集值信息系统的公理系统  

Axiomatic System of the Set-Valued Information System

作　　者：曹发生 Fasheng Cao(College of National Culture and Cognitive Science,Guizhou Minzu University)

机构地区：[1]贵州民族大学民族文化与认知科学学院

出　　处：《逻辑学研究》2022年第5期51-69,共19页Studies in Logic

基　　金：国家社科基金项目“多模态逻辑的代数语义研究”(项目批准号20XZX017)。

摘　　要：自从波兰数学家Z.Pawlak建立信息表的逻辑系统以来,出现了各种信息系统及其逻辑的研究。集值信息系统在机器学习方面有着重要的应用,本文从一个具体的集值信息系统的例子引发出建立集值信息系统的公理系统必要性。首先借助相容性关系给出模态算子的语义;然后给出集值信息系统的逻辑的语法和语义;最后建立集值信息系统的公理系统的公理和推理规则,并且利用传统方法证明集值信息系统的逻辑系统的可靠性和完全性。从逻辑本质上看,集值信息系统的逻辑系统就是一种多模态逻辑系统,它也给出多模态逻辑的非常完美的诠释。Since the Polish mathematician Z.Pawlak established the logical system of information tables,there have been studies on various information systems and their logics.Set-valued information systems have important applications in machine learning.In this paper,necessity of establishing the axiomatic system for set-valued information system is derived from a specific example of set-valued information system.Firstly,the semantics of modal operators are given by means of compatibility relation?Then the syntax and semantics of the logic for set-valued information system are given?Finally,the axioms and reasoning rules of the axiom system for the set-valued information system are established,and the reliability and completeness of the logic system for the set-valued information system are proved by using traditional methods.In terms of the logic essence,the logic system for set-valued information system is a multimodal logic system,which also gives a perfect interpretation of multimodal logic.

关 键 词：集值信息系统 过滤 典范模型 公理系统 

分 类 号：B81[哲学宗教—逻辑学]