计算机科学 ›› 2016, Vol. 43 ›› Issue (9): 87-90.doi: 10.11896/j.issn.1002-137X.2016.09.016

• 2015 年第三届CCF 大数据学术会议 • 上一篇    下一篇

AGM信念收缩算子的拓扑式刻画

孟华,原雅燕,储节磊,王红军   

  1. 西南交通大学数学学院 成都611756;西南交通大学信息科学与技术学院 成都611756,河南师范大学数学与信息科学学院 新乡453007,西南交通大学力学与工程学院 成都611756,西南交通大学信息科学与技术学院 成都611756
  • 出版日期:2018-12-01 发布日期:2018-12-01
  • 基金资助:
    本文受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

Topological Characterization of AGM Belief Contraction Operator

MENG Hua, YUAN Ya-yan, CHU Jie-lei and WANG Hong-jun   

  • Online:2018-12-01 Published:2018-12-01

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。

关键词: 知识表示,信念收缩,认知牢固度,拓扑空间

Abstract: 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 unsuitable.Grdenfors 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 epistemic 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 epistemic entrenchment,epistemic chain is simpler in structure and easier to construct.

Key words: Knowledge representation,Belief contraction,Epistemic entrenchment,Topological space

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