基于逻辑视角的不完备形式背景上知识相容表示与推理  

Knowledge Compatibility Representation and Reasoning in Incomplete Formal Contexts from Logical Perspective

作　　者：张少霞 李德玉[2,3] 翟岩慧[2,3] ZHANG Shaoxia;LI Deyu;ZHAI Yanhui(School of Information,Shanxi University of Finance and Economics,Taiyuan 030006,China;School of Computer and Information Technology,Shanxi University,Taiyuan 030006,China;Key Laboratory of Computational Intelligence and Chinese Information Processing(Shanxi University),Ministry of Education,Taiyuan 030006,China)

机构地区：[1]山西财经大学信息学院,太原030006 [2]山西大学计算机与信息技术学院,太原030006 [3]计算智能与中文信息处理教育部重点实验室(山西大学),太原030006

出　　处：《计算机科学》2024年第8期75-82,共8页Computer Science

基　　金：国家自然科学基金(62072294);山西省基础研究计划(202103021223303);山西省重点实验室开放课题(CICIP2022006)。

摘　　要：形式背景中的信息不完备引起了知识的不相容性,即蕴涵在不完备形式背景的任一完备化形式背景不能同时成立。逻辑描述是从语义上进行知识表示、语构上制定语义协调推理规则的方法论。首先,从逻辑角度研究不完备数据上的知识相容语义表示,通过定义不完备实例刻画知识的合理性和相容性,并构造最紧致的相容集(相容规范基)。其次,语构上制定具有语义合理性、相容性和完备性的推理规则,从而避免知识推理过程中产生不相容知识和无效知识。最后,将逻辑研究结果运用在不完备形式背景上,引入两类蕴涵形式:↓↓-型蕴涵和↑↑-型蕴涵。这两类蕴涵兼具相容性且相对于可接受性蕴涵尺度更加严格,构造这两类蕴涵的相容规范基并验证其完备性和无冗余性。The incomplete information in formal contexts leads to the incompatibility of knowledge,that is,implications cannot hold simultaneously in any completion of an incomplete formal context.Logical description is a methodology for representing knowledge from a semantic aspect and establishing inference rules with semantic coordination from a syntactic aspect.This paper firstly studies the compatibility semantic representation within incomplete data from a logical perspective,characterizes the soundness and compatibility of knowledge via incomplete instances,and constructs the most compact compatible set(namely compatible canonical basis).Secondly,this paper establishes inference rules with semantic soundness,compatibility,and completeness to avoid incompatible knowledge and invalid knowledge in knowledge reasoning.Finally,this paper applies the logical research results to incomplete formal contexts by introducing two types of implication forms,namely↓↓-type implication and↑↑-type implication,which are both compatible and more stringent than acceptable implication.The compatible canonical bases of the two types of implications are constructed and their completeness and non-redundancy are verified.

关 键 词：不完备形式背景 知识相容性 知识表示 相容规范基 知识推理 

分 类 号：TP182[自动化与计算机技术—控制理论与控制工程]