Abstract:

Epistemic logic is a branch of modal logic that studies knowledge reasoning and belief change. It is widely used in artificial intelligence, multi-agent systems and game theory. In order to provide new logic tools for the study of computer science related fields that emphasize constructivity and versatility, a group of scholars begin to combine intuitionistic constructive ideas with epistemic logic and develop epistemic logic on the basis of intuitionistic logic. This paper is based on Jäger and Marti??s research on intuitionistic distributed knowledge and common knowledge.   Under the framework of intuitionistic logic, it deals with both common and distributed knowledge. According to the different nature and different characteristics of the knowledge accessibility relation satisfied, two intuitionistic epistemic logic axiom systems ICDK and ICDT are given. The canonical model is constructed by successively transforming the model and the complete reliability proof is given.

Key words: intuitionistic epistemic logic, distributed knowledge, common knowledge

摘要：

认知逻辑是研究知识推理和信念变化的模态逻辑的一个分支，在人工智能、多agent系统以及对策论等领域有着广泛应用。为给强调构造性和能行性的计算机科学相关领域的研究提供新的逻辑工具，一批学者开始将直觉主义构造性观点和认知逻辑相结合，在直觉主义逻辑基础上对认知逻辑展开研究。基于Jäger和Marti对直觉主义分布式知识和公共知识的研究，在直觉主义逻辑框架下同时处理公共知识和分布式知识。针对知识满足的不同性质及不同可达关系特性，建立了含分布式知识和公共知识的两个直觉主义认知逻辑公理系统ICDK和ICDT。通过对模型进行逐次变换的方法构造了典范模型并给出了完备可靠性证明。

关键词: 直觉主义认知逻辑, 分布式知识, 公共知识