由常模态公式集定义的充分必要条件,是它对满射互模拟象和不相交并封闭。这两条定理中后一条可推广至直觉主义逻辑。
英文摘要:
      Constant logical formulas are those without propositional variable. They can be used to define classes of structures, while some classes of structures cannot be defined by any set of constant logical formulas. In modal logic, a first-order definable class of frames is definable by a set of constant modal formulas if and only if it is closed under subjective bisimulation images, disjoint unions, while its complement is closed under ultra-filter extensions. A class of finite transitive frames is relatively definable by constant modal formulas if and only if it is closed under subjective bisimulations and disjoint unions. The second theorem can be extended to intuitionistic logic.
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