AGM信念收缩算子的拓扑式刻画  

Topological Characterization of AGM Belief Contraction Operator

作　　者：孟华[1,2] 原雅燕[3] 储节磊[4] 王红军[2] 

机构地区：[1]西南交通大学数学学院,成都611756 [2]西南交通大学信息科学与技术学院,成都611756 [3]河南师范大学数学与信息科学学院,新乡453007 [4]西南交通大学力学与工程学院,成都611756

出　　处：《计算机科学》2016年第9期87-90,共4页Computer Science

基　　金：NSFC(61402382;11501177);中央高校基础研究基金(2682014ZT28);河南省高等学校重点科研项目计划(15A110034);西南交通大学创新项目(2682014CX054)资助

摘　　要：当agent的信念集是无限集时,传统的基于有限逻辑语言的刻画信念变化(belief change)的简单语义模型通常不再适用。Grdenfors和Makinson引入的epistemic entrenchment(认知牢固度)模型虽然可以用来从语义上刻画AGM型信念收缩算子,但他们并未给出如何构造一个具体的epistemic entrenchment的方法。在无限命题逻辑语言的背景下,通过在模型集上引入一个拓扑结构,构造出一种新的用来刻画AGM信念收缩的语义结构,称为认知链,并给出相应表示定理。讨论了epistemic entrenchment与认知链之间的关系。相对epistemic entrenchment而言,认知链具有结构简单并易于构造的特点。When the background language is finite, there are different semantic methods to characterize belief change ope- rators, which are easy to construct. However, when the background language is infinite, these methods are usually un- suitable. G/irdenfors and Makinson proposed a representation model using epistemic entrenchment to characterize belief contraction over an infinite language. But they did not show us how to construct a concrete epistemic entrenchment. In this paper, a new model called ＂epistemic chain＂ was introduced to characterize AGM-style belief contraction operators. An epistemie chain was a chain of closed set （about set inclusion） based on a topology on the set of all possible worlds. The relation between epistemic entrenchment and epistemic chain was discussed. Comparing with epistemie entrench- ment,epistemic chain is simpler in structure and easier to construct.

关 键 词：知识表示 信念收缩 认知牢固度 拓扑空间 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]