基于广义框架的概率认知逻辑  

Probabilistic Epistemic Logic Based on General Frame

作　　者：邓美林 郭美云[1] Meilin Deng;Meiyun Guo(Institute of Logic and Intelligence,Southwest University)

机构地区：[1]西南大学逻辑与智能研究中心

出　　处：《逻辑学研究》2022年第4期57-75,共19页Studies in Logic

基　　金：国家社科基金重点项目“概率更新的动态认知逻辑研究”(21AZX013);西南大学创新研究2035先导计划(SWUPilotPlan030)。

摘　　要：概率认知逻辑将认知和概率推理融合到同一个逻辑框架中。本文提出了一个基于广义框架的概率认知模型,并讨论了这一模型与已有两种概率认知模型的关系。基于广义框架的概率认知模型能为任意概率认知逻辑公式指派概率,因而是一种比较理想的概率认知逻辑语义模型。本文给出了一个可靠且完全的概率认知逻辑公理系统,提出并证明了概率函数存在引理,进而给出了这一逻辑的完全性证明。最后,本文运用这一逻辑刻画了混合策略博弈的两种状态,为进一步讨论混合策略博弈奠定了基础。Probabilistic epistemic logic integrates knowledge and probabilistic reasoning into the same logical framework.In order to solve the problem of probability assignment in probabilistic epistemic model,we provide a probabilistic epistemic model based on general frame,and discusses the relationship between this model and two existing probabilistic epistemic models.Probabilistic epistemic model based on general framework can assign probability to any formula in the language defined in this paper,so it is an ideal semantic model for probabilistic epistemic logic.We present a sound and complete proof system of probabilistic epistemic logic.The existence lemma of probability function is proposed and proved,as well as the completeness of this logic is proved.Finally,two states of a mixed strategy game are described by this logic,which lays a foundation for further discussion of mixed strategy game.

关 键 词：概率认知逻辑 广义框架 认知逻辑 概率逻辑 概率指派 

分 类 号：B81[哲学宗教—逻辑学]